Question

The correctly reported answers of the addition of \(294.406,280.208\) and 24 will be (1) \(598.61\) (2) 599 (3) \(598.6\) (4) \(598.614\)

Short answer

Option (2) 599

Step-by-step solution

- Understand the problem

Need to add three numbers: 294.406, 280.208, and 24, then choose the correctly reported answer.

- Perform the addition

Compute the sum of the numbers 294.406, 280.208, and 24: \[ 294.406 + 280.208 + 24 = 598.614 \]

- Determine the correct significant figures

Analyze the number of significant figures in the original numbers. The first number has 6 significant figures, the second has 6 significant figures, and the third has 2 significant figures.

- Round the result

Since the number with the fewest decimal places is 24 (0 decimal places), round the result to the nearest whole number: \[ 598.614 \approx 599 \]

- Select the correct option

Based on the rounding, the correctly reported answer is option (2) 599.

Key concepts

Addition

When adding numbers, it's important to combine them accurately. In the given exercise, we have three numbers: 294.406, 280.208, and 24. Adding these together, we get the sum: \[ 294.406 + 280.208 + 24 = 598.614 \] Accurate addition is crucial to ensure that subsequent steps like rounding are performed correctly. Make sure to line up the decimal points when adding numbers with decimals for accuracy. Use tools like calculators to avoid simple arithmetic errors.

Rounding

Rounding is the process of adjusting the digits of a number to reduce the number of decimal places while keeping the same overall value. After performing the addition, we get the result 598.614. However, because our original numbers had varied decimal places, we need to round the result to match the least precise measurement. Here, the number 24 has 0 decimal places. This means we should round 598.614 to the nearest whole number. When rounding, look at the digit immediately after the place value you’re rounding to. If this digit is 5 or higher, round up. If it's less than 5, round down. Hence, 598.614 rounded to the nearest whole number is: \[ 598.614 \rightarrow 599 \]

Decimal Places

Decimal places are the digits that appear after the decimal point in a number. In our exercise, the decimal places of the numbers involved were crucial for determining how to report the final answer. The rule of thumb is to ensure that the final result doesn’t have more decimal places than the original number with the fewest decimal places. Here are the given numbers and their decimal places:

• 294.406 has 3 decimal places
• 280.208 has 3 decimal places
• 24 has 0 decimal places

Since the number 24 has no decimal places, our answer must be rounded to the nearest whole number, aligning with the number that has the fewest decimal places. This is to ensure the precision and accuracy of the reported answer. Therefore, the rounded sum 598.614 becomes 599.