How to Convert a Decimal into a Fraction

Decimal and Fraction are both the representation for rational numbers yet the two are very different from each other. Fractions are expressed as a division of two numbers. It has two parts named numerator which is the upper number and the denominator which is the bottom number. Usually, the denominator is a larger number as it represents the total parts of a whole and the numerator is smaller than the denominator as it represents the number of parts we consider. The basic example would be a pizza. The total number of pieces that a pizza has will be the denominator and the number of pieces that you ate will be the numerator. Now consider that a pizza had 8 slices and you ate 4 of them then the fraction would be \[\frac{4}{8}\]

A decimal number, on the other hand, has two parts which are separated by a decimal point, in simple word a “dot”. For example, in the decimal number 357.951, the digits to the left of the decimal point, are the whole number whereas the digits to the right of the decimal point are the fractional part.

What is a Decimal Number?

Decimal numbers are the numbers that fall between integers and non-integers. They are described as digits following a decimal point. Decimals use a system of numbers which is based on units of tens. In this system, the results in the spaces past the decimal point are as tenths, hundredths, thousandths, and so on.

What is a Fraction?

Fractions are basically the ratios of two numbers. Often, these numbers are whole numbers, such as \[\frac{3}{4}\] or \[\frac{19}{40}\]. Fractions are also a different way to represent division. For example,\[\frac{3}{4}\] can also mean "three fourths" or "three divided by four."

How to Convert a Decimal into a Fraction

To convert a decimal into a fraction there is no need for decimal to fraction formula but just three simple steps that we need to follow.

Step 1) Write the given decimal without the decimal point as a numerator.

Step 2) Take 1 annexed with as many zeros as is the number of decimal places in the given decimal as a denominator.

Step 3) Reduce the above fraction in the simplest form.

For example, 13.484 = \[\frac{13484}{1000}\] = \[\frac{3371}{250}\] = 13\[\frac{121}{250}\]

For convenience, always try to make a decimal to fraction table and always keep it ready before you start solving the problems. Google more an example of decimal fraction and practice it. Always go through questions like how to change a decimal to a fraction? Or how to convert decimal number to a fraction or maybe how to convert a decimal into an improper fraction? These questions will help you to understand the topic better.

Recurring Decimals

We know that \[\frac{3}{5}\] = 0.6, in this case, the dividend is exactly divisible after a few steps i.e., the remainder is zero. Such decimal numbers are called terminating decimals. However, there are fractions that give unending decimal values. Now look at this,

\[\frac{2}{3}\] = 0.66666………., in some fractions, the division does not stop and we obtain a certain block of digits which repeat over and over again. Such decimals numbers are called recurring decimals.

Solved Examples

Example 1) convert decimal to fraction:

i) 0.8

ii) 4.75

iii) 0.056

iv) 32.7

v) 0.4

vi) 3.54

vii) 0.36

viii) 85.473

ix) 0.013

x) 3.7

xi) 57.4

xii) 41.02

xiii) 3.137

xiv) 0.7

xv) 0.06

xvi) 0.012

xvii) 0.25

xviii) 31.08

xix) 74.085

xx) 0.225

Solution 1) Conversion from decimal to fraction can be done as follows:

i) 0.8 = \[\frac{8}{10}\] = \[\frac{4}{5}\]

ii) 4.75 = \[\frac{475}{100}\] = \[\frac{19}{4}\] = 4\[\frac{3}{4}\]

iii) 0.056 = \[\frac{56}{1000}\] = \[\frac{7}{125}\]

iv) 32.7 = \[\frac{327}{10}\]

v) 0.4 = \[\frac{4}{10}\] = \[\frac{2}{5}\]

vi) 3.54 = \[\frac{354}{100}\] = \[\frac{177}{50}\]

vii) 0.36 = \[\frac{36}{100}\] \[\frac{18}{50}\] = \[\frac{9}{25}\]

viii) 85.473 = \[\frac{85473}{1000}\]

ix) 0.013 = \[\frac{13}{1000}\]

x) 3.7 = \[\frac{37}{10}\]

xi) 57.4 = \[\frac{574}{10}\]

xii) 41.02 = \[\frac{4102}{100}\]

xiii) 3.137 = \[\frac{3137}{1000}\]

xiv) 0.7 = \[\frac{7}{10}\]

xv) 0.06 = \[\frac{6}{100}\]

xvi) 0.012 = \[\frac{12}{1000}\]

xvii) 0.25 = \[\frac{25}{100}\] = \[\frac{1}{4}\]

xviii) 31.08 = 31+ \[\frac{8}{100}\] = 31 \[\frac{2}{25}\] = 31 \[\frac{2}{25}\]

xix) 74.085 = 74+ \[\frac{85}{1000}\] = 74 + \[\frac{17}{200}\] = 74\[\frac{17}{200}\]

xx) 0.225 = \[\frac{9}{40}\]

FAQ (Frequently Asked Questions)

Q1. What are the Similarities Between a Decimal and a Fraction?

Ans. Fractions and decimals are similar because they both in a way express partial numbers. Just as a decimal can be expressed as a fraction, it can be another way round as well. A fraction can also be converted into a decimal by simply dividing the numerator with the denominator. Also, fractions can be expressed as decimals by simply performing the division of the ratio. For example, 3/4 is equal to 3 divided by 4, or 0.75. We can also express decimals as fractions in terms of tenths, hundredths, thousandths, and so on.

Q2. What are the Differences Between a Decimal and a Fraction?

Ans. The only main difference between a fraction and a decimal is that fractions tend to be simpler than decimals in expressions of ratios of whole numbers. Fractions do not always divide into an easy-to-express decimal. For example, on dividing ⅓, it becomes a repeating decimal of 0.33333 ... Fractions can also be easily converted into reciprocal. For example, the reciprocal of ⅖ is 5/2. Conversely, decimals are used to describe long, complex, and potentially infinite numbers, such as the value of pi. Decimals are very useful in describing partial numbers when a whole-number ratio is not available to make a fraction.