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Ch.1 - Introduction: Matter, Energy, and Measurement
Brown - Chemistry: The Central Science 14th Edition
Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232Not the one you use?Change textbook
All textbooksBrown 14th EditionCh.1 - Introduction: Matter, Energy, and MeasurementProblem 45d
Chapter 1, Problem 45d

What is the number of significant figures in each of the following measured quantities? (d) 2.94×103 m2

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1
Identify the digits in the number 2.94\(\times\)10^3.
Determine which digits are significant. In this case, all non-zero digits are significant.
Count the number of significant digits in the base number 2.94.
Recognize that the exponent in scientific notation (10^3) does not affect the number of significant figures.
Conclude that the number of significant figures in 2.94\(\times\)10^3 is the same as in 2.94.

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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 ensuring that calculations reflect the precision of the data.
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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. For example, 2.94×10³ indicates that the number is 2.94 multiplied by 1,000, which helps in identifying significant figures more easily.
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Rules for Counting Significant Figures

There are specific rules for counting significant figures in a number. For example, in scientific notation, all digits in the coefficient (the number before the exponent) are significant. Therefore, in 2.94×10³, the digits 2, 9, and 4 are all significant, leading to a total of three significant figures in this measurement.
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Related Practice
Textbook Question

Carry out the following operations and express the answers with the appropriate number of significant numbers. (a) 14.3505 + 2.65 (b) 952.72 - 73.4201

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(a) The diameter of Earth at the equator is 7926.381 mi. Round this number to three significant figures and express it in standard exponential notation.

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What is the number of significant figures in each of the following measured quantities? (b) 3ⅹ10-6 m

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Indicate which of the following are exact numbers: (a) the mass of a 3- by 5-in. index card, (b) the number of ounces in a pound, (c) the volume of a cup of Seattle's Best coffee, (d) the number of inches in a mile, (e) the number of microseconds in a week, (f) the number of pages in this book.

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Textbook Question

Indicate the number of significant figures in each of the following measured quantities: (e) 89.2 metr ic tons

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