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By rounding to 1 significant figure, estimate the answers to these questions:
a) $12 \times 89$
b) $157 \times 189$
c) $687 \times 894$
Answer (2)
Round each number to 1 significant figure.
Multiply the rounded numbers to estimate the answer.
a) 12 × 89 ≈ 10 × 90 = 900
b) 157 × 189 ≈ 200 × 200 = 40000
c) 687 × 894 ≈ 700 × 900 = 630000
The estimated answers are: a) 900 , b) 40000 , c) 630000
Explanation
Problem Analysis We are asked to estimate the answers to the given multiplication problems by rounding each number to 1 significant figure. Let's tackle each question one by one.
Estimating a) 12 × 89 a) For the expression 12 × 89 , we first round each number to 1 significant figure. 12 rounds to 10, and 89 rounds to 90. Then we multiply the rounded numbers: 10 × 90 = 900 .
Estimating b) 157 × 189 b) For the expression 157 × 189 , we round each number to 1 significant figure. 157 rounds to 200, and 189 rounds to 200. Then we multiply the rounded numbers: 200 × 200 = 40000 .
Estimating c) 687 × 894 c) For the expression 687 × 894 , we round each number to 1 significant figure. 687 rounds to 700, and 894 rounds to 900. Then we multiply the rounded numbers: 700 × 900 = 630000 .
Final Answer Therefore, the estimated answers are: a) 900, b) 40000, and c) 630000.
Examples
Estimating calculations by rounding to one significant figure is useful in everyday situations. For instance, when grocery shopping, you can quickly estimate the total cost of your items by rounding each price to the nearest dollar or ten cents and then adding them up. This helps you stay within your budget without needing exact calculations on the spot. Similarly, when planning a road trip, you can estimate the total distance and travel time by rounding the distances between cities to the nearest hundred miles and using an average speed rounded to the nearest ten miles per hour.
We estimate the answers to three multiplication problems by rounding to one significant figure. The estimated products are: a) 900, b) 40000, and c) 630000. This method helps simplify calculations for quick estimates.
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