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Ch.1 - Matter, Measurement & Problem Solving
All textbooksTro 4th EditionCh.1 - Matter, Measurement & Problem SolvingProblem 77
Chapter 1, Problem 77

How many significant figures are in each number? a. 0.000312 m b. 312,000 s c. 3.12 × 105 km d. 13,127 s e. 2000

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Identify the non-zero digits in each number, as they are always significant.
For numbers with leading zeros, such as in part (a), note that leading zeros are not significant.
For numbers with trailing zeros, such as in part (b) and (e), determine if the zeros are significant by checking if there is a decimal point present.
For numbers in scientific notation, such as in part (c), focus on the digits in the coefficient (the number before the multiplication sign) as they are significant.
For whole numbers without a decimal point, such as in part (d), consider all non-zero digits as significant and evaluate if any trailing zeros are significant based on context or additional information.

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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 scientific contexts.
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Leading Zeros

Leading zeros are the zeros that precede all non-zero digits in a number. They are not considered significant because they do not affect the value of the number. For example, in the number 0.000312, the leading zeros do not count towards the significant figures, which are only the '312'.
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Trailing Zeros

Trailing zeros are the zeros that follow non-zero digits in a number. Their significance depends on the presence of a decimal point. For instance, in the number 312,000, the trailing zeros are ambiguous without a decimal point, while in 2000, they are not considered significant unless specified otherwise (e.g., 2000. has four significant figures).
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Related Practice
Textbook Question

Read each measurement to the correct number of significant figures. Laboratory glassware should always be read from the bottom of the meniscus. Digital balances normally display mass to the correct number of significant figures for that particular balance.

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Textbook Question

For each number, underline the zeroes that are significant and draw an x through the zeroes that are not. a. 1,050,501 km b. 0.0020 m c. 0.000000000000002 s d. 0.001090 cm

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Textbook Question

For each number, underline the zeroes that are significant and draw an x through the zeroes that are not. a. 180,701 mi b. 0.001040 m c. 0.005710 km d. 90,201 m

Textbook Question

How many significant figures are in each number? d. 1.563300×1011 m

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Textbook Question

How many significant figures are in each number? c. 108,700 km