Write your answer to the following problems with the...

Write your answer to the following problems with the appropriate number of significant figures. (a) $6.85 \times 10^{-5} \mathrm{m}+2.7 \times 10^{-7} \mathrm{m}$ (b) $702.35 \mathrm{km}+1897.648 \mathrm{km}$ (c) $5.0 \mathrm{m} \times 4.3 \mathrm{m}$ (d) $(0.04 / \pi) \mathrm{cm}$ (e) $(0.040 / \pi) \mathrm{m}$

Write your answer to the following problems with the appropriate number of significant figures.
(a) $6.85 \times 10^{-5} \mathrm{m}+2.7 \times 10^{-7} \mathrm{m}$
(b) $702.35 \mathrm{km}+1897.648 \mathrm{km}$
(c) $5.0 \mathrm{m} \times 4.3 \mathrm{m}$
(d) $(0.04 / \pi) \mathrm{cm}$
(e) $(0.040 / \pi) \mathrm{m}$

Key Concepts

Multiplication and Division with Significant Figures

For multiplication and division, the number of significant figures in the final result should match that of the operand with the fewest significant figures. This rule ensures that uncertainties in measurements are properly maintained through the calculation, reflecting the least precise value in the product or quotient.

Significant Figures

Significant figures are the digits in a number that carry meaning contributing to its precision. They include all the non-zero digits, any zeroes between them, and sometimes trailing zeroes in the decimal part. This concept is essential in scientific and engineering measurements to express accuracy and uncertainty in numerical values.

Rounding

Rounding is the process of adjusting the digits of a number to provide an approximation that fits the desired level of precision. When rounding to a specific number of significant figures, the number is altered by either increasing or leaving the digits, depending on the digit immediately after the last significant digit, ensuring that the uncertainty due to limited precision is properly conveyed.

Addition and Subtraction with Significant Figures

In addition and subtraction, the number of significant figures is governed by the least precise decimal place among the numbers involved in the operation. This means the result should be rounded to the same decimal place as the term with the fewest digits to the right of the decimal point, ensuring that one does not imply false precision in the result.

Transcript

Please give Ace some feedback