Question
Multiplying using Scientific Notation
(8.03 × 10^ -8) x (2.56 × 10 ^-2)
(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:
\[
\boxed{2.05728 \times 10^{-9}}
\]
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:
\[
\boxed{2.05728 \times 10^{-9}}
\]