Problem 28 - Prealgebra

Question

Multiply. Round to nearest hundredth if necessary. $$0.12(8,000)$$

Step-by-Step Solution

Answer

The product is 960.

Step 1: Understand the Problem

The task requires multiplying the number 0.12 by 8,000 and rounding the result to the nearest hundredth if necessary.

Step 2: Perform the Multiplication

Calculate the product of 0.12 and 8,000: 0.12 multiplied by 8,000 equals 960. The multiplication can be performed as follows:\[0.12 \times 8,000 = 960\]

Step 3: Check for Rounding

The result from multiplication is 960, which is already a whole number. It does not have decimal places, thus no rounding to the nearest hundredth is needed.

Key Concepts

Rounding in Math

Rounding is a helpful technique used to simplify numbers, making them easier to understand and work with. When you round a number, you are essentially finding a nearby value with fewer digits. For instance, rounding to the nearest hundredth means adjusting a decimal number to have two digits after the decimal point.
Here's how to round:

• Identify what place value you are rounding to (e.g., the hundredth place).
• Look at the next digit to the right (e.g., the thousandth place).
• If that digit is 5 or greater, round up. If it is less than 5, round down.

In our exercise, the result of multiplication was a whole number (960), which doesn’t require rounding since it has no decimal places to adjust. However, understanding rounding ensures you handle more complex problems efficiently.

Understanding Whole Numbers

Whole numbers are exactly what they sound like—numbers without fractions or decimals. They include all the non-negative integers starting from zero and going upwards (0, 1, 2, 3, and so on).
Whole numbers are important for simple counting and for many everyday activities. They provide a basic framework in math without the complications that fractions and decimals can present.

• They are easy to understand and use.
• They simplify mathematical operations, avoiding potential errors from decimal places.
• Whole numbers are always rounded automatically, since they lack fractional parts.

In this exercise example, 960 is a whole number, which contributes to the simplicity of the problem since no further adjustment is needed.

Basics of Decimal Multiplication

Decimal multiplication involves numbers that have parts less than a whole, represented by digits following the decimal point. It can be a bit trickier than multiplying whole numbers, but with practice, it becomes straightforward. To multiply decimals:

• Ignore the decimal points and multiply the numbers as if they are whole numbers.
• Count the total number of decimal places in both numbers you are multiplying.
• In the product, place the decimal point so that there are as many digits to the right of the decimal as there are in total from the numbers you multiplied.

For example, when multiplying 0.12 by 8,000, you treat the 0.12 as 12 (shifting the decimal) and proceed to multiply by 8,000. After the multiplication, you adjust the decimal point to reflect the two original decimal places, confirming that the product is indeed 960, requiring no further rounding.