To solve the question of converting the fraction [tex]\(\frac{4}{13}\)[/tex] to a decimal and then rounding it to the nearest thousandth, follow these steps:
1. Convert the fraction to a decimal:
Deal with the fraction [tex]\(\frac{4}{13}\)[/tex]. To convert this fraction to a decimal, divide 4 by 13. This calculation gives:
[tex]\[
\frac{4}{13} \approx 0.3076923076923077
\][/tex]
2. Round the decimal to the nearest thousandth:
The decimal obtained from the division is approximately 0.3076923076923077. To round this to the nearest thousandth, look at the fourth digit after the decimal point. In this case, the fourth digit is 6. Since it's 5 or higher, you round the third digit up from 7 to 8. Thus, the rounded decimal is:
[tex]\[
0.308
\][/tex]
3. Identify the best answer from the given choices:
Now, compare the rounded result to the choices provided:
- A. 0.413
- B. 0.308
- C. 0.134
- D. 0.325
The correct rounded decimal [tex]\(0.308\)[/tex] matches choice B.
Therefore, the best answer to the question is B. 0.308.
