Question

Mixed Recurring Decimal.

Answer 1

Mixed Recurring Decimal : A decimal fraction in which some figures do not recur is called a mixed recurring decimal. For example $: 0.2954$ is a mixed recurring decimal.

Note : 1. If the denominator of a vulgar fraction in its lowest terms be wholly made up of powers of 2 and 5 either along or multiplied together, the fraction is convertible into a terminating decimal.

Example :

1. $\frac{12}{25}=\frac{12}{5^2}=0.48$
2. $\frac{19}{50}=\frac{19}{5^2 \times 2}=0.38$

2. A pure recurring decimal is produced by a vulgar fraction in its lowest terms, whose denominator is neither divisible by 2 nor by 5.

Example :

1. $\frac{2}{3}=0 . \overline{6}$
2. $\frac{3}{11}=0 . \overline{27}$

3. A mixed recurring decimal is produced by a vulgar fraction in its lowest terms whose denominator contains powers of 2 or 5 in addition to other factors.

Example :

1. $\frac{1}{6}=\frac{1}{2 \times 3}=0.1 \overline{6}$
2. $\frac{1}{15}=\frac{1}{5 \times 3}=0.0 \overline{6}$