**Decimals and Fractions: Solved Examples**

**Example 1:**Convert the decimal

**Sol:**Let x = 0.737373 …..(i)

Multiplying both sides by 100 we get

100x = 73.737373……(ii)

Subtract equation (i) from (ii) we get

99x = 73 ⇒ x = 73/99.

**Example 2:**Convert

**Sol:**Let x =

Multiplying both sides by 100 we get

100x = 21.3333…(ii)

Multiplying both sides of equation (ii) by 10 we get

1000x = 213.3333…(iii )

Subtract equation (ii) from (i) we get

900x = 192 ⇒ x = 192/900.

**Example 3:**Find the fractional equivalent of

**Sol:**As it is case of pure recurring

**Example 4:**Find the fractional equivalent of

**Sol:**As it is case of mixed recurring

**Example 5:**Find the fractional equivalent of

**Sol:**As it is case of mixed recurring

**Example 6:**Find the fractional equivalent of

**Sol:**As it is case of mixed recurring

**Example 7:**Akshay spends 20% of his income, and then he spends 30% of his income, if he still has Rs. 900 with him. Find his total income.

**Sol:**In this case, the second expenditure is 30% of his income. Thus in total he spends 50% of his income, means he is left with 50% of his income, which is given to be Rs. 900. Thus his income is 900 × 100/50 = Rs. 1800

**Example 8:**Raj spends 4/9

^{th}of his income, then he spends 4/5 of the remaining. If he still has Rs. 2000 with him. Find his total income.

**Sol:**Let total income = K. Firstly he spend 4/9

^{th}of his income, thus he is left with 5/9

^{th}of the same. Then he spends 4/5

^{th}of the remaining, means he is left with 1/5

^{th}of the remaining.

Hence K x 5/9 x 1/5 = 2000

So K = 2000 x 9 = 18000.