Question

Evaluate. Express your answer in scientific notation

8.03 x 10-5 + 2.15 x 10-5
Answered by GPT-4o mini
To add the numbers in scientific notation, you first ensure they have the same power of ten. In this case, both numbers already have the same exponent, which is \(10^{-5}\).

Now, you can add the coefficients:

\[
8.03 + 2.15 = 10.18
\]

Now, the sum in scientific notation is:

\[
10.18 \times 10^{-5}
\]

However, to express this in proper scientific notation, you need to adjust the coefficient to fall between 1 and 10. Thus, you convert \(10.18\) into \(1.018\) and adjust the power of ten accordingly:

\[
10.18 \times 10^{-5} = 1.018 \times 10^{0} \times 10^{-5} = 1.018 \times 10^{-5}
\]

So, the final answer in scientific notation is:

\[
\boxed{1.018 \times 10^{-4}}
\]
Answer
Evaluate. Express your answer in scientific notation

6.89 x 10^-4 - 4.23 x 10^-4
Answered by GPT-4o mini
To subtract the numbers in scientific notation, ensure they have the same power of ten. Here, both numbers have the same exponent, \(10^{-4}\).

Now, subtract the coefficients:

\[
6.89 - 4.23 = 2.66
\]

Now, the result in scientific notation is:

\[
2.66 \times 10^{-4}
\]

Since \(2.66\) is between 1 and 10, it is already in proper scientific notation.

Thus, the final answer is:

\[
\boxed{2.66 \times 10^{-4}}
\]
Answer
Evaluate. Express your answer in scientific notation

9.5 x 10^-5 - 1.7 x 10^-5
Answered by GPT-4o mini
To subtract the numbers in scientific notation, we first ensure they have the same power of ten. In this case, both numbers have the same exponent, which is \(10^{-5}\).

Now, subtract the coefficients:

\[
9.5 - 1.7 = 7.8
\]

Now, we write the result in scientific notation:

\[
7.8 \times 10^{-5}
\]

Since \(7.8\) is between 1 and 10, it is already in proper scientific notation.

Thus, the final answer is:

\[
\boxed{7.8 \times 10^{-5}}
\]
Answer
Evaluate. Express your answer in scientific notation

0.0582 - 1.73 x 10^-2
Answered by GPT-4o mini
To perform the operation \(0.0582 - 1.73 \times 10^{-2}\), we first need to express \(0.0582\) in scientific notation.

The number \(0.0582\) can be written as:

\[
5.82 \times 10^{-2}
\]

Now we can rewrite the expression:

\[
5.82 \times 10^{-2} - 1.73 \times 10^{-2}
\]

Since both terms have the same exponent (\(10^{-2}\)), we can subtract the coefficients:

\[
5.82 - 1.73 = 4.09
\]

Now, we combine this result with the common exponent:

\[
4.09 \times 10^{-2}
\]

Since \(4.09\) is between 1 and 10, it is in proper scientific notation.

Thus, the final answer is:

\[
\boxed{4.09 \times 10^{-2}}
\]