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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 63
Chapter 1, Problem 63

Find each product or quotient where possible. -0.06(0.4)

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Identify the operation: The problem asks to find the product of -0.06 and 0.4, which means we need to multiply these two numbers.
Rewrite the multiplication in mathematical form: \(-0.06 \times 0.4\).
Convert the decimals to fractions or work directly with decimals: For example, \(-0.06\) can be seen as \(-\frac{6}{100}\) and \(0.4\) as \(\frac{4}{10}\), or multiply directly as decimals.
Multiply the absolute values: Calculate \(0.06 \times 0.4\) by multiplying the numbers ignoring the negative sign for now.
Determine the sign of the product: Since one number is negative and the other is positive, the product will be negative.

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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 multiplying the numbers as if they were whole numbers, 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. For example, multiplying 0.06 (two decimal places) by 0.4 (one decimal place) results in a product with three decimal places.
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Handling Negative Numbers in Multiplication

When multiplying numbers, the sign of the product depends on the signs of the factors. Multiplying a negative number by a positive number results in a negative product. Here, -0.06 multiplied by 0.4 will yield a negative result because one factor is negative.
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Product and Quotient Operations

The problem asks for the product or quotient where possible, meaning multiplication or division should be performed if defined. Understanding when these operations are valid and how to compute them correctly is essential. In this case, multiplication is straightforward and defined for all real numbers.
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Related Practice
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Textbook Question

Insert ⊆ or ⊈ in each blank to make the resulting statement true. {2, 4, 6} ____ {2, 3, 4, 5, 6}