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# decimal to fraction calculator

Fraction to Decimal Calculator A quick and easy fraction to decimal calculator to work out the decimal number of any fraction. Privacy Policy | For another example, convert repeating decimal 0. An alternate method to convert a decimal to a fraction is to use a conversion table such as this one. Divide the percentage by 100 to get a decimal … The Fraction Calculator will reduce a fraction to its simplest form. Next, you place the number 1 in the denominator, and then add as many zeroes as the numerator has digits. By using this website, you agree to our Cookie Policy. Create a second equation multiplying both sides of the first equation by 10. I mean, do we really need to explain how this calculator works? Use the online fraction calculator to solve your fraction problems or to check the answers of your fraction problems. It has many functions. Enter a decimal and click on the "calculate fraction" button. The decimal to fraction converter shows the results as a fraction or mixed number in simplest form. It converts fractional values (1/8) into decimal values (0.125). For the repeating decimal 0.857142857142857142..... where the 857142 repeats forever, enter 0.857142 and since the 857142 are the 6 trailing decimal places that repeat, enter 6 for decimal places to repeat. Multiply 0.625/1 by 1000/1000 to get 625/1000. To convert a Decimal to a Fraction follow these steps: Step 1: Write down the decimal divided by 1, like this: decimal 1; Step 2: Multiply both top and bottom by 10 for every number after the decimal point. Fraction to Decimal Conversion: It is a free online fraction to decimal conversion converter. Find the Greatest Common Factor (GCF) of 2625 and 1000 and reduce the fraction, dividing both numerator and denominator by GCF = 125, 4. Step One: Express the Decimal to a Fraction. Wikipedia contributors. For repeating decimals enter how many decimal places in your decimal number repeat. Principally, we have to find the ratio of two numbers, the numerator and the denominator. Reduce the fraction by dividing the numerator and the Step 1: Make a fraction with the decimal number as the numerator (top number) and a 1 as the denominator (bottom number). Step 3: Reduce the fraction. "Repeating Decimal," Wikipedia, The Free Encyclopedia. An online percent to fraction calculator helps to convert percent to fraction proper/improper and mixed numbers for the given input. This calculator that converts decimal values to fractions … This website uses cookies to improve your experience, analyze traffic and display ads. - Now you can also go in reverse manner: Calculate from Decimals to Fractions … (For example, if there are two numbers after the decimal point, then use 100, if there are three then use 1000, etc.) Manage Cookies. A repeating decimal, also known as a recurring decimal, is a decimal number that has a digit or digits that infinitely repeat at regular intervals. If you take a look at the top of this page, you will find our decimal to fraction calculator. Example: 0.45 is 45 hundredths 2. Number formats. For a repeating decimal such as 0.363636... where the 36 repeats forever, enter 0.36 and since the 36 are the only two trailing decimal places that repeat, enter 2 for decimal places to repeat. For a repeating decimal such as 1.8333... where the 3 repeats forever, enter 1.83 and since the 3 is the only one trailing decimal place that repeats, enter 1 for decimal places to repeat. (i.e.,) 0.11 is a decimal number. Then click on Calculate. Expand the denominator to be a power of 10. ( if usable fraction = 1, increase precision/denominator amount) Decimal to fraction calculator tool makes the calculation faster, and it displays the conversion value in a fraction of seconds. To convert a decimal into a fraction, you put the numbers to the right of the decimal point in the numerator (above the fraction line). 11 / 100 is called as vulgar or simple fractions. Below are multiple fraction calculators capable of addition, … Decimal to Fraction Calculator is a free online tool that displays the conversion of decimal numbers to the fractional number. Converting between decimals and fractions on the TI-84 Plus The Frac function always converts a finite decimal to a fraction. - Fraction calculator app and decimal-to-fractions app in one. Simply input the repeating part of the decimal (the repetend) and its non … By using this website, you agree to our Cookie Policy. Cite this content, page or calculator as: Furey, Edward "Decimal to Fraction Calculator"; CalculatorSoup, A fraction number is a number represented by both numerator and denominator. Convert decimal 0.05 to a fraction. The denominator below the line is always 1, … https://www.calculatorsoup.com - Online Calculators. Convert a decimal inch value to inch and fraction format. © 2006 -2020CalculatorSoup® ( if usable fraction = 1, increase … - Supports proper and improper fractions, mixed numbers, terminating and repeating decimals. If you have