Question

Show that the Reciprocal of 0.13bar is 7.5

Answer 1

Define x:

$\text {Let x = } 0.1 \overline 3$

Find 10x:

$\text {10x = } 1.3 \overline 3$

Find 9x:

$\text {10x - x = } 1.3 \overline 3 - 0.1 \overline 3$

$\text {9x = } 1.2$

Find x:

$\text {x = } 1.2 \div 9$

$\text {x = } \dfrac{2}{15}$

Find the reciprocal of x:

$\text {x = } \dfrac{2}{15}$

$\dfrac{1}{x} = \dfrac{15}{2}$

$\dfrac{1}{x} = 7.5$

Answer:  Reciprocal of 0.13bar is 7.5

Answer 2

Answer:

Define x:

\text {Let x = } 0.1 \overline 3Let x = 0.1

3

Find 10x:

\text {10x = } 1.3 \overline 310x = 1.3

3

Find 9x:

\text {10x - x = } 1.3 \overline 3 - 0.1 \overline 310x - x = 1.3

3

−0.1

3

\text {9x = } 1.29x = 1.2

Find x:

\text {x = } 1.2 \div 9x = 1.2÷9

\text {x = } \dfrac{2}{15}x =

15

2

Find the reciprocal of x:

\text {x = } \dfrac{2}{15}x =

15

2

\dfrac{1}{x} = \dfrac{15}{2}

x

1

=

2

15

\dfrac{1}{x} = 7.5

x

1

=7.5

Answer: Reciprocal of 0.13bar is 7.5