Question

Multiplying using Scientific Notation
(8.03 × 10^ -8) x (2.56 × 10 ^-2)

Answers

GPT-4o mini
To multiply numbers in scientific notation, you can follow these steps:

1. Multiply the coefficients (the numbers in front).
2. Add the exponents of the 10s.

Let's apply this to \( (8.03 \times 10^{-8}) \times (2.56 \times 10^{-2}) \):

1. Multiply the coefficients:
\[
8.03 \times 2.56 = 20.5728
\]

2. Add the exponents:
\[
-8 + (-2) = -10
\]

Now, combine these results:
\[
20.5728 \times 10^{-10}
\]

Next, we want to express \( 20.5728 \) in proper scientific notation. This means it should be between 1 and 10. To do this, we can rewrite \( 20.5728 \) as \( 2.05728 \times 10^1 \).

Now combine this with \( 10^{-10} \):
\[
2.05728 \times 10^{1} \times 10^{-10} = 2.05728 \times 10^{-9}
\]

Thus, the final result is:
\[
\boxed{2.05728 \times 10^{-9}}
\]

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