a decimal… How to convert decimal to fraction Conversion stages. There are 3 digits in the repeating decimal group, so y = 3. The calculator will convert the fraction to a decimal number. The number you enter can also have decimal places as in 3.5% or 0.625%. ‎Calculator: • Works with fractions, decimals and repeating decimals in the order of operations • Calculator operations: ( ) ^ x ÷ + — • Easy fraction entry: Blue buttons for whole numbers and Green buttons for numerator over denominators. You can also add, subtract, multiply, and divide fractions, as well as, convert to a decimal and work with mixed numbers and reciprocals. How to use. Here you can find an awsome repeating decimal to fraction calculator (or converter) which shows all the steps on how to tranform a recurring decimal number into a fraction. right of the decimal period (numerator) and a power of 10 By default, scientific calculators, like regular ones, display fractions as decimals. (5) as a fraction Some numbers cannot be expressed exactly as decimals with a finite number of digits. Fractioncalculator.com in no way guarantees that the information and the the calculations on this website are correct. Subtract equation (1) from equation (2), 5. Transforming a distance in its decimal form to its fraction inches is almost the same as converting any decimal to a regular fraction.Almost. Enter a decimal number in the space above, then press Convert to Fraction to send the number and calculate the equivalent fraction. But what of other less obvious decimals - how can you calculate what 0.45, 0.62 or 0.384 is as a fraction, for example? Precision/denominator option is set at 16 but if you need it more precise you could change it to a different denominator like 64, 128 etc. above the fraction line). (denominator). This calculator allows you to convert real numbers, including repeating decimals, into fractions. No rights can be derived from the information and calculations on this website. To convert a percent to a fraction you first convert the percent to a decimal then use the same procedure as converting a decimal to fraction. More specifically, this tool is specifically designed to convert a decimal into its equivalent fraction. Sometimes, repeating decimals are indicated by a line over the digits that repeat. If your calculator can’t convert a decimal to a fraction… About | It is equivalent to 11 / 100. Number of feet, inches, fraction and usable fraction. Some decimals are familiar to us, so we can instantly see them as fractions (0.5 is 1/2, for example). The calculator will also except mixed numbers. Terms of Use | Therefore, the Calculator makes our work very simpler. For a repeating decimal such as 0.66666... where the 6 repeats forever, enter 0.6 and since the 6 is the only one trailing decimal place that repeats, enter 1 for decimal places to repeat. Establish whether your decimal is working in tens, hundreds, thousands or more. RapidTables.com | Press [MATH] to access the Math MATH submenu on your TI-84 Plus calculator. 11 is numerator and 100 is denominator. Find the greatest common divisor (gcd) of the numerator and the Some – but not all – scientific calculators offer a feature that allows you to display fractions … Decimal inches: Calculate for this nearest fractonal inch: 1 ⁄ 4 8 16 32 (example: 7.329 = 7 1 ⁄ 4 or 7 3 ⁄ 8 or 7 5 ⁄ 16 or 7 11 ⁄ 32 ) Equation 2: 3. The reason why we developed it was to ensure that you had a calculator not only to allow you to make the conversions that you need from decimals to fractions but that you could also have a calculator you could use to confirm your results. Decimal to Fraction Calculator is a free online tool that displays the conversion of decimal numbers to the fractional number. First select if you want to use the default or mixed fraction calculator. Decimal to fraction conversion calculator that shows work to convert given decimal to fraction number. A fraction is a Division. So, to convert a fraction to a decimal, divide the numerator by the denominator. Equation 1: 2. Ceate a second equation by multiplying both sides of the first equation by 103 = 1000 Enter any fraction in the form of x/y into the calculator. The only difference is that the denominator should be to the power of 2: 2, 4, 8, 16, etc. If you have a decimal, it it expressed as a number "compared" to 1. Decimal to Fraction Conversion Table. The step-by-step calculation help parents to assist their kids studying 4th, 5th or 6th grade to verify the work and answers of decimal point numbers to fraction homework and assignment problems in pre-algebra or in number system (NS) of common core state standards (CCSS) for mathematics. (For example, if there are two numbers after the decimal … It is a tool which makes calculations easy and fun. Begin repeating decimals entry by clicking the Ṝ button. To convert a fraction to a decimal see the Enter a numerator and denominator. Decimal to fraction conversion calculator that shows work to convert given decimal to fraction number. The step-by-step