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decimal to fraction calculator

Decimal to Fraction Calculator

Decimal

Repeating Digits

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An online decimal to fraction calculator that simply converts decimal number to fraction and revert a repeating decimal to its original fraction form instantly. Read on to learn about decimal fraction its conversion chart and how to turn decimal into a fraction in the blink of an eye.

About Decimal Fraction:

It is the term of algebra in which a decimal fraction represents a number whose denominator or bottom number is 10. It can be a multiple or power of 10 for example 100, 1,000, 10,000, etc. All the decimal fractions can be written along with a decimal or point. In this way it will be easier to do addition and multiplication calculations that involves fractions.

Example of Decimal Fraction:

7/10 is known as decimal fraction. If we write it as 0.7 then it will be known as decimal number. For converting decimals to fraction there is set of certain rules however for a convenient conversion we can use decimals to fraction calculator as well.

Decimal to Fraction chart:

Decimal to fraction chart can be used for converting some commonly-used fractions to their equivalent decimal numbers.

How to convert decimal to fraction?

Basically decimal and fractional numbers always denote that number which is not an even integer. Convert decimals to fraction by following a simple set of rules.

  • First of all, we have to make a fraction by using the decimal number. In starting fraction, we will use decimal as a numerator that is also known as the number which is present on the top. Denominator will be 1. Denominator is the number that is present in the bottom. For example, in case of .65 to change decimal to fraction we will write it as .65/1 according to this rule. In this example .65 is numerator and 1 is denominator.
  • In the second step we will multiply the top and bottom numbers by 10. This multiplication will remove the decimal place. We will keep on multiplying these both numbers by 10 until the numerator or top number changes into an integer value, or a whole number. We will Continue the above example to explain this step mathematically:

.65/1 = (.65 × 10) / (1 × 10) = 6.5 / 10

6.5 / 10 is not an integer or whole number so we will multiply it by 10 once again

6.5 / 10 = (6.5 × 10) / (10 × 10) = 65 / 100

  • In the third step we will decrease the fraction. For this purpose, we have to find the greatest Common factor of the top and bottom number and then divide both numbers by this GCF or greatest common factor. In the above example GFC is 5 for both numbers so will simply divide them by 5 as follows:

(65 divided by 5) / (100 divided by 5) = 13 / 20

Here is a quick tip that you can use decimal fraction calculator for quick and accurate calculations.

Example:

We have a decimal number 2.625 to convert it into a fraction. How it can be done?

  • First of all, rewrite the given decimal number. Divide it by 1:

2.625 will be changes into 2.625 / 1

  • Now we have to multiply both the numbers by 1000 as after decimal there are 3 digits. It will eliminate the decimal:

2.625 / 1 ×1000 / 1000 = 2625 / 1000

  • Now in the third step look for the GFC for both numbers. In this example it will be 125.
  • Divide both numbers by the GFC:

2625÷125 / 1000÷125 = 21 / 8

  • 21 / 8 is an improper fraction so we will simplify it.

2. 5 / 8

2.625=2. 5 / 8

Conversion of a Negative Decimal into a Fraction:

Sometimes we get decimal values with the negative sign. In such cases in the first place we have to eliminate the negative sign from the present decimal number. Now we have to perform the conversion at the positive value. Once we get the answer we will put the negative sign again. For example, if c = b then it is right that –b = -c. Decimal to fraction calculator is also functioned to deal with the negative decimal values.

How to Convert a Repeating Decimal to a Fraction?

  • To convert repeating decimal to fraction we have to formulate an equation in which x will be equals to the decimal number.
  • Now we have to count the digits that are present after decimal that will be y.
  • For creating second equation, both sides of first equation will be multiplied by 10y.
  • Subtraction of equation 2 from the equation 1 will be done.
  • Now we will do calculations for the x
  • In the last step fraction will be reduce. This calculation seems little tricky therefore to avoid the confusion taking help from the repeating decimal to fraction calculator will be a better option.

Example:

How to Convert repeating decimal number “2.666” to a fraction?

Follow all the above explained steps one by one.

  • For creating an equation, the give repeating decimal number will be equal to x.

