Inconverting 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 thefollowing steps:

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

You are watching: 9/1000 as a decimal

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 putthe decimal point one place left of the first digit in the numerator.

For example:

(i) $$\frac610$$ = .6 or 0.6

(ii) $$\frac1610$$ = 1.6

(iii) $$\frac11610$$ = 11.6

(iv) $$\frac111610$$ = 111.6

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

For example:

(i) $$\frac7100$$ = 0.07

(ii) $$\frac77100$$ = 0.77

(iii) $$\frac777100$$ = 7.77

(iv) $$\frac7777100$$ = 77.77

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

For example:

(i) $$\frac91000$$ = 0.009

(ii) $$\frac991000$$ = 0.099

(iii) $$\frac9991000$$ = 0.999

(iv) $$\frac99991000$$ = 9.999

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

In $$\frac351100$$ we will change the fractionto decimal.

First write the numerator andthen 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.

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

There can be two situations in convertingfractions to decimals:

• When division stops after acertain number of steps as the remainder becomes zero.

• When division continues asthere is a remainder after every step.

Here, we will discuss when thedivision is complete.

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

• Divide the numerator bydenominator and complete the division.

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

• Now, put zero to the right ofdividend and to the right of remainder.

• Divide as in case of wholenumber by repeating the above process until the remainder becomes zero.

1. Convert $$\frac233100$$ into decimal.

Solution:

2. Express each of the following as decimals.

(i) $$\frac152$$

Solution:

$$\frac152$$

= $$\frac15 × 52 × 5$$

= $$\frac7510$$

= 7.5

(Making the denominator10 or higher power of 10)

(ii) $$\frac1925$$

Solution:

$$\frac1925$$

= $$\frac19 × 425 × 4$$

= $$\frac76100$$

= 0.76

(iii) $$\frac750$$

Solution:

$$\frac750$$ = $$\frac7 × 250 × 2$$ = $$\frac14100$$ = 0.14

Note:

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

Examples on Conversion of Fractions into Decimal Numbers:

Express the following fractions as decimals:

1. $$\frac310$$

Solution:

Using the above method, we have

$$\frac310$$

= 0.3

2. $$\frac14791000$$

Solution:

$$\frac14791000$$

= 1.479

3. 7$$\frac12$$

Solution:

7$$\frac12$$

= 7 + $$\frac12$$

= 7 + $$\frac5 × 15 × 2$$

= 7 + $$\frac510$$

= 7 + 0.5

= 7.5

4. 9$$\frac14$$

Solution:

9$$\frac14$$

= 9 + $$\frac14$$

= 9 + $$\frac25 × 125 × 4$$

= 9 + $$\frac25100$$

= 9 + 0.25

= 9.25

5.

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12$$\frac18$$

Solution:

12$$\frac18$$

= 12 + $$\frac18$$

= 12 + $$\frac125 × 1125 × 8$$

= 12 + $$\frac1251000$$

= 12 + 0.125

= 12.125

Practice Problems on Converting Fractions to Decimals:

1. Convert the following fractional numbers to decimal numbers:

(i) $$\frac710$$

(ii) $$\frac23100$$

(iii) $$\frac172100$$

(iv) $$\frac4905100$$

(v) $$\frac91000$$

(vi) $$\frac841000$$

(i) $$\frac6721000$$

(i) $$\frac47471000$$

(i) 0.7

(ii) 0.23

(iii) 1.72

(iv) 49.05

(v) 0.009

(vi) 0.084

(i) 0.672

(i) 4.747

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● Decimals

● Decimal Numbers

● Decimal Fractions

● Like and UnlikeDecimals

● Comparing Decimals

● Decimal Places

● Conversion ofUnlike Decimals to Like Decimals

● Decimal andFractional Expansion

● Terminating Decimal

● Non-TerminatingDecimal

● Converting Decimalsto Fractions

● ConvertingFractions to Decimals

● H.C.F. and L.C.M.of Decimals

● Repeating orRecurring Decimal

● Pure RecurringDecimal

● Mixed RecurringDecimal

● BODMAS Rule

● BODMAS/PEMDAS Rules- Involving Decimals

● PEMDAS Rules -Involving Integers

● PEMDAS Rules -Involving Decimals

● PEMDAS Rule

● BODMAS Rules -Involving Integers

● Conversion of PureRecurring Decimal into Vulgar Fraction

● Conversion of MixedRecurring Decimals into Vulgar Fractions

● Simplification ofDecimal

● Rounding Decimals

● Rounding Decimalsto the Nearest Whole Number

● Rounding Decimalsto the Nearest Tenths

● Rounding Decimalsto the Nearest Hundredths

● Round a Decimal

● SubtractingDecimals

● Simplify DecimalsInvolving Addition and Subtraction Decimals

● Multiplying Decimalby a Decimal Number

● Multiplying Decimalby a Whole Number

● Dividing Decimal bya Whole Number

● Dividing Decimal bya Decimal Number