Question
Basic 1. Which of the following is less than \( \frac{1}{6} \) ? (A) 0.1667 (B) \( \frac{3}{18} \) (C) 0.167 (D) 0.1666 (E) \( \frac{8}{47} \)
Ask by Johnson Klein. in China
Mar 18,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Option (D) \( 0.1666 \) is less than \( \frac{1}{6} \).
Solution
**Step 1: Write down \( \frac{1}{6} \) as a decimal**
\[
\frac{1}{6} \approx 0.1666666\ldots
\]
**Step 2: Compare each option to \( 0.1666666\ldots \)**
- **Option (A):** \( 0.1667 \)
\( 0.1667 > 0.1666666\ldots \)
- **Option (B):** \( \frac{3}{18} \)
Simplify:
\[
\frac{3}{18} = \frac{1}{6} \approx 0.1666666\ldots
\]
So, it is equal to \( \frac{1}{6} \).
- **Option (C):** \( 0.167 \)
\( 0.167 > 0.1666666\ldots \)
- **Option (D):** \( 0.1666 \)
\( 0.1666 < 0.1666666\ldots \)
- **Option (E):** \( \frac{8}{47} \)
Calculate the decimal approximation:
\[
\frac{8}{47} \approx 0.1702
\]
\( 0.1702 > 0.1666666\ldots \)
**Step 3: Identify the option that is less than \( \frac{1}{6} \)**
The only option less than \( \frac{1}{6} \) is **Option (D)**.
**Answer:** Option (D) \( 0.1666 \).
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Simplify this solution The Deep Dive
To determine which of the given options is less than \( \frac{1}{6} \), we can first convert \( \frac{1}{6} \) into decimal form. \( \frac{1}{6} \) is approximately 0.1667. Therefore, we are looking for values that are numerically smaller than this. - (A) 0.1667 is equal to \( \frac{1}{6} \), not less. - (B) \( \frac{3}{18} = \frac{1}{6} \), not less. - (C) 0.167 is greater than \( \frac{1}{6} \). - (D) 0.1666 is less than \( \frac{1}{6} \). - (E) To evaluate \( \frac{8}{47} \), divide 8 by 47, which results in approximately 0.1702, greater than \( \frac{1}{6} \). Thus, the only option less than \( \frac{1}{6} \) is (D) 0.1666.
