M08.B-E.1.1.4

How many times smaller is 5 x 10−7 than 8.5 x 10−4?

Group of answer choices

59

170

1,700

1 answer

To find out how many times smaller \( 5 \times 10^{-7} \) is than \( 8.5 \times 10^{-4} \), you can divide the two numbers:

\[ \text{Factor} = \frac{8.5 \times 10^{-4}}{5 \times 10^{-7}} \]

First, simplify the exponents:

\[ = \frac{8.5}{5} \times \frac{10^{-4}}{10^{-7}} = \frac{8.5}{5} \times 10^{-4 + 7} = \frac{8.5}{5} \times 10^{3} \]

Now, calculate \( \frac{8.5}{5} \):

\[ \frac{8.5}{5} = 1.7 \]

Multiply by \( 10^{3} \):

\[ 1.7 \times 10^{3} = 1,700 \]

Thus, \( 5 \times 10^{-7} \) is \( 1,700 \) times smaller than \( 8.5 \times 10^{-4} \).

The correct answer is 1,700.