Question

Suppose you want to estimate 43,572 - 18,489. Will rounding each number to the nearest thousand give an answer closer to the actual sum than rounding to the nearest hundred?

A. Yes. Rounding to the nearest thousand: 26,000. Rounding to the nearest hundred: 25,100. The actual difference is 25,083. 25,083 is closer to 26,000 than to 25,100.
B. Yes. Rounding to the nearest thousand: 26,000. Rounding to the nearest hundred: 25,000. The actual difference is 25,083. 25,083 is closer to 26,000 than to 25,000.
C. No. Rounding to the nearest thousand: 26,000. Rounding to the nearest hundred: 25,100. The actual difference is 25,083. 25,083 is closer to 25,100 than to 26,000.
D. No. Rounding to the nearest thousand: 26,000. Rounding to the nearest hundred: 25,000. The actual difference is 25,983. 25,983 is closer to 26,000 than to 25,000.

Answer 1

When estimating the difference between 43,572 and 18,489, rounding each number to the nearest thousand gives an answer closer to the actual difference than rounding to the nearest hundred.

Step-by-step explanation:

When estimating the difference between 43,572 and 18,489 by rounding each number to the nearest thousand and nearest hundred, we can compare the rounded answers to the actual difference. Rounding 43,572 to the nearest thousand gives 44,000, and rounding 18,489 to the nearest thousand gives 18,000. Therefore, the rounded difference is 44,000 - 18,000 = 26,000. Rounding 43,572 to the nearest hundred gives 43,600, and rounding 18,489 to the nearest hundred gives 18,500. Therefore, the rounded difference is 43,600 - 18,500 = 25,100.

The actual difference between 43,572 and 18,489 is 43,572 - 18,489 = 25,083. Comparing the rounded answers to the actual difference, we can see that 25,083 is closer to 26,000 (rounded to the nearest thousand) than to 25,100 (rounded to the nearest hundred).

Hence, the correct answer is A. Yes. Rounding each number to the nearest thousand gives an answer closer to the actual sum than rounding to the nearest hundred.