Question

write the rational number as a decimal.

1. $-\frac{8}{15}$
2. $\frac{5}{8}$
3. $-\frac{13}{6}$
4. $1\frac{7}{16}$

write the decimal as a fraction or a mixed number in simplest form.

1. $-0.6$
2. $-0.35$
3. $-5.8$
4. $24.23$

Explanation:

Problem 1: $-\frac{8}{15}$ as a decimal

Step1: Divide 8 by 15

$8\div15 = 0.533\cdots$ (repeating decimal, the 3 repeats)

Step2: Apply the negative sign

Since the fraction is $-\frac{8}{15}$, the decimal is $-0.5\overline{3}$ (the bar is over the 3 to indicate it repeats)

Step1: Divide 5 by 8

$5\div8 = 0.625$

Step1: Divide 13 by 6

$13\div6 = 2.166\cdots$ (repeating decimal, the 6 repeats)

Step2: Apply the negative sign

Since the fraction is $-\frac{13}{6}$, the decimal is $-2.1\overline{6}$ (bar over the 6)

Answer:

$-0.5\overline{3}$ (or approximately $-0.533\cdots$)

Problem 2: $\frac{5}{8}$ as a decimal