1. The problem is to convert the fractions $\frac{5}{8}$, $\frac{5}{6}$, and $\frac{9}{22}$ into decimal form. 2. The formula to convert a fraction to a decimal is to divide the numerator by the denominator: $$\text{Decimal} = \frac{\text{Numerator}}{\text{Denominator}}$$ 3. Let's perform the division for each fraction step-by-step. 4. For $\frac{5}{8}$: - Divide 5 by 8. - 8 goes into 5 zero times, so we add a decimal point and zero: 0. - Multiply 0 by 8 = 0, subtract from 5 gives remainder 5. - Bring down 0 to make 50. - 8 goes into 50 six times (6 x 8 = 48), remainder 2. - Bring down 0 to make 20. - 8 goes into 20 two times (2 x 8 = 16), remainder 4. - Bring down 0 to make 40. - 8 goes into 40 five times (5 x 8 = 40), remainder 0. - So, $\frac{5}{8} = 0.625$. 5. For $\frac{5}{6}$: - Divide 5 by 6. - 6 goes into 5 zero times, so 0. - Add decimal point and zero: 0. - Multiply 0 by 6 = 0, subtract from 5 gives remainder 5. - Bring down 0 to make 50. - 6 goes into 50 eight times (8 x 6 = 48), remainder 2. - Bring down 0 to make 20. - 6 goes into 20 three times (3 x 6 = 18), remainder 2. - This remainder repeats, so the decimal repeats 3. - So, $\frac{5}{6} = 0.8\overline{3}$ (0.8333... repeating). 6. For $\frac{9}{22}$: - Divide 9 by 22. - 22 goes into 9 zero times, so 0. - Add decimal point and zero: 0. - Multiply 0 by 22 = 0, subtract from 9 gives remainder 9. - Bring down 0 to make 90. - 22 goes into 90 four times (4 x 22 = 88), remainder 2. - Bring down 0 to make 20. - 22 goes into 20 zero times, remainder 20. - Bring down 0 to make 200. - 22 goes into 200 nine times (9 x 22 = 198), remainder 2. - The remainder 2 repeats, so the decimal repeats 09. - So, $\frac{9}{22} = 0.4\overline{09}$ (0.4090909... repeating). Final answers: - $\frac{5}{8} = 0.625$ - $\frac{5}{6} = 0.8\overline{3}$ - $\frac{9}{22} = 0.4\overline{09}$