Question

The ratio of 8th graders in a chess club to the total number of members is 0.45.What is the decimal in fraction form?Enter the correct answers in the boxes.

Answer 1

The ratio of 8th graders in a chess club to the total number of members is 0.454545...

This is called a repeating decimal.

Let us convert this decimal into a fraction.

$x=0.4545\ldots$

Step 1:

Multiply by 100

$\begin{gathered} 100\times x=100\times0.4545\ldots \\ 100x=45.45\ldots \end{gathered}$

Step 2:

Subtract x

$\begin{gathered} 100x-x=45.45\ldots-0.4545 \\ 99x=45 \end{gathered}$

Step 3:

Finally, divide by 99

$\begin{gathered} \frac{99x}{99}=\frac{45}{99} \\ x=\frac{45}{99} \end{gathered}$

Therefore, the fraction form is

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