Problem 40 - Prealgebra

Question

Multiply the decimals (57.7)(?0.04)

Step-by-Step Solution

Answer

The product of 57.7 and 0.04 is 2.308.

Step 1: Ignore the Decimals

Before dealing with the decimal points, first multiply the numbers as if they were whole numbers. So, multiply 577 by 4.

Step 2: Perform the Multiplication

Multiply 577 by 4: \[ 577 \times 4 = 2308 \]

Step 3: Count the Decimal Places

Count the total number of decimal places in the original numbers. The number 57.7 has one decimal place and 0.04 has two decimal places. In total, there are three decimal places.

Step 4: Place the Decimal Point

Take the number from Step 2, which is 2308, and place the decimal point in it according to the total number of decimal places counted in Step 3. Move the decimal point three places from the right: \[ 2.308 \]

Step 5: Verify the Answer

Ensure the decimal placement corresponds to the product of the original decimals. The numbers 57.7 and 0.04 together have three decimal places, and the final result 2.308 matches this.

Key Concepts

Decimal Places

When working with decimal multiplication, understanding decimal places is crucial. Decimal places are the number of digits to the right of the decimal point. For example, in 57.7, there is one decimal place, while 0.04 has two decimal places.

• Counting decimal places is essential because the final answer must have a specific number of decimal places.
• This ensures the precision of the number and makes sure the multiplication is accurate.
• The total number of decimal places in the result is the sum of the decimal places in the numbers being multiplied.

Knowing how many decimal places to include in your final result helps prevent common mistakes and ensures that the product of the multiplication is valid. Pay close attention at each step.

Multiplying Decimals Step by Step

To multiply decimals, follow a series of straightforward steps to simplify the process. First, consider the numbers without their decimal points, just as whole numbers. For example:

• Suppose you need to multiply 57.7 and 0.04. Ignore the decimal points initially, and instead multiply 577 by 4.
• The calculation yields 2308.

Once you complete the multiplication like this, determine the correct placement of the decimal point. Look back at the original numbers:

• 57.7 has one decimal place, and 0.04 has two.
• Add these together, and your final product must have three decimal places.
• Place the decimal point three positions from the right of 2308, resulting in 2.308.

This systematic approach makes the process easy, even with more complex numbers.

Multiplication Verification

After obtaining your product, verifying your work is an essential step in decimal multiplication. Verification confirms that the decimal point is correctly placed, ensuring the result accurately represents the multiplication of the original numbers.

• First, check that the number of decimal places in your result matches the total decimal places counted in your initial step.
• For example, examine that 2.308 indeed has three decimal places, aligning with the sum of decimal places in 57.7 and 0.04.
• Look back to see if the simpler multiplication (577 by 4) was executed correctly.

With thorough verification, you gain confidence in your solution, reinforcing your understanding of decimal multiplication. Don't skip this step, as it helps catch easy mistakes and ensures precision.