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Chapter 1: Problem 589

Multiply. $$ (9.24)(10) $$

Short Answer

Expert verified
92.4

Step by step solution

01

Understand the multiplication

Recognize that the problem requires multiplying two numbers: 9.24 and 10.
02

Multiply the numbers

To multiply the numbers, simply perform the arithmetic operation: \( 9.24 \times 10 = 92.4 \)
03

Verify the placement of the decimal point

Recall that multiplying by 10 shifts the decimal point one place to the right. Thus, 9.24 (one place left of the decimal) becomes 92.4.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Arithmetic Operations
Arithmetic operations are basic mathematical procedures that include addition, subtraction, multiplication, and division. In this exercise, we are focusing on multiplication. Understanding arithmetic operations is fundamental since they are used in everyday calculations.
Multiplication, in particular, involves finding the total number of objects in a specified number of groups. For example, multiplying 9.24 by 10 can be thought of as having ten groups of 9.24.
Using arithmetic operations accurately ensures the correct answer, which is critical for real-life applications and more advanced mathematical concepts.
Decimal Point
The decimal point is a symbol used to separate the whole number part from the fractional part of a number. For instance, in the number 9.24, '9' is the whole number, and '.24' is the fractional part. The position of the decimal point determines the value of the number. Moving the decimal point to the right increases the number's value.
In our exercise, multiplying by 10 involves shifting the decimal point one place to the right. So, 9.24 becomes 92.4 (the decimal point moves from between '9' and '2' to the right of '4').
Understanding how the decimal point works is essential in properly working with decimal numbers and achieving accurate results.
Multiplication of Decimals
Multiplication of decimals follows the same principles as multiplication of whole numbers, but you need to pay extra attention to the decimal point. Here's the multiplier:
  • First, multiply the numbers as if they were whole numbers, ignoring the decimal points initially.
  • Count the total number of decimal places in both numbers being multiplied. This will help position the decimal point in the final product.
.
For example, when multiplying 9.24 by 10, initially ignore the decimal and multiply 924 by 10 to get 9240. Then, since 9.24 has two decimal places, we reintroduce the decimal point two places from the end, resulting in 92.4.
By mastering this process, you can handle any decimal multiplication problem with confidence.

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