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Ch.1 - Matter, Measurement & Problem Solving
All textbooksTro 4th EditionCh.1 - Matter, Measurement & Problem SolvingProblem 83
Chapter 1, Problem 83

Calculate to the correct number of significant figures. a. 9.15 ÷ 4.970 b. 1.54 × 0.03060 × 0.69 c. 27.5 × 1.82 ÷ 100.04 d. (2.290 × 106) ÷ (6.7 × 104)

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1
Identify the number of significant figures in each number involved in the calculations.
For division and multiplication, the result should have the same number of significant figures as the number with the fewest significant figures in the calculation.
a. Divide 9.15 by 4.970. Determine the number of significant figures in each number: 9.15 has 3 significant figures, and 4.970 has 4 significant figures. The result should have 3 significant figures.
b. Multiply 1.54, 0.03060, and 0.69. Determine the number of significant figures in each number: 1.54 has 3 significant figures, 0.03060 has 4 significant figures, and 0.69 has 2 significant figures. The result should have 2 significant figures.
c. Multiply 27.5 by 1.82, then divide by 100.04. Determine the number of significant figures in each number: 27.5 has 3 significant figures, 1.82 has 3 significant figures, and 100.04 has 5 significant figures. The result should have 3 significant figures.
d. Divide 2.290 × 10^6 by 6.7 × 10^4. Determine the number of significant figures in each number: 2.290 has 4 significant figures, and 6.7 has 2 significant figures. The result should have 2 significant figures.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Significant Figures

Significant figures are the digits in a number that contribute to its precision. This includes all non-zero digits, any zeros between significant digits, and trailing zeros in the decimal portion. Understanding significant figures is crucial for accurately reporting measurements and calculations in chemistry, as it reflects the precision of the data.
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Rules for Operations with Significant Figures

When performing calculations, the number of significant figures in the result is determined by the operation being performed. For multiplication and division, the result should have the same number of significant figures as the measurement with the least significant figures. For addition and subtraction, the result should be rounded to the least precise decimal place.
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Scientific Notation

Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form. It is represented as a product of a number between 1 and 10 and a power of ten. Understanding how to manipulate numbers in scientific notation is essential for performing calculations involving very large or very small quantities, especially in chemistry.
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