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Ch. R - Review of Basic Concepts
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
All textbooksLial 13th EditionCh. R - Review of Basic ConceptsProblem 82d
Chapter 1, Problem 82d

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

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1
Understand that rounding to the nearest thousandth means keeping three digits after the decimal point and deciding whether to round the last digit up or keep it the same based on the digit immediately after it.
For each decimal, identify the digit in the thousandths place (the third digit after the decimal point). If the number has fewer than three digits after the decimal, consider adding zeros to reach the thousandths place.
Look at the digit immediately to the right of the thousandths place (the fourth digit after the decimal). If this digit is 5 or greater, increase the thousandths digit by 1; if it is less than 5, leave the thousandths digit as is.
Apply this rule to each decimal: (a) 0.8 (with a repeating 8), (b) 0.4 (with a repeating 4), (c) 0.9762, and (d) 0.8645, carefully determining the thousandths digit and the next digit to decide rounding.
Write the rounded number for each part, ensuring it has exactly three digits after the decimal point, reflecting the rounding decision made.

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Key Concepts

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

Place Value and Decimal Notation

Understanding place value is essential for rounding decimals. Each digit in a decimal number has a specific place value, such as tenths, hundredths, and thousandths. Recognizing these positions helps determine which digit to round to and which digit influences the rounding.
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Rounding Rules for Decimals

Rounding decimals involves looking at the digit immediately to the right of the target place value. If this digit is 5 or greater, the target digit is increased by one; if less than 5, it remains the same. This rule ensures numbers are approximated correctly to the desired precision.
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Cramer's Rule - 2 Equations with 2 Unknowns

Repeating Decimals and Their Representation

A repeating decimal has one or more digits that repeat infinitely, often indicated by a line over the repeating digit(s). When rounding repeating decimals, it is important to consider the repeating pattern to determine the correct digit for rounding at the specified place value.
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Related Practice
Textbook Question

Let U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}, M = {0, 2, 4, 6, 8}, N = {1, 3, 5, 7, 9, 11, 13}, Q = {0, 2, 4, 6, 8, 10, 12}, and R = {0, 1, 2, 3, 4}.Use these sets to find each of the following. Identify any disjoint sets. M ∪ N

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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

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

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

Textbook Question

Simplify each expression. Write answers without negative exponents. Assume all variables represent positive real numbers. 82/3

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Textbook Question

Evaluate each expression. (-2)4