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Ch.1 - Chemical Tools: Experimentation & Measurement
McMurry - Chemistry 8th Edition
McMurry8th EditionChemistryISBN: 9781292336145Not the one you use?Change textbook
All textbooksMcMurry 8th EditionCh.1 - Chemical Tools: Experimentation & MeasurementProblem 90c
Chapter 1, Problem 90c

Round off the following quantities to the number of significant figures indicated in parentheses. (c) 4.995⨉103 cm (3)

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1
Identify the number of significant figures required, which is 3 in this case.
Look at the given number: \(4.995 \times 10^3\) cm.
Focus on the digits in the coefficient (4.995) since the power of ten does not affect significant figures.
Round the coefficient 4.995 to 3 significant figures. To do this, look at the fourth digit (5) to decide whether to round up or down.
Since the fourth digit is 5, round the third digit up, resulting in the rounded 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. Understanding significant figures is crucial for accurately reporting measurements and calculations in scientific contexts.
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Rounding Rules

Rounding rules dictate how to adjust numbers to the desired level of precision. When rounding, if the digit to the right of the last significant figure is less than 5, the last significant figure remains unchanged. If it is 5 or greater, the last significant figure is increased by one. These rules ensure that the rounded number reflects the appropriate level of accuracy.
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Scientific Notation

Scientific notation is a way of expressing numbers that are too large or too small in a compact form, using powers of ten. A number is written as a product of a coefficient (between 1 and 10) and a power of ten. This notation simplifies calculations and helps maintain significant figures, especially in measurements like 4.995⨉10^3 cm.
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Related Practice
Textbook Question

Round off the following quantities to the number of signifi-cant figures indicated in parentheses. (a) 7.0001 kg (4)

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Textbook Question

Round off the following quantities to the number of significant figures indicated in parentheses. (a) 35,670.06 m (4, 6)

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Express the results of the following calculations with the correct number of significant figures. (b) 94.61 / 3.7

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The diameter of the Earth at the equator is 7926.381 mi. (b) Express the answers in scientific notation.

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Round off the following quantities to the number of signifi-cant figures indicated in parentheses. (b) 68.507 g (2, 3)

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Textbook Question

Express the results of the following calculations with the correct number of significant figures. (c) 3.7 / 94.61

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