The Correct Answer and Explanation is:
The correct answer is 7.35.
Here is the explanation:
To find the correct answer, we must first perform the subtraction and then apply the specific rule for significant figures in addition and subtraction.
The rule states that when adding or subtracting numbers, the result should have the same number of decimal places as the number in the original calculation with the fewest decimal places. This rule is different from the one used for multiplication and division, which focuses on the total number of significant figures.
Let’s examine the two numbers in the problem:
- 8.070: This number is measured to the thousandths place, meaning it has three decimal places.
- 0.72: This number is measured to the hundredths place, meaning it has two decimal places.
According to the rule, our final answer must be rounded to the number of decimal places of the least precise measurement. In this case, the least precise measurement is 0.72, which has two decimal places. Therefore, our answer must also be rounded to two decimal places.
First, let’s perform the subtraction without considering significant figures:
8.070 – 0.72 = 7.350
The raw mathematical answer is 7.350. Now, we need to round this value to two decimal places. To do this, we look at the third digit after the decimal point. In 7.350, the third decimal digit is 0. Since this digit is less than 5, we do not round up the previous digit. We simply keep the number as it is up to the second decimal place.
So, rounding 7.350 to two decimal places gives us 7.35.
Comparing this result to the options provided:
- 7 is incorrectly rounded to the ones place.
- 7.35 is correctly rounded to two decimal places.
- 7.4 is incorrectly rounded to one decimal place.
- 7.350 is the unrounded calculator answer and has an incorrect number of decimal places.
