Evaluate. Express your answer in scientific notation

Question

8.03 x 10-5 + 2.15 x 10-5

Answer 1

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 2

Evaluate. Express your answer in scientific notation

6.89 x 10^-4 - 4.23 x 10^-4

Answer 3

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 4

Evaluate. Express your answer in scientific notation

9.5 x 10^-5 - 1.7 x 10^-5

Answer 5

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 6

Evaluate. Express your answer in scientific notation

0.0582 - 1.73 x 10^-2

Answer 7

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:

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