Would it be more accurate to round $135+(-110)+83$ to the nearest tens or hundreds place?
Answer (2)
Evaluate the expression: 135 + ( − 110 ) + 83 = 108 .
Round 108 to the nearest ten: 110 .
Round 108 to the nearest hundred: 100 .
Compare the absolute differences: ∣108 − 110∣ = 2 and ∣108 − 100∣ = 8 . Since 2 < 8, rounding to the nearest ten is more accurate.
The final answer is: T e n s .
Explanation
Problem Analysis We are asked to determine whether rounding the result of the expression 135 + ( − 110 ) + 83 to the nearest ten's place or hundred's place would be more accurate. To do this, we need to evaluate the expression, round the result to the nearest ten and nearest hundred, and then compare the differences between the original result and the rounded values.
Evaluate the Expression First, let's evaluate the expression: 135 + ( − 110 ) + 83 = 135 − 110 + 83 = 25 + 83 = 108 So, the result of the expression is 108.
Round to Nearest Ten Next, we round 108 to the nearest ten. The tens place is 0, and the digit to the right is 8, which is greater than or equal to 5, so we round up to 110.
Round to Nearest Hundred Now, we round 108 to the nearest hundred. The hundreds place is 1, and the digit to the right is 0, which is less than 5, so we round down to 100.
Calculate Difference for Nearest Ten Now, we calculate the absolute difference between the original result (108) and the rounded result to the nearest ten (110): ∣108 − 110∣ = ∣ − 2∣ = 2
Calculate Difference for Nearest Hundred Next, we calculate the absolute difference between the original result (108) and the rounded result to the nearest hundred (100): ∣108 − 100∣ = ∣8∣ = 8
Compare the Differences Comparing the two absolute differences, we have 2 for the nearest ten and 8 for the nearest hundred. Since 2 is less than 8, rounding to the nearest ten is more accurate.
Final Answer Therefore, it is more accurate to round to the nearest ten's place.
Examples
When estimating expenses or quantities, deciding whether to round to the nearest ten or hundred depends on the numbers involved. For instance, if you have a total expense of $108, rounding to the nearest ten ($110) gives a closer estimate than rounding to the nearest hundred ($100). This is useful in budgeting or quick mental calculations where accuracy is important but exact figures aren't necessary.
After evaluating the expression 135 + ( − 110 ) + 83 , which equals 108, rounding to the nearest ten gives 110, while rounding to the nearest hundred gives 100. The absolute difference when rounding to the nearest ten is 2, compared to 8 for the nearest hundred. Thus, rounding to the nearest ten is more accurate.
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