Question
4 times 10^negative 2 plus 1.3 times 10^negative 1
use scientific notation to express your answer to 1 decimal place
use scientific notation to express your answer to 1 decimal place
Answers
GPT-4o mini
To solve the expression \( 4 \times 10^{-2} + 1.3 \times 10^{-1} \), we first need to express both terms with the same power of 10.
The term \( 1.3 \times 10^{-1} \) can be rewritten to have the same exponent as \( 4 \times 10^{-2} \):
\[
1.3 \times 10^{-1} = 1.3 \times 10^{-1} \times \frac{10}{10} = 13 \times 10^{-2}
\]
Now we can combine the two terms:
\[
4 \times 10^{-2} + 13 \times 10^{-2} = (4 + 13) \times 10^{-2} = 17 \times 10^{-2}
\]
Next, we convert \( 17 \times 10^{-2} \) into scientific notation. We can express \( 17 \) as \( 1.7 \times 10^{1} \):
\[
17 \times 10^{-2} = 1.7 \times 10^{1} \times 10^{-2} = 1.7 \times 10^{-1}
\]
So, the final result in scientific notation, rounded to one decimal place, is:
\[
\boxed{1.7 \times 10^{-1}}
\]
The term \( 1.3 \times 10^{-1} \) can be rewritten to have the same exponent as \( 4 \times 10^{-2} \):
\[
1.3 \times 10^{-1} = 1.3 \times 10^{-1} \times \frac{10}{10} = 13 \times 10^{-2}
\]
Now we can combine the two terms:
\[
4 \times 10^{-2} + 13 \times 10^{-2} = (4 + 13) \times 10^{-2} = 17 \times 10^{-2}
\]
Next, we convert \( 17 \times 10^{-2} \) into scientific notation. We can express \( 17 \) as \( 1.7 \times 10^{1} \):
\[
17 \times 10^{-2} = 1.7 \times 10^{1} \times 10^{-2} = 1.7 \times 10^{-1}
\]
So, the final result in scientific notation, rounded to one decimal place, is:
\[
\boxed{1.7 \times 10^{-1}}
\]