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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 110
Chapter 1, Problem 110

Multiply or divide as indicated. 0.07 × 0.004

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1
Identify the operation: The problem asks to multiply 0.07 by 0.004.
Rewrite the decimals as fractions to understand the multiplication better: 0.07 = \(\frac{7}{100}\) and 0.004 = \(\frac{4}{1000}\).
Multiply the fractions: \(\frac{7}{100}\) \(\times\) \(\frac{4}{1000}\) = \(\frac{7 \times 4}{100 \times 1000}\).
Calculate the numerator and denominator separately: numerator = 7 \(\times\) 4, denominator = 100 \(\times\) 1000.
Convert the resulting fraction back to a decimal by dividing the numerator by the denominator.

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Key Concepts

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

Multiplication of Decimals

Multiplying decimals involves ignoring the decimal points initially, multiplying the numbers as whole numbers, and then placing the decimal point in the product. The total number of decimal places in the product equals the sum of the decimal places in the factors.
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Place Value and Decimal Places

Understanding place value is crucial when working with decimals. Each digit's position relative to the decimal point determines its value, and counting decimal places helps correctly position the decimal in the result after multiplication or division.
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Basic Arithmetic Operations

Performing multiplication or division accurately requires a solid grasp of basic arithmetic operations. This includes multiplying numbers, handling zeros, and correctly interpreting the result in the context of decimals.
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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. {x | x ∈ M or x ∈ Q}