Tech

# Conversion of Decimal to Fraction

A decimal is a number that expresses a ratio (the number of equal parts one entity is divided into and the number of equal parts another entity is divided into).

A Conversion of Decimal to Fraction is simple math, a decimal system allows for any integral power of ten to be assigned as a digit. For instance, in the decimal system the numbers 10, 100, 1000, and 10000 are all valid digits.

## 1. Steps to convert Decimal to Fractions:

You can use the following steps to convert a decimal to a fraction:

Write the decimal as a fraction with one digit on top and the rest of the digits on bottom (Example: 0.6 = 6/10; 3.8 = 3 8/100; 4.999 = 4 999/1000). If necessary, write out numerals for each of the numbers in #2 that are less than or equal to 1. Use a denominator that is a multiple of 10, 100, 1000, or 10000. If the denominator is not a multiple of 10, simply choose one that is.

To convert a decimal number to a fraction, simply find the original fraction that best matches your decimal number. That is, find the fraction in #2 where you have one digit in the numerator and the rest of the digits in the denominator. Note that when you are working with decimals, there are often alternative ways to represent a single number. For instance, 0.59 is equivalent to 0.590059. There are many equivalent ways to represent a number in a decimal system.

### 2. Examples:

1) Convert 0.6 into a fraction with one digit on top and the rest of the digits on bottom: [0.6] [1/10] [6/100] [200/1000] [2000/10000]

2) Convert 0.6 into a fraction with one digit on top and the rest of the digits on the bottom which is a multiple of 10, 100, 1000, or 10000: [0.6] [1/10] [6/100] [0.6]

3) Convert 3.8 into a fraction with one digit on top and the rest of the digits on the bottom which is a multiple of 10, 100, 1000, or 10000:

3.8 = 3 8/100 or 3 8/100 = 3 8

4) Convert 4.999 into a fraction with one digit on top and the rest of the digits on the bottom which is a multiple of 10, 100, 1000, or 10000:

4.999 = 4 999/1000 or 4 999/1000 = 4 999

To make a fraction with more digits on top, sometimes we have to borrow a digit from the bottom. This is most commonly done in an attempt to make 10 or 100 be part of the denominator. Here are two examples of how to borrow a digit:

To borrow a digit from the bottom with one digit on top and the rest of the digits on bottom: [0.6] [1/10] [6/100] [200/1000] [2010/10000] To borrow a digit from the bottom with two digits on top and one digit on top: [0.6] [6/10] [600/1000] [60010/10000]

To convert a decimal with one digit in the numerator, with the rest of the digits on the denominator

To convert a single-digit number in a decimal system to a fraction, you can use the following math:

1) Divide the numerator by 10, and the denominator by 100. There will be one remainder left over.

2) Multiply by ten to get rid of that remainder. The result is your answer.

Here is an example: 0.6 = 6/10

The numerator 0.6 can be divided by 10 to get 0.6/10, which has a remainder of 6.

The denominator 6/10 can be multiplied by ten to get 60/100, which has no remainder.