Question

1. which fraction is equivalent of 0.333? a. \\(\frac{3}{10}\\) b. \\(\frac{1}{3}\\) c. \\(\frac{33}{100}\\) d. the number cannot be written as a fraction.

Explanation:

Step1: Convert Option A to decimal

To convert $\frac{3}{10}$ to decimal, we divide 3 by 10. So, $\frac{3}{10} = 0.3$.

Step2: Convert Option B to decimal

To convert $\frac{1}{3}$ to decimal, we divide 1 by 3. So, $\frac{1}{3} \approx 0.333\cdots$ (the 3s repeat infinitely).

Step3: Convert Option C to decimal

To convert $\frac{33}{100}$ to decimal, we divide 33 by 100. So, $\frac{33}{100} = 0.33$.

Step4: Analyze Option D

0.333 is a terminating decimal, and all terminating decimals can be written as a fraction (for example, 0.333 = $\frac{333}{1000}$), so Option D is incorrect.

Step5: Compare with 0.333

We are looking for the fraction equivalent to 0.333. Option A is 0.3, Option C is 0.33, Option B is approximately 0.333$\cdots$ (very close to 0.333). Among the given options, $\frac{1}{3}$ is the closest approximation (and in the context of such questions, it's considered the equivalent for 0.333, especially since 0.333 is likely a truncated version of 0.333$\cdots$).

Answer:

B. $\frac{1}{3}$