Problem 15 - Algebra 1

Question

Perform any indicated operation. Round the result to the nearest tenth and then to the nearest hundredth. $$ 5.34(6.79) $$

Step-by-Step Solution

Answer

The result of 5.34 multiplied by 6.79, rounded to the nearest tenth is 36.3 and to the nearest hundredth is 36.25

Step 1: Perform the Multiplication

Multiply 5.34 by 6.79. Using a calculator, the product will be 36.2506. It's important to carry out the operation to a few more decimal places than needed, so the rounding will be accurate.

Step 2: Round to the Nearest Tenth

Round 36.2506 to the nearest tenth. Look at the digits in the hundredths place. If that number is 5 or above, round up. If it's 4 or lower, round down. In this case, it's 5, so we round up. The result is 36.3.

Step 3: Round to the Nearest Hundredth

Rounding the original product (36.2506) to the nearest hundredth, we again examine the digit in the next place (the thousandths place). Since it's 0, we round down. The resulting number is 36.25

Key Concepts

Multiplication in Decimal Numbers

To multiply decimal numbers like 5.34 and 6.79, you can use a calculator for precision, but it is also worthwhile to understand the process manually. Move the decimal points to the right to turn the numbers into whole numbers - this simplifies multiplication.

• First, consider how many total decimal places are in both numbers combined. In this case, 5.34 has two decimal places, and 6.79 has two as well, making a total of four decimal places.
• Multiply 534 by 679 (ignore the decimals temporarily). The product is 362506.
• Now, divide this result by 10000 (since that equals adding four decimal places). The answer is 36.2506, exactly what you'd calculate with the decimals taken into account.

Understanding this ensures you know where the decimals originate and avoids common errors when performing manual calculations.

Rounding to Nearest Tenth

Rounding to the nearest tenth involves examining the hundredths place of a decimal number. This determines whether the tenths place should go up or remain the same.
Let's use the number 36.2506:

• The number in the hundredths place is 5.
• If this number is 5 or greater, you round up the number in the tenths place. If it's less than 5, you leave it as it is.
• Here, since the hundredths place is 5, increase the tenths place by 1. So, 36.2506 rounds to 36.3.

This rule helps simplify numerical data and can be crucial in applications like statistics and science where precision might warrant such rounding.

Rounding to Nearest Hundredth

Rounding a number like 36.2506 to the nearest hundredth requires observing the digit in the thousandths place. This step aims to make the number visually simpler while preserving the necessary precision for calculations.

• Consider the digit in the thousandths place: in 36.2506, it is 0.
• If this digit is less than 5, the hundredths place remains unchanged. If it's 5 or more, the hundredths place would increase by 1.
• Here, since the thousandths digit is 0, the number rounds to 36.25.

This method is useful for preparing data for reports or financial statements where clarity and precision are critical.