By rounding to 1 significant figure, estimate the answers to these questions:
a) $17 \times 82$
b) $54 \times 671$
c) $207 \times 643$
Answer (2)
Round each number to 1 significant figure.
Multiply the rounded numbers to estimate the answer.
a) 17 × 82 ≈ 20 × 80 = 1600
b) 54 × 671 ≈ 50 × 700 = 35000
c) 207 × 643 ≈ 200 × 600 = 120000
1600 , 35000 , 120000
Explanation
Problem Analysis We are asked to estimate the answers to the given multiplication problems by rounding each number to 1 significant figure.
Estimating a) a) To estimate 17 × 82 , we first round each number to 1 significant figure. 17 rounded to 1 significant figure is 20. 82 rounded to 1 significant figure is 80. Then, we multiply the rounded numbers: 20 × 80 = 1600 .
Estimating b) b) To estimate 54 × 671 , we first round each number to 1 significant figure. 54 rounded to 1 significant figure is 50. 671 rounded to 1 significant figure is 700. Then, we multiply the rounded numbers: 50 × 700 = 35000 .
Estimating c) c) To estimate 207 × 643 , we first round each number to 1 significant figure. 207 rounded to 1 significant figure is 200. 643 rounded to 1 significant figure is 600. Then, we multiply the rounded numbers: 200 × 600 = 120000 .
Final Answer Therefore, the estimated answers are: a) 17 × 82 ≈ 1600 b) 54 × 671 ≈ 35000 c) 207 × 643 ≈ 120000
Examples
Estimating calculations by rounding to one significant figure is useful in everyday situations, such as quickly calculating the approximate cost of multiple items while shopping. For example, if you are buying 17 items that cost $82 each, rounding to 1 significant figure gives you 20 items at $80 each, making the estimated total cost $1600. This allows for a fast mental check to ensure you're within your budget without needing exact calculations.
By rounding to 1 significant figure, the estimates for the multiplications are: a) 1600, b) 35000, and c) 120000. Each number was rounded to its nearest significant figure before performing the multiplication. This method provides quick estimates for calculations.
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