Problem 263 - Intermediate Algebra

Question

In the following exercises, multiply. $$ (9.24)(10) $$

Step-by-Step Solution

Answer

92.4

Step 1: Understand the Problem

You need to multiply two numbers: 9.24 and 10.

Step 2: Set Up the Multiplication

Write the problem as a multiplication equation: \( 9.24 \times 10 \)

Step 3: Perform the Multiplication

Multiply the decimal number by 10. To do this, move the decimal point one place to the right: 9.24 becomes 92.4

Step 4: Write the Final Answer

The result of the multiplication is 92.4.

Key Concepts

Decimal Multiplication

When you multiply decimals, it might seem a bit tricky at first. The key is to ignore the decimal point initially and treat it like you are multiplying whole numbers. Once you’ve completed the multiplication, you can place the decimal in the correct position.

For example, given the problem \( (9.24)(10) \), you would first ignore the decimal and multiply 924 by 10.

So, \( 924 \times 10 = 9240 \).

Next, count the total number of decimal places in the numbers you multiplied. In this case, 9.24 has two decimal places. Since you are multiplying by 10, which has no decimal places, you simply need to move the decimal point back two places to the left.

Therefore, \( 9240 \) becomes 92.40, which is simplified to 92.4.

Place Value

Understanding place value is essential when working with decimals. Each digit in a number has a value based on its position. For example, in the number 9.24, the 9 is in the 'ones' place, the 2 is in the 'tenths' place, and the 4 is in the 'hundredths' place.

Place value helps in determining where to position the decimal point after multiplication.

• Ones place: This is the digit immediately before the decimal point.
• Tenths place: This is the first digit after the decimal point.
• Hundredths place: This is the second digit after the decimal point.

When multiplying decimals, shift the decimal point to the right according to the number of zeroes in the multiplier. Multiplying by 10 results in the decimal moving one place to the right.

So, 9.24 becomes 92.4 because the decimal moves one spot.

Arithmetic Operations

Arithmetic operations include addition, subtraction, multiplication, and division. Each operation follows specific rules:

• Addition and Subtraction: Align the numbers by their decimal points before performing the operation.
• Multiplication: Multiply the numbers without considering the decimal first. Count the total decimal places in the factors and apply the same to the product.
• Division: Move the decimal point in both the divisor and the dividend to make the divisor a whole number. Perform the division as with whole numbers and place the decimal in the quotient appropriately.

In decimal multiplication, you don't need to align decimals. Multiply normally and adjust the decimal in the result accordingly. For instance, multiplying 9.24 by 10 shifts the decimal one place right, resulting in 92.4.

Understanding these fundamentals simplifies operations with decimals, making problems like \( (9.24)(10) \) straightforward.