Question

Which number is equivalent to 0.45? line over .45

Answer 1

Answer:

$\frac{5}{11}$

Step-by-step explanation:

The line over 45 indicates 45 is being repeated, that is

0.4545....

Create 2 equations with the repeating values after the decimal point

let x = 0.4545..... → (1) ( multiply both sides by 100 )

100x = 45.4545..... → (2)

Subtract (1) from (2) eliminating the repeating decimal

99x = 45 ( divide both sides by 99 )

x = $\frac{45}{99}$ = $\frac{5}{11}$

Thus 0.4545... = $\frac{5}{11}$