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

Brown 14th Edition

Ch.1 - Introduction: Matter, Energy, and Measurement

Problem 48a

Chapter 1, Problem 48a

(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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Identify the number of significant figures required, which is three in this case.

Round the given number, 7926.381 miles, to three significant figures. Focus on the first three digits and adjust the third digit based on the value of the fourth digit.

Convert the rounded number into standard exponential notation. This involves expressing the number as a product of a number between 1 and 10 and a power of 10.

Check that the number in front of the multiplication sign has only three significant figures, as required.

Ensure the exponent in the power of 10 correctly represents the order of magnitude of the original number.

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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. When rounding a number, it is essential to retain the correct number of significant figures to accurately represent the precision of the measurement.

Rounding Rules

Rounding rules dictate how to adjust a number to the nearest desired place value. When rounding to three significant figures, if the digit following the last significant figure is 5 or greater, the last significant figure is increased by one. If it is less than 5, the last significant figure remains unchanged, ensuring the number is expressed accurately.

Standard Exponential Notation

Standard exponential notation expresses numbers as a product of a coefficient and a power of ten. This format is useful for simplifying large or small numbers, making them easier to read and compare. For example, the number 7926.381 can be expressed as 7.926381 x 10^3, which highlights its magnitude while maintaining precision.

Related Practice

Textbook Question

Carry out the following operations and express the answers with the appropriate number of significant numbers. (a) 16.234 + 8.722 × 0.6746

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Textbook Question

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

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Textbook Question

Carry out the following operations and express the answers with the appropriate number of significant numbers. (c) (3.29×10⁴)(0.2501)

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

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

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