Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

0. Review of Algebra

Exponents

College Algebra

0. Review of Algebra

Exponents

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1:21 minutes

Problem 82

Textbook Question

Round each decimal to the nearest thousandth.(a) 0.8 (line above 8) (b) 0.4 (line above 4) (c) 0.9762 (d) 0.8645

Verified step by step guidance

Identify the decimal number that needs rounding for each part of the problem.

For part (a), recognize that 0.8 with a line above 8 indicates a repeating decimal: 0.8888... and round it to the nearest thousandth.

For part (b), recognize that 0.4 with a line above 4 indicates a repeating decimal: 0.4444... and round it to the nearest thousandth.

For part (c), look at the number 0.9762 and identify the digit in the thousandths place, then determine if the digit in the ten-thousandths place requires rounding up or down.

For part (d), look at the number 0.8645 and identify the digit in the thousandths place, then determine if the digit in the ten-thousandths place requires rounding up or down.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Rounding Decimals

Rounding decimals involves adjusting a number to a specified degree of accuracy, typically to the nearest whole number, tenth, hundredth, or thousandth. When rounding to the nearest thousandth, you look at the digit in the fourth decimal place to determine whether to round up or down. If this digit is 5 or greater, you increase the third decimal place by one; if it is less than 5, you leave the third decimal place unchanged.

Place Value

Place value refers to the value of a digit based on its position within a number. In decimal numbers, each position to the right of the decimal point represents a fractional value, with the first position being tenths, the second hundredths, and the third thousandths. Understanding place value is crucial for accurately rounding numbers, as it helps identify which digit to adjust based on the rounding rules.

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, it is important to consider significant figures to maintain the integrity of the number's precision, especially in scientific and mathematical contexts where accuracy is critical.