Equation number 1: x=2.666

  • In the second step we will count the digits that are present after decimal. In this case there are three numbers. Therefore, according to the rule y = 3.
  • In the third step we have to create another equation. For this purpose, both sides of equation 1 will be multiplied by 1000.

Equation number 2: 1000x=2666.666

  • Now equation 1 will be subtracted from second equation.

1000x = 2666.666 – x = 2.666

999x = 2664

  • Now we will do calculations for x.

X = 2664 / 999

  • In the last step we have to reduce the fraction. For this purpose, simply find the GFC.

2664÷333 / 999÷333 = 83

  • On simplification of this improper fraction we will get:

Answer: 2. 2 / 3

Answer can be verified by online decimal to fraction calculator for accuracy.

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. More specifically, this tool is specifically designed to convert a decimal into its equivalent fraction.

Well, swipe down to know how this decimal fraction calculator converts decimal numbers into the simplest fraction form!

How to turn a decimal into a fraction With Decimal to Fraction Calculator:

Quit worrying, this calculator is very easy to use as it is packed with user-friendly interface, it doesn’t matter whether you want to convert repeating decimal to fraction or real numbers into decimal, this tool do all for you to provide a precise results within a couple of seconds.

Inputs:

  • First of all, you have to enter the decimal number into the designated field of this calculator
  • Very next, you have to enter the repeating of the decimal (repetend) into the designated box, but you just have to enter a repeating value (where it applicable)

Outputs:

Once done, then all you have to hit the calculate button, this decimal to fraction calculator generates:

  • Decimal to Fraction Number
  • Detailed explanation (step-by-step) calculations corresponding to the given inputs

FAQ’s (Decimal to Fraction, Repeating Decimals):

How do you convert decimals to fractions on a scientific calculator?

Remember that you can’t convert a decimal number into a fraction form on the calculator; the calculator only can help you to do it with a pencil and paper.

How do I convert decimals to fractions of an inch?

When it comes to converting a decimal to a fraction, you first decide what type of fraction your want to use, it can either be the nearest sixteenth of an inch, nearest eighth of an inch, etc. Then, you ought to simply multiply the decimal by the fraction that you desire and round off the answer to the nearest whole number.

What is 0.1 as a fraction?

0.1 is expressed in fraction form as 1/10.

What is .05 as a fraction?

.05 is expressed in fraction form as 1/20.

What is 0.5 as a fraction?

0.5 is expressed in fraction form as 1/2.

What is difference between decimal and fraction?

Well, fractions is said to be as the simple mathematical expression of ratios of whole numbers and even they do not always divide into an easy to express decimal. While, decimals are the term that can be used to describe long, complex & potentially infinite numbers, like a value of pi.

What is the relationship between fraction and decimal?

The relationship between decimals, fractions, and percents is that they all are the different numerical expressions those have the same value.

How does 0.043 turn into a fraction?

0.043 is expressed in fraction form as 43/1000, but (if you need), you can readily reduce further that fraction to approximately 1/25.

How do I convert 1666.67 to a fraction?

All you need to move the decimal point two places to the right, means 166667, that’s the numerator and the denominator is 100. So, 1666.67 expressed in fraction form as 166667/100.

What are 12.8 as a fraction?

12.8 are expressed in fraction form as 64/5.

What is 0.06 repeating as a fraction?

0.6 expression repeating as a fraction is equal to 2/33.

What is 0.5 Repeating as a fraction?

0.5 decimal expression repeating is equal to 5/9.

What is 0.15 repeating as a fraction?

0.15 repeating is expressed in fraction as 5/33.

What is .81 repeating as a fraction?

.81 repeating is expressed in fraction as 9/11.

Takeaway:

This online decimal to fraction calculator is functioned to work on the basis of advanced algorithm for solving the equation that involves decimal numbers. Whenever you wish to double check your calculations related to decimal fractions for accuracy, or if the conversion that you are seeking cannot be done manually, you can use this online tool to get your desired outcomes.

References:

From the source of Wikipedia, the free encyclopedia – Decimal fractions – The decimal numerical expression/system also said to be as base-ten potential numeral system

From the source of study – A Repeating Decimal – Converting Repeating Decimals into Fractions

From the source of mathsisfun – definition of Decimal Fraction along with example