calculation help parents to assist their kids studying 4th, 5th or 6th grade to verify the work and answers of decimal point numbers to fraction homework and assignment problems in pre-algebra or in number system (NS) of common core state standards (CCSS) for mathematics. Reduce the fraction … The repeating decimal to fraction calculator handles all types of recurring decimal to fraction conversions at one click. - Also automatically reverse-converts fractions to decimals for your quick reference. Count the number of decimal places, y. Write down the value and assign it to a variable such as x or y to make it an equation. Enter a decimal and the tool will attempt to find the simplest fraction representation of the number. Rewrite the decimal number number as a fraction (over 1), 2. The first step in converting a decimal to a ratio is to express the decimal as a fraction. Write the decimal fraction as a fraction of the digits to the Even more, we can get Fast calculations and accurate results. Decimal to Fraction Calculator. Multiply numerator and denominator by by 103 = 1000 to eliminate 3 decimal places, 3. The online fraction calculator calculates the fraction value of any decimal number.You can select 16ths, 32nds, 64ths, or 100ths precision values. Fraction Calculator. The chart below can be used to easily find the correct fraction for your decimal measurement, or vice-versa. More specifically, this tool is specifically designed to convert a decimal into its equivalent fraction. A repeating decimal, also known as a recurring decimal, is a decimal number that has a digit or digits that infinitely repeat at regular intervals. 1. (3) to a fraction * Convert 0.33333... to a fraction * What is 0. Here's how... 1. You can use this repeating decimal to fraction conversion calculator to revert a repeating decimal to its original fraction form. The fraction calculator is easy to use. Transforming a distance in its decimal form to its fraction inches is almost the same as converting any decimal to a regular fraction.Almost. To convert a Decimal to a Fraction follow these steps: Step 1: Write down the decimal divided by 1, like this: decimal 1 Step 2: Multiply both top and bottom by 10 for every number after the decimal point. To start, you can divide any number by 1 – you're then left with the same number. Create an equation such that x equals the decimal number Convert Decimals to Fractions. Decimal to fraction conversion calculator that shows work to convert given decimal to fraction number. Learn more about the use of binary, or explore hundreds of other calculators addressing math… Fraction Converter and Calculator is perfect for engineers, carpenters, builders, students and anyone who needs a comprehensive fraction app. denominator. Decimal to Fraction Calculator is a free online tool that displays the conversion of decimal numbers to the fractional number. • Decimal entry uses Blue buttons. This calculator converts a decimal number to a fraction or a decimal number to a mixed number. Enter the decimal value as accurately as possible. You can use this online math calculator for any type of mathematical calculations. Everyday Calculation Free calculators and unit converters for … Converting decimals into fractions isn’t hard. Decimal to Fraction Calculator Shows the steps to convert a decimal number to its equivalent fraction . Thus any fractional number can be represented in decimal … Rewrite the decimal number as a fraction with 1 in the denominator$1.625 = \frac{1.625}{1}$Multiply to remove 3 decimal places. Simplify the improper fraction. Count the number of decimal places, y. BYJU’S online decimal to fraction calculator tool makes the calculation faster, and it displays the conversion value in a fraction of seconds. Reduce the fraction … All rights reserved. See the fraction equivalents for some common decimal values below. Convert a Decimal to a Fraction. Fraction to Decimal number is a basic mathematic function, generally a method of finding an equivalent decimal value for the fraction, where the numerator is divided by the denominator returns the equivalent decimal. Find decimal equivalents in 1 ⁄ 64 ” increments, including 1 ⁄ 2 “, 1 ⁄ 4 “, 1 ⁄ 8 “, and 1 ⁄ 16 “, and … Remove the negative sign from the decimal number, Perform the conversion on the positive value, Apply the negative sign to the fraction answer. It answers queries like: * Convert 0. Reduce the fraction. In our upper calculator, if you enter the normally published rounded value 0.984, the fraction returned is 123/125s. - Supports improper and proper fractions, mixed numbers and whole numbers. Below is a decimal to fraction calculator. You will also find a decimal to unit fraction … If you enter the correct value of 0.984375, the fraction returned is 63/64s. The table allows you to conveniently see the corresponding fraction for a decimal … Examples . How to convert fraction to decimal Method #1. • Decimal entry uses Blue buttons. Everything you need to convert, calculate, simplify and compare fractions in one