Questions: Adding and Subtracting with Significant Figures Calculate the following to the correct number of significant figures. 0.157+0.16= 357.95-152= 1.030 x 10^-9 + 5.721 x 10^-8= Note: You can earn partial credit on this problem.

Solution Steps

When adding numbers, the result should be reported with the same number of decimal places as the number with the fewest decimal places. Here, 0.16 has two decimal places, and 0.157 has three decimal places. Therefore, the result should have two decimal places.

\[ 0.157 + 0.16 = 0.317 \]

Rounded to two decimal places, the result is:

\[ 0.32 \]

For subtraction, the result should have the same number of decimal places as the number with the fewest decimal places. Here, 152 has zero decimal places, and 357.95 has two decimal places. Therefore, the result should have zero decimal places.

\[ 357.95 - 152 = 205.95 \]

Rounded to zero decimal places, the result is:

\[ 206 \]

When adding numbers in scientific notation, first ensure they have the same exponent. Here, we convert \(1.030 \times 10^{-9}\) to \(0.1030 \times 10^{-8}\).

\[ 0.1030 \times 10^{-8} + 5.721 \times 10^{-8} = 5.824 \times 10^{-8} \]

The number with the fewest significant figures is \(1.030 \times 10^{-9}\) with four significant figures. Therefore, the result should also have four significant figures.

Final Answer