Question

Use scientific notation to find the product of 20.5 × 10 7 and 0.000036.

73.8 × 10 2
7.38 × 10 3
5.69 × 10 12
7.38 × 10 2

Answer 1

To find the product of \( 20.5 \times 10^7 \) and \( 0.000036 \), we first express \( 0.000036 \) in scientific notation.

The number \( 0.000036 \) can be written as \( 3.6 \times 10^{-5} \).

Now, we can multiply the two quantities in scientific notation:

\[
(20.5 \times 10^7) \times (3.6 \times 10^{-5}) = (20.5 \times 3.6) \times (10^7 \times 10^{-5})
\]

Next, we calculate \( 20.5 \times 3.6 \):

\[
20.5 \times 3.6 = 73.8
\]

Now we calculate the powers of ten:

\[
10^7 \times 10^{-5} = 10^{7 - 5} = 10^2
\]

Now we combine these results:

\[
73.8 \times 10^2
\]

To express this in standard scientific notation, we need to express \( 73.8 \) as \( 7.38 \) multiplied by \( 10^1 \):

\[
73.8 \times 10^2 = 7.38 \times 10^1 \times 10^2 = 7.38 \times 10^{1+2} = 7.38 \times 10^3
\]

Therefore, the product \( 20.5 \times 10^7 \times 0.000036 \) in scientific notation is:

\[
\boxed{7.38 \times 10^3}
\]