Converting Fractions to Decimals

In converting fractions to decimals, we know that decimals are fractions with denominators 10, 100, 1000 etc. In order to convert other fractions into decimals, we follow the following steps:

Step I: Convert the fraction into an equivalent fraction with denominator 10 or 100 or 1000 if it is not so.

Step II: Take the given fraction’s numerator. Then mark the decimal point after one place or two places or three places from right towards left if the given fraction’s denominator is 10 or 100 or 1000 respectively.

Note that; insert zeroes at the left of the numerator if the numerator has fewer digits.

● To convert a fraction having 10 in the denominator, we put the decimal point one place left of the first digit in the numerator.

For example:

(i) \(\frac{6}{10}\) = .6 or 0.6

(ii) \(\frac{16}{10}\) = 1.6

(iii) \(\frac{116}{10}\) = 11.6

(iv) \(\frac{1116}{10}\) = 111.6


● To convert a fraction having 100 in the denominator, we put the decimal point two places left of the first digit in the numerator.

For example:

(i) \(\frac{7}{100}\) = 0.07

(ii) \(\frac{77}{100}\) = 0.77

(iii) \(\frac{777}{100}\) = 7.77

(iv) \(\frac{7777}{100}\) = 77.77


● To convert a fraction having 1000 in the denominator, we put the decimal point three places left of the first digit in the numerator.

For example:

(i) \(\frac{9}{1000}\) = 0.009

(ii) \(\frac{99}{1000}\) = 0.099

(iii) \(\frac{999}{1000}\) = 0.999

(iv) \(\frac{9999}{1000}\) = 9.999


The problem will help us to understand how to convert fraction into decimal.

In \(\frac{351}{100}\) we will change the fraction to decimal.

First write the numerator and then divide the numerator by denominator and complete the division.

Put the decimal point such that the number of digits in the decimal part is the same as the number of zeros in the denominator.

Converting Fractions to Decimals

Let us check the division of decimal by showing a complete step by step decimal divide.

Fractions to Decimals












We know that when the number obtained by dividing by the denominator is the decimal form of the fraction.

There can be two situations in converting fractions to decimals:

When division stops after a certain number of steps as the remainder becomes zero.

When division continues as there is a remainder after every step.

Here, we will discuss when the division is complete.


Explanation on the method using a step-by-step example:

Divide the numerator by denominator and complete the division.

If a non-zero remainder is left, then put the decimal point in the dividend and the quotient.

Now, put zero to the right of dividend and to the right of remainder.

Divide as in case of whole number by repeating the above process until the remainder becomes zero.


1. Convert \(\frac{233}{100}\) into decimal.

Solution:

How to Convert Fraction into Decimal
















2. Express each of the following as decimals.

(i) \(\frac{15}{2}\)

Solution:

\(\frac{15}{2}\)

= \(\frac{15 × 5}{2 × 5}\)

= \(\frac{75}{10}\)

= 7.5

(Making the denominator 10 or higher power of 10)


(ii) \(\frac{19}{25}\)

Solution:

\(\frac{19}{25}\)

= \(\frac{19 × 4}{25 × 4}\)

= \(\frac{76}{100}\)

= 0.76


(iii) \(\frac{7}{50}\)

Solution:

\(\frac{7}{50}\) = \(\frac{7 × 2}{50 × 2}\) = \(\frac{14}{100}\) = 0.14


Note:

Conversion of fractions into decimals when denominator cannot be converted to 10 or higher power of 10 will be done in division of decimals.

Converting Fractions to Decimals



Examples on Conversion of Fractions into Decimal Numbers:

Express the following fractions as decimals:

1. \(\frac{3}{10}\)

Solution:

Using the above method, we have

\(\frac{3}{10}\)

= 0.3


2. \(\frac{1479}{1000}\)

Solution:

\(\frac{1479}{1000}\)

= 1.479


3. 7\(\frac{1}{2}\)

Solution:

7\(\frac{1}{2}\)

= 7 + \(\frac{1}{2}\)

= 7 + \(\frac{5 × 1}{5 × 2}\)

= 7 + \(\frac{5}{10}\)

= 7 + 0.5

= 7.5


4. 9\(\frac{1}{4}\)

Solution:

9\(\frac{1}{4}\)

= 9 + \(\frac{1}{4}\)

= 9 + \(\frac{25 × 1}{25 × 4}\)

= 9 + \(\frac{25}{100}\)

= 9 + 0.25

= 9.25


5. 12\(\frac{1}{8}\)

Solution:

12\(\frac{1}{8}\)

= 12 + \(\frac{1}{8}\)

= 12 + \(\frac{125 × 1}{125 × 8}\)

= 12 + \(\frac{125}{1000}\)

= 12 + 0.125

= 12.125


Practice Problems on Converting Fractions to Decimals:

1. Convert the following fractional numbers to decimal numbers:

(i) \(\frac{7}{10}\)

(ii) \(\frac{23}{100}\)

(iii) \(\frac{172}{100}\)

(iv) \(\frac{4905}{100}\)

(v) \(\frac{9}{1000}\)

(vi) \(\frac{84}{1000}\)

(i) \(\frac{672}{1000}\)

(i) \(\frac{4747}{1000}\)


Answers:

(i) 0.7

(ii) 0.23

(iii) 1.72

(iv) 49.05

(v) 0.009

(vi) 0.084

(i) 0.672

(i) 4.747

Related Concept

Decimals

Decimal Numbers

Decimal Fractions

Like and Unlike Decimals

Comparing Decimals

Decimal Places

Conversion of Unlike Decimals to Like Decimals

Decimal and Fractional Expansion

Terminating Decimal

Non-Terminating Decimal

Converting Decimals to Fractions

Converting Fractions to Decimals

H.C.F. and L.C.M. of Decimals

Repeating or Recurring Decimal

Pure Recurring Decimal

Mixed Recurring Decimal

BODMAS Rule

BODMAS/PEMDAS Rules - Involving Decimals

PEMDAS Rules - Involving Integers

PEMDAS Rules - Involving Decimals

PEMDAS Rule

BODMAS Rules - Involving Integers

Conversion of Pure Recurring Decimal into Vulgar Fraction

Conversion of Mixed Recurring Decimals into Vulgar Fractions

Simplification of Decimal

Rounding Decimals

Rounding Decimals to the Nearest Whole Number

Rounding Decimals to the Nearest Tenths

Rounding Decimals to the Nearest Hundredths

Round a Decimal

Adding Decimals

Subtracting Decimals

Simplify Decimals Involving Addition and Subtraction Decimals

Multiplying Decimal by a Decimal Number

Multiplying Decimal by a Whole Number

Dividing Decimal by a Whole Number

Dividing Decimal by a Decimal Number


7th Grade Math Problems

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