Question

Which sign makes the statement true.
0.000090 times 10^-10 ? 9.0 times 10^-14
responses
>
<
=

Answer 1

can u do another one

Answer 2

To determine if \(0.000090 \times 10^{-10}\) is equal to, greater than, or less than \(9.0 \times 10^{-14}\), let's first convert \(0.000090\) to scientific notation.

\[
0.000090 = 9.0 \times 10^{-5}
\]

Now we can rewrite the expression:

\[
0.000090 \times 10^{-10} = (9.0 \times 10^{-5}) \times 10^{-10}
\]

Using the properties of exponents, we combine the powers of ten:

\[
9.0 \times 10^{-5 - 10} = 9.0 \times 10^{-15}
\]

Now we compare \(9.0 \times 10^{-15}\) to \(9.0 \times 10^{-14}\).

Since:

\[
10^{-15} < 10^{-14}
\]

It follows that:

\[
9.0 \times 10^{-15} < 9.0 \times 10^{-14}
\]

Thus, the correct sign to place in the statement \(0.000090 \times 10^{-10} ? 9.0 \times 10^{-14}\) is:

\[
<
\]

So the final answer is:

\[
0.000090 \times 10^{-10} < 9.0 \times 10^{-14}
\]