Compare 7.6 × 10−25 and 6.7 × 10−52. Which statement is true?(1 point)

Question

Responses

7.6 × 10−25 = 6.7 × 10−52
7.6 times 10 Superscript negative 25 Baseline equals 6.7 times 10 Superscript negative 52 Baseline
7.6 × 10−25 > 6.7 × 10−52
7.6 times 10 Superscript negative 25 Baseline is greater than 6.7 times 10 Superscript negative 52 Baseline
7.6 × 10−25 < 6.7 × 10−52
7.6 times 10 Superscript negative 25 Baseline is less than 6.7 times 10 Superscript negative 52 Baseline
7.6 × 10−25 ≤ 6.7 × 10−52

Answer 1

To compare \( 7.6 \times 10^{-25} \) and \( 6.7 \times 10^{-52} \), we can rewrite both numbers in a compatible form for comparison.

First, we can convert \( 7.6 \times 10^{-25} \) to a form that uses a common exponent for easier comparison.

Notice that: \[ 7.6 \times 10^{-25} = 7.6 \times 10^{-25} \times \frac{10^{27}}{10^{27}} = 7.6 \times 10^{2} \times 10^{-52} \]

This means: \[ 7.6 \times 10^{-25} = 760 \times 10^{-52} \]

Now we can compare \( 760 \times 10^{-52} \) and \( 6.7 \times 10^{-52} \): \[ 760 \times 10^{-52} > 6.7 \times 10^{-52} \]

Since both terms share the same \( 10^{-52} \) factor, we can ignore it for comparison of the coefficients: \[ 760 > 6.7 \]

Thus: \[ 7.6 \times 10^{-25} > 6.7 \times 10^{-52} \]

The correct statement is:

• \( 7.6 \times 10^{-25} > 6.7 \times 10^{-52} \)