Question

Match the rational numbers with their equivalent forms.

Answer 1

Answer:

(a) $0.0\overline{5}$ is equivalent to 1/18.

(b) 0.5 is equivalent to $\sqrt{0.25}$.

(c) 1/7 is equivalent to $0.\overline{142857}$.

(d) $0.\overline{6}$ is equivalent to 2/3.

Step-by-step explanation:

The simplify the given numbers

The given number is

$0.0\overline{5}$

It can be written as

$0.0\overline{5}=0.0555..$

$\frac{1}{18}=0.0555..$

It means $0.0\overline{5}$ is equivalent to 1/18.

(b)

The given number is

$\sqrt{0.25}$

It can be written as

$\sqrt{0.25}=0.5$

It means 0.5 is equivalent to $\sqrt{0.25}$.

(c)

The given number is

$\frac{1}{7}$

It can be written as

$\frac{1}{7}=0.142857142857=0.\overline{142857}$

It means 1/7 is equivalent to $0.\overline{142857}$.

(d)

The given number is

$0.\overline{6}$

It can be written as

$0.\overline{6}=\frac{6}{10-1}$

$0.\overline{6}=\frac{6}{9}$

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

It means $0.\overline{6}$ is equivalent to 2/3.

Answer 2

0.6 repeating is 2/3
The square root of 0.25 is 0.5
1/7 is 0.142857 repeating
1/18 is 0.05 repeating