The Decimal to Fraction Calculator

This online calculator by MathMaster simplifies the process of converting decisions to fractions. It works for terminating and recurring decimals, giving you results in seconds. Converting decimals to fractions provides an exact representation of numbers and makes it easier to compare quantities.

How to Convert Decimal to Fraction

Converting a decimal to a fraction requires that you understand the relationship between a decimal point and its fractional representation. Here are the steps to follow.

Step 1: Count the number of decimal places after the decimal point. Let n represent the number of decimal places. 

Step 2: Write the decimal number as a fraction by placing the decimal number over a power of 10. For example, if there is one decimal place (n = 1), the fraction is written as the decimal number divided by 10.

Step 3: Simplify the fraction to its lowest form.

For example:

Convert 0.75 to a fraction.

• The number of decimal places n = 2.

• Write the decimal as a fraction, which becomes 0.75/1.

• Simplify the Fraction. Remove the decimals by multiplying the numerator and denominator by the power of 10, which is 100 in this case(two decimal places).

0.75/1 x (100/100) = (0.75 * 100) / (1 * 100) = 75/100

• Simplify 75/100 further by dividing the numerator and the denominator with the largest number that can evenly divide both numbers.

In this case, the GCD (greatest common divisor) of 75 and 100 is 25.

(75 ÷ 25) / (100 ÷ 25) = 3/4

Converting Recurring Decimals to Fractions

Converting recurring decimals, which have repeating patterns, is slightly different.

Step 1: Create an equation where '𝓍' equals the recurring decimal.  For example, 0.454545… 𝓍 = 0.454545…

Step 2: Eliminate the recurring digits by creating a second equation with the same recurring part. Since there are two recurring decimal places, you must find a power of 10 that allows the recurring part to appear at the same place value. 

So, the second equation is 100𝓍 = 45.4545…

Subtract the second equation from the first to remove the recurring part:

100𝓍 - 𝓍 = 45.4545... - 0.4545…

This gives us 99𝓍 = 45.

Step 4: Solve for '𝓍' by dividing both sides by 99 to get 𝓍 = 45/99.

Step 4: Simplify the fraction to its lowest form using the GCD of 45 and 99(it’s 9), which gives us 5/11.

Converting Negative Decimals to Fractions

1. Remove the negative sign from the decimal.

2. Convert the positive value to a fraction.

3. Reapply the negative sign to the fraction.

Using the decimal to fraction calculator saves you time and effort. MathMaster is a trusted source for online math tools and calculators. Our calculators are user-friendly and efficient, ensuring that you perform mathematical operations easily and convert decimal to fraction without any problem. 

FAQs

1. What is the difference between terminating and recurring decimals?

Terminating has a finite number of decimal places (e.g., 0.25), while recurring decimals have a repeating pattern (e.g., 0.333...).

2. How can I convert a recurring decimal to a fraction?

You can convert a recurring decimal to a fraction using the Decimal to Fraction MathMaster Calculator. It can handle even recurring decimals. Simply input the recurring decimal, and it will provide the equivalent fraction.

3. Can I use the MathMaster calculator on mobile devices?

Yes, MathMaster's Decimal to Fraction Calculator is responsive, and you can easily use it on smartphones and tablets, making it a versatile tool for users on the go.