Question

How many times larger is (1.176 × 101) than (8 × 10−1)?

Group of answer choices

14.7

6.802

6.824

0.147

Answer 1

To find out how many times larger \( (1.176 \times 10^1) \) is than \( (8 \times 10^{-1}) \), we can set up the following division:

\[
\frac{1.176 \times 10^1}{8 \times 10^{-1}}
\]

First, we can simplify the expression step by step.

1. **Calculate the numerical part**:
\[
\frac{1.176}{8} = 0.147
\]

2. **Calculate the powers of ten**:
\[
\frac{10^1}{10^{-1}} = 10^{1 - (-1)} = 10^{1 + 1} = 10^2 = 100
\]

Now we can multiply the two results:

\[
0.147 \times 100 = 14.7
\]

Thus, \( (1.176 \times 10^1) \) is **14.7 times larger** than \( (8 \times 10^{-1}) \).

The answer is \( \boxed{14.7} \).