How many fractions of the form n/30 (with 1

Question

How many fractions of the form n/30 (with 1 <= n <= 29, in lowest terms) have a terminating decimal expansion? (30 = 2 × 3 × 5; the fraction terminates only when the factor 3 cancels, i.e. when n is a multiple of 3.)

Accepted Answer

9. n/30 terminates only if the 3 in the denominator cancels, i.e. n is a multiple of 3. Multiples of 3 from 1 to 29: 3,6,9,12,15,18,21,24,27 -> 9 values. (Each then reduces to a denominator of only 2 and 5.)

How many fractions of the form $\frac{n}{30}$ (with $1 <= n <= 29$ , in lowest terms) have a terminating decimal expansion?
$(30 = 2 \times 3 \times 5$ ; the fraction terminates only when the factor 3 cancels, i.e. when $n$ is a multiple of 3.)

Step-by-Step Solution

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More Class 10 Decimal Expansions practice

How many fractions of the form 30n​ (with 1<=n<=29, in lowest terms) have a terminating decimal expansion?(30=2×3×5; the fraction terminates only when the factor 3 cancels, i.e. when n is a multiple of 3.)

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 10 Decimal Expansions practice

How many fractions of the form $\frac{n}{30}$ (with $1 <= n <= 29$ , in lowest terms) have a terminating decimal expansion?
$(30 = 2 \times 3 \times 5$ ; the fraction terminates only when the factor 3 cancels, i.e. when $n$ is a multiple of 3.)