By rounding to 1 significant figure, estimate the answers to these questions:
a) $31 \times 75$
b) $29 \times 564$
c) $765 \times 273$
Answer (2)
Round each number to 1 significant figure.
Multiply the rounded numbers for each question.
a) 30 × 80 = 2400
b) 30 × 600 = 18000
c) 800 × 300 = 240000
The estimated answers are 2400 , 18000 , 240000 .
Explanation
Problem Analysis We are asked to estimate the answers to the given multiplication questions 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 perform the multiplication.
Estimating a) 31 × 75 For question a) 31 × 75 , we round 31 to 30 and 75 to 80. Then we multiply the rounded numbers: 30 × 80 = 2400 .
Estimating b) 29 × 564 For question b) 29 × 564 , we round 29 to 30 and 564 to 600. Then we multiply the rounded numbers: 30 × 600 = 18000 .
Estimating c) 765 × 273 For question c) 765 × 273 , we round 765 to 800 and 273 to 300. Then we multiply the rounded numbers: 800 × 300 = 240000 .
Final Answer Therefore, the estimated answers are: a) 31 × 75 ≈ 2400 b) 29 × 564 ≈ 18000 c) 765 × 273 ≈ 240000
Examples
Estimating calculations by rounding to one significant figure is useful in everyday situations, such as when you're shopping and want to quickly estimate the total cost of your items. For example, if you're buying 3 items that cost $28, $52, and $19, you can round these to $30, $50, and $20, respectively, and quickly estimate the total cost to be $30 + $50 + $20 = $100. This helps you to quickly check if you have enough money or if the cashier made a mistake.
To estimate the multiplication problems, we round each number to one significant figure and then multiply. The estimated answers are: a) 2400, b) 18000, and c) 240000. This method simplifies calculations and gives a quick approximation of results.
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