Evaluate each of the following and write the answer to the...

Evaluate each of the following and write the answer to the appropriate number of significant figures.
a. $212.2+26.7+402.09$
b. $1.0028+0.221+0.10337$
c. $52.331+26.01-0.9981$
d. $2.01 \times 10^{2}+3.014 \times 10^{3}$
e. $7.255-6.8350$

Key Concepts

Scientific Notation

Scientific notation is a method of writing numbers that accommodates values too large or too small to be conveniently written in standard decimal form. It expresses numbers as a product of a coefficient and a power of ten, and it is especially useful in significant figure calculations to clearly indicate precision and avoid errors in interpretation.

Multiplication and Division with Significant Figures

In multiplication or division, the number of significant figures in the final answer should be the same as that of the measurement with the least number of significant figures in the calculation. This rule maintains the integrity and accuracy of the reported result in light of the precision of the input values.

Significant Figures

Significant figures represent the digits in a numerical value that contribute to its accuracy. They reflect the precision of a measured or calculated quantity and help in expressing the result to the appropriate level of confidence. This concept is crucial when reporting results because it prevents overstatement of the precision in the computed value.

Rounding

Rounding is the process of reducing the number of digits in a number while maintaining a value that is as close as possible to the original. It is used to adjust the number to the correct number of significant figures or decimal places. Proper rounding ensures the result is not more precise than the measurement supports.

Addition and Subtraction with Significant Figures

When performing addition or subtraction, the final answer should be reported to the least number of decimal places present in any of the measurements involved. This rule ensures that the result reflects the precision of the least precise measurement, thus adhering to proper significant figure rules in these operations.

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