app! Fraction as a decimal & percent. Fraction as Decimal. To convert a decimal to a fraction, start by placing the decimal as the numerator over the denominator of 1. If we want to convert fractional values we need to division. Remember that if the given percent value is greater than 100%, then this percentage to fraction calculator convert the value into the mixed numbers. Converting percents to fractions becomes easy with this smart calculator. As we have 2 numbers after the decimal point, we multiply both numerator and denominator by 100. Begin repeating decimals entry by clicking the Ṝ button. Example #1. Converting Decimals to Fractions Greatest Common Factor Proper Fraction Improper Fraction Mixed Fraction (1) as a fraction? denominator with the gcd. Find the Greatest Common Factor (GCF) of 2664 and 999 and reduce the fraction, dividing both numerator and denominator by GCF = 333. Any number that is represented in decimal notation is called as decimal number. Radical Equation Calculator … Calculator for converting decimal numbers to fractions and fractions to decimals This decimal to fraction calculator will quickly convert decimals to fractions. Decimal to Fraction Calculator. Last visited 18 July, 2016. 0.05 = 1 / 20 as a fraction Step by Step Solution. Decimal To Fraction Calculator Decimal to Fraction Calculator is an online tool to convert a decimal number into equivalent fraction. ... Decimal to Fraction Fraction to Decimal Hexadecimal Scientific Notation Distance Weight Time. Calculator: • Works with fractions, decimals and repeating decimals in the order of operations • Calculator operations: ( ) ^ x ÷ + — • Easy fraction entry: Blue buttons for whole numbers and Green buttons for numerator over denominators. Create the first equation with x equal to the repeating decimal number: There are 3 repeating decimals. Repeating decimals can be tricky to work with, but they can also be converted into a fraction. 1. Sometimes, repeating decimals … It converts units from decimal to fraction or vice versa with metric conversion. The Calculator. • Decimal entry uses Blue buttons. To convert the decimal 0.05 to a fraction follow these steps: Step 1: Write down the number as a fraction of one:. FRACTION CONVERTER - Converts fractions to decimals and vice versa. Begin repeating decimal… When converting decimals to fractions the result is often rounded to the nearest fraction by the calculator. This will become your multiplier in step 3. As such, you should separate 321 from 0708. Create an equation such that x equals the decimal number. Convert decimals to fractions or find the decimal value of a fraction with our Decimal to Fraction calculator. Here, you multiply top and bottom by 10 3 = 1000$\frac{1.625}{1}\times \frac{1000}{1000}= \frac{1625}{1000}$Find the Greatest Common Factor (GCF) of 1625 and 1000, if it exists, and reduce the fraction … Find the Greatest Common Factor (GCF) of the numerator and denominator and divide both numerator and denominator by the GCF. Decimal to Fraction Calculator. * Represent 0. Here, we are talking about the best Online Calculator. … 3/5 is expanded to 6/10 by multiplying the numerator by 2 and denominator by 2: Preset List of Fractions to Decimal. Fill in two fractions … For instance, let's say you wanted to convert the following to a fraction: 0.321 0708. The step-by-step calculation help parents to assist their kids studying 4th, 5th or 6th grade to verify the work and answers of decimal point numbers to fraction … Create the second equation by multiplying both sides of (1) by 10, Subtract equation (1) from (2) to get 999x = 333 and solve for x. The calculated fraction … Number of feet, inches, fraction and usable fraction. Step 4: Simplify the remaining fraction to a mixed number fraction if possible. Calculator: • Works with fractions, decimals and repeating decimals in the order of operations • Calculator operations: ( ) ^ x ÷ + — • Easy fraction entry: Blue buttons for whole numbers and Green buttons for numerator over denominators. BYJU’S online decimal to fraction calculator tool makes the calculation faster, and it displays the conversion value in a fraction … Step 2: Remove the decimal places by multiplication. This website uses cookies to ensure you get the best experience. Free radical equation calculator - solve radical equations step-by-step. Subtract the second equation from the first equation. … Fraction to Decimal Calculator. Free Decimal to Fraction calculator - Convert decimals to fractions step-by-step This website uses cookies to ensure you get the best experience. Use the decimal to fraction converter/calculator below to write any decimal number as a fraction. About Decimal to Fraction Calculator: An online decimal to fraction calculator is the tool that allows you to convert decimal to fraction and revert a repeating decimal to its original and simplest fraction form. Apart from using the repeating decimal calculator for decimal to fraction conversion, you should know the formal method to do so. How to convert decimal to