Question

1. the decimal equivalent of which fraction has a repeating digit of 7?

a. \\(\frac{7}{9}\\)
b. \\(\frac{7}{10}\\)
c. \\(\frac{1}{7}\\)
d. \\(\frac{7}{11}\\)

Explanation:

Step1: Convert Option a to decimal

To convert $\frac{7}{9}$ to a decimal, we perform the division: $7\div9 = 0.\overline{7}$ (the digit 7 repeats indefinitely).

Step2: Convert Option b to decimal

For $\frac{7}{10}$, we know that dividing by 10 moves the decimal one place to the left, so $\frac{7}{10}=0.7$ (this is a terminating decimal, no repeating digit).

Step3: Convert Option c to decimal

Calculating $\frac{1}{7}$: $1\div7\approx0.142857\overline{142857}$ (the repeating cycle is 142857, not just 7).

Step4: Convert Option d to decimal

For $\frac{7}{11}$, we do the division: $7\div11 = 0.\overline{63}$ (the repeating cycle is 63, not 7).

Answer:

a. $\frac{7}{9}$