## Decimal Fractions

### What is decimal fraction

Decimal Fractions:

Fractions in which denominators are powers of 10 are known as decimal fractions.

$$Thus, \frac{1}{10}=1 \ \text{tenth} =0.1$$ $$\frac{1}{100}=1 \text { hundredth }=0.01$$

$$\frac{99}{100}=99 \text { hundredths }=.99$$  $$\frac{8}{1000}=8 \text { thousandths }=.008,$$

### Conversion of a Decimal into Vulgar Fraction

Conversion of a Decimal into Vulgar Fraction

Put 1 in the denominator under the decimal point and annex with it as many zeros as is the number of digits after the decimal point. Now, remove the decimal point and reduce the fraction to its lowest terms.

Example:$$0.25=\frac{25}{100}=\frac{1}{4}$$ ;           $$2.008=\frac{2008}{1000}=\frac{251}{125}$$  ;

### Annexing Zeros and Removing Decimal Signs

Annexing Zeros and Removing Decimal Signs:

Annexing zeros to the extreme right of a decimal fraction does not change its value. Thus, 0.8 = 0.80 = 0.800, etc.

If the numerator and denominator of a fraction contain the same number of decimal places, then we remove the decimal sign.

Example : $$\frac{1.84}{2.99}=\frac{184}{299}=\frac{8}{13}$$