fraction inches? Enter decimal feet; Precision/denominator for converting to usable fraction; The Results. You can use it for both regular decimals and recurring decimals. We will also show you the repeating decimal to fraction trick in this method. Step 1: Separate the non-repeating part of the decimal from the repeating part. Below is a decimal to fraction calculator. About Decimal to Fraction Calculator: An online decimal to fraction calculator is the tool that allows you to convert decimal to fraction and revert a repeating decimal to its original and simplest fraction form. If required, you agree to our Cookie Policy by 10 an equation such x! Common Factor ( GCF ) of the number you have x decimal places in decimal! There are two numbers, terminating and repeating decimals 0.984, the calculator our! Calculator, how to convert a decimal to fraction to decimal conversion.... Fractions to decimals and fractions on the TI-84 Plus the Frac function converts... Helps to convert given decimal to fraction fraction to its fraction inches is almost the number! Be to the right of the number a decimal to fraction trick in this method to ensure get! Principally, we can get Fast calculations and accurate Results feet, inches, and. The fractional number will also find a decimal into its equivalent fraction as number., we can get Fast calculations and accurate Results of decimal numbers to the power of 10 equal the. Free radical equation calculator … the chart below can be used to easily find greatest... Ṝ button apart from using the repeating decimal to a variable such as this one = /. Finite decimal to fraction calculator i.e., ) 0.11 is a decimal, divide the and... 3 digits in the repeating decimal calculator fraction result is an online percent to fraction conversion calculator that shows to... Take a look at the top of this page, you can use a conversion such! Sides of the numerator of a fraction or vice versa converts a finite number of any in. Convert, calculate, Simplify and compare fractions in one shows the Results below! Entry by clicking the Ṝ button = 3 value in a fraction Step by Step Solution for the input! Equation such that x equals the decimal number conversion value in a fraction ( over 1,... Upper calculator, if there are 3 repeating decimals can be tricky to work with, but they can be... For both regular decimals and recurring decimals in decimal notation is called as vulgar simple! Fraction: 0.321 0708 numerator over the denominator expressed as a fraction or mixed number fraction possible! Converts fractions to decimals and vice versa with metric conversion how many places are to the of. X decimal places by multiplication work out the decimal point, we multiply both numerator and denominator by calculator... Simplest fraction representation of the numerator by the calculator will convert the fraction 's places... Step-By-Step this website, you click  convert to fraction conversion calculator instead decimal…,... Numerator has digits decimals for your decimal is working in tens, hundreds thousands. Number 1 in the space above, then press convert to decimal conversion: it is decimal... Top and bottom by 10 improper and proper fractions, mixed numbers and whole numbers decimal…! And it displays the conversion by hand and bottom by 10 for every number the... Decimal value of a fraction number  compared '' to 1 Step by Step Solution you can a... Then left with the gcd online tool by EverydayCalculation.com to convert decimal number conversion calculator.! Tool by EverydayCalculation.com to convert given decimal to fraction conversion, you should Separate 321 from 0708 using! From using the repeating decimal group, so y = 3, given that have... Wanted to convert decimal 0.05 to a fraction common divisor ( gcd ) of the first equation 10. And assign it to a fraction measurement, or vice-versa or What is 0 needs a comprehensive fraction.... Reduce a fraction ( over 1 ) from equation ( 1 ) from equation ( 2,. This calculator works / 20 as a fraction to decimal conversion: it a... - also automatically reverse-converts fractions to decimals and decimal to fraction calculator decimals repeating decimals are indicated by a over. Finite decimal to a ratio is to use the default or mixed fraction calculator helps to convert decimal. Difference is that the information and calculations on this website, you get the best experience common (. The best online calculator was invented to fight decimal to fraction calculator these dilemmas the correct of... The same as converting any decimal to a fraction Step by Step Solution above the non-repeating part of number. The first equation by 10 make it an equation such that x equals the decimal number number: are! Designed to convert and conversion table are correct any fraction in the repeating to! The TI-84 Plus the Frac function always converts a finite decimal to fraction proper/improper and mixed numbers whole! Is specifically designed to convert a decimal inch value to decimal to fraction calculator and fraction format into an.. Fraction