Year 7A3 - Homework
By rounding to 1 significant figure, estimate the answers to these questions:
a) $76 \times 23$
b) $297 \times 589$
c) $715 \times 283$
Answer (2)
Round each number to 1 significant figure.
Multiply the rounded numbers to estimate the answer.
a) 76 × 23 ≈ 80 × 20 = 1600
b) 297 × 589 ≈ 300 × 600 = 180000
c) 715 × 283 ≈ 700 × 300 = 210000
1600 , 180000 , 210000
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) For question a), we need to estimate 76 × 23 . First, we round 76 to 1 significant figure, which is 80. Then, we round 23 to 1 significant figure, which is 20. Now, we multiply the rounded values: 80 × 20 = 1600 .
Estimating b) For question b), we need to estimate 297 × 589 . First, we round 297 to 1 significant figure, which is 300. Then, we round 589 to 1 significant figure, which is 600. Now, we multiply the rounded values: 300 × 600 = 180000 .
Estimating c) For question c), we need to estimate 715 × 283 . First, we round 715 to 1 significant figure, which is 700. Then, we round 283 to 1 significant figure, which is 300. Now, we multiply the rounded values: 700 × 300 = 210000 .
Final Answer Therefore, the estimated answers are: a) 76 × 23 ≈ 1600 b) 297 × 589 ≈ 180000 c) 715 × 283 ≈ 210000
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 8 items that cost $22 each, you can round $22 to $20 and quickly estimate the total cost as $8 \times 20 = $160. This gives you a rough idea of the total amount you'll spend without needing exact calculations.
By rounding each number to 1 significant figure, the estimated products for the given multiplications are: a) 1600, b) 180000, and c) 210000. This method helps simplify calculations for quick estimations. Rounding makes it easier to handle larger numbers in everyday situations.
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