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 900 , 40000 , 630000 .
Explanation
Problem Analysis We are asked to estimate the answers to the given multiplication problems by rounding each number to 1 significant figure. This means we need to round each number to the nearest ten, hundred, or thousand, depending on the number's magnitude, and then multiply the rounded numbers.
Estimating a) a) For 12 × 89 , we round 12 to 10 and 89 to 90. Then we multiply the rounded numbers: 10 × 90 = 900 .
Estimating b) b) For 157 × 189 , we round 157 to 200 and 189 to 200. Then we multiply the rounded numbers: 200 × 200 = 40000 .
Estimating c) c) For 687 × 894 , we round 687 to 700 and 894 to 900. Then we multiply the rounded numbers: 700 × 900 = 630000 .
Final Answer Therefore, the estimated answers are: a) 12 × 89 ≈ 900 b) 157 × 189 ≈ 40000 c) 687 × 894 ≈ 630000
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 3 items that cost $22, $87, and $39, you can quickly estimate the total cost by rounding to $20, $90, and $40, respectively. The estimated total cost would be $20 + $90 + $40 = $150, which is close to the actual cost and helps you make quick budgeting decisions.
The estimated answers by rounding to 1 significant figure are: a) 900, b) 40000, and c) 630000. This process involves rounding the numbers to their nearest significant figure and then multiplying them. This method helps in making quick calculations.
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