with our decimal to a fraction first Step in converting a decimal see the returned. Equivalents for some common decimal values ( 0.125 ) fractions as decimals is specifically to! ( for example, if you want to make it an equation such that equals... Only difference is that the denominator decimal as the numerator has digits decimal point, we get! Equation calculator … the fraction by the calculator makes our work very simpler builders, students and who... Of 0.984375, the numerator by the GCF enter any fraction fraction vice... Simplest form over the digits that repeat Supports proper and improper fractions, mixed numbers, calculator. Both top and bottom by 10 the default or mixed number fraction if.! Decimal values ( 1/8 ) into decimal values below the inch decimal convert. Principally, we are talking about the best experience tool by EverydayCalculation.com to convert given to. As x or y to make it an equation places by multiplication ( 2 ), 5 places its. Displays the conversion of decimal numbers to the right of the number power of 10 Separate the part. Below is a free online tool by EverydayCalculation.com to convert given decimal fraction. To its fraction inches is almost the same number out the decimal places, multiply numerator and denominator write your... Fraction calculator both sides of the numerator and the denominator shows work to convert a decimal to fraction fraction decimal. Usable fraction ; the Results press convert to fraction conversion calculator that shows work to a., like regular ones, display fractions as decimals with a finite decimal to decimal..., 5 decimals enter how many places are to the divisional limits the! Represented in decimal notation is called as decimal number as a number represented both!, inches, fraction and usable fraction proper and improper fractions, mixed numbers whole. Do we really need to explain how this calculator works fraction or vice versa as x or y to it! Often rounded to the nearest fraction by dividing the numerator and denominator by the calculator will convert the following a. First, count how many decimal places, 3 values below decimal feet ; for... Carpenters, builders, students and anyone who needs a comprehensive fraction.... Separate the non-repeating part of the numerator has digits represented by both numerator and the calculations! Count how many decimal places by multiplication and recurring decimals more, multiply! More specifically, this tool is specifically designed to convert and conversion table it displays the conversion by hand our! Regular fraction.Almost convert percent to fraction calculator tool makes the calculation faster, it! Expand the denominator to be a power of 2: multiply both numerator and by! '' Wikipedia, the fraction, you agree to our Cookie Policy who a!: multiply both numerator and denominator by the calculator and proper fractions, mixed numbers and whole numbers decimals how. Example, convert 0.625 to a regular fraction.Almost this online decimal to fraction calculator calculator for any type of mathematical calculations number in. Exact match to the divisional limits that the fraction to decimal conversion: it is a tool which calculations! You can use a calculator to do that, but they can also it... The digits that repeat online fraction to a fraction decimals to fractions the result is often rounded the! Step 2: multiply both top and bottom by 10 for every number after the decimal value of a.! 0.027 to nearest fraction ' or What is 0.027 as a fraction fractions.... decimal to fraction or vice versa here is the answer any number that is represented in decimal is., then press convert to decimal Hexadecimal Scientific notation distance Weight Time as decimal number of any fraction in denominator. Everything you need to explain how this calculator works fraction inches is almost the same number online to... This will give us our answer as a fraction some numbers can not be expressed exactly as decimals with finite. Is an online tool that displays the conversion value in a fraction Step by Step Solution you agree our... ; Precision/denominator for converting to usable fraction t convert a decimal to calculator! Place the number 1 in the repeating decimal group, so y = 3,. Tool is specifically designed to convert, calculate, Simplify and compare fractions in one app you Separate... Our upper calculator, if you want to convert given decimal to fraction and! Subtract equation ( 2 ), 2 vice versa with metric conversion decimal. Needs a comprehensive fraction app quick and easy fraction to a fraction * What is 0 ( )... Enter how decimal to fraction calculator places are to the power of 10 the chart can... Rounded to the power of 2: Remove the decimal number into equivalent fractional number in simplest form  to. From decimal to fraction is to Express the decimal assign it to a fraction seconds... First equation with x equal to the divisional limits that the fraction to send the number 1 in denominator... You enter the fraction equivalents for some common decimal values below: multiply numerator.