Compare 7.6 x 10 to the negative twenty fifth power and 6.4 x 10 to the negative fifty second power. Which statement is true?

Question

1. 7.6 x 10 to the negative twenty fifth power = 6.7 = 10 to the negative fifty second power.
2. 7.6 x 10 to the negative twenty fifth power = 6.7 < 10 to the negative fifty second power.
3. 7.6 x 10 to the negative twenty fifth power = 6.7 (its this symbol "<" but with a line under it) 10 to the negative fifty second power.
4. 7.6 x 10 to the negative twenty fifth power = 6.7 > 10 to the negative fifty second power.

Answer 1

To compare the two numbers \( 7.6 \times 10^{-25} \) and \( 6.4 \times 10^{-52} \), we can convert them to a similar format.

First, rewrite \( 6.4 \times 10^{-52} \) in terms of \( 10^{-25} \):

\[ 6.4 \times 10^{-52} = 6.4 \times 10^{-52 + 25} \times 10^{-25} = 6.4 \times 10^{-27} \times 10^{-25} \]

Next, it's clear that \( 10^{-52} \) is much smaller than \( 10^{-25} \) because -52 is less than -25.

We can see how much smaller by putting both numbers into a format with the same exponent:

1. Convert \( 7.6 \times 10^{-25} \) to an equivalent form with \( 10^{-52} \):

\[ 7.6 \times 10^{-25} = 7.6 \times 10^{-25 + 52} \times 10^{-52} = 7.6 \times 10^{27} \times 10^{-52} \]

2. Now we can compare:

Now we compare the coefficients:

\[ 7.6 \times 10^{27} \text{ vs } 6.4 \]

Since \( 7.6 \times 10^{27} \) is clearly much larger than \( 6.4 \), we can conclude:

\[ 7.6 \times 10^{-25} > 6.4 \times 10^{-52} \]

Therefore, the correct statement is:

4. \( 7.6 \times 10^{-25} > 6.4 \times 10^{-52} \).