Question

a cake is divided into 15 pieces of equal size. anita’s portion of cake can be represented by the decimal 0.13. select options below anita’s portion can be represented as . so, she has pieces of the cake.

Explanation:

Step1: Convert repeating decimal to fraction

Let $x = 0.\overline{13}$, so $100x = 13.\overline{13}$. Subtract:
$$100x - x = 13.\overline{13} - 0.\overline{13}$$
$$99x = 13$$
$$x = \frac{13}{99} = \frac{1}{7.615...}$$
Correction: Match denominator to 15

Step1: Set up fraction for cake pieces

Let $n$ = number of pieces. Fraction: $\frac{n}{15}$

Step2: Equate to repeating decimal

$$\frac{n}{15} = 0.\overline{13}$$
$$n = 15 \times 0.\overline{13}$$

Step3: Calculate $n$

$0.\overline{13} = \frac{13}{99}$, so:
$$n = 15 \times \frac{13}{99} = \frac{195}{99} = 2$$

Step4: Write the fraction

$$\frac{n}{15} = \frac{2}{15}$$

Answer:

Anita's portion can be represented as $\frac{2}{15}$. So, she has 2 pieces of the cake.