Ch.1 - Matter, Measurement & Problem Solving

Tro - Chemistry: A Molecular Approach 5th Edition

Tro5th EditionChemistry: A Molecular ApproachISBN: 9780134874371Not the one you use?Change textbook

Tro 5th Edition

Ch.1 - Matter, Measurement & Problem Solving

Problem 82

Chapter 1, Problem 82

Round each number to three significant figures. a. 79,845.82 b. 1.548937×10⁷ c. 2.3499999995 d. 0.000045389

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Identify the first three significant figures in each number.

For each number, look at the digit immediately following the third significant figure to determine if rounding is necessary.

If the digit is 5 or greater, round up the third significant figure by one. If it is less than 5, keep the third significant figure as is.

Apply the rounding rule to each number individually.

Rewrite each number with only the first three significant figures, ensuring the correct placement of the decimal point or scientific notation.

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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.

Rounding Rules

Rounding rules dictate how to adjust numbers to a specified number of significant figures. When rounding, 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. This ensures that the rounded number reflects the appropriate level of precision.

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 is particularly useful for handling very large or very small values, making it easier to perform calculations and maintain significant figures.

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