Question

Which sign makes the statement true?
3.1 *10^-7 3.10 *10^-7
><=

Answer 1

0.000032 3.2*10^-6

Answer 2

To determine which sign makes the statement true between \(3.1 \times 10^{-7}\) and \(3.10 \times 10^{-7}\), let's compare the two numbers.

First, note that \(3.10\) can be rewritten as \(3.1\) since \(3.10\) is simply \(3.1\).

Now we have:
- \(3.1 \times 10^{-7}\)
- \(3.1 \times 10^{-7}\)

Both numbers are equal, so the correct sign to use is:

\[
3.1 \times 10^{-7} \, = \, 3.10 \times 10^{-7}
\]

So the true statement is:

\[
3.1 \times 10^{-7} \, = \, 3.10 \times 10^{-7}
\]

Answer 3

To compare \(0.000032\) and \(3.2 \times 10^{-6}\), let's convert \(0.000032\) into scientific notation:

1. Move the decimal point 5 places to the right to express it in scientific notation:
\[
0.000032 = 3.2 \times 10^{-5}
\]

Now we can compare:
- \(3.2 \times 10^{-5}\)
- \(3.2 \times 10^{-6}\)

To compare these two values, it's easier to compare their exponents.

Since \(10^{-5}\) is greater than \(10^{-6}\) (because moving the decimal to the right increases the value), we can conclude:

\[
3.2 \times 10^{-5} > 3.2 \times 10^{-6}
\]

Thus, the relationship is:

\[
0.000032 > 3.2 \times 10^{-6}
\]

So you would use the ">" sign here.