Homework Progress
33 / 95 Marks
By rounding to 1 significant figure, estimate the answers to these questions:
a) $78 \times 92$
b) $615 \times 38$
c) $423 \times 764$
Answer (2)
Round 78 and 92 to one significant figure, resulting in 80 and 90, and then multiply: 80 × 90 = 7200 .
Round 615 and 38 to one significant figure, resulting in 600 and 40, and then multiply: 600 × 40 = 24000 .
Round 423 and 764 to one significant figure, resulting in 400 and 800, and then multiply: 400 × 800 = 320000 .
The estimated answers are 7200 , 24000 , 320000 .
Explanation
Problem Analysis We are asked to estimate the answers to the 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 multiply the rounded numbers.
Estimating a) 78 × 92 For question a) we need to estimate 78 × 92 . First, we round 78 to 1 significant figure, which gives us 80. Then, we round 92 to 1 significant figure, which gives us 90. Now we multiply the rounded values: 80 × 90 = 7200 .
Estimating b) 615 × 38 For question b) we need to estimate 615 × 38 . First, we round 615 to 1 significant figure, which gives us 600. Then, we round 38 to 1 significant figure, which gives us 40. Now we multiply the rounded values: 600 × 40 = 24000 .
Estimating c) 423 × 764 For question c) we need to estimate 423 × 764 . First, we round 423 to 1 significant figure, which gives us 400. Then, we round 764 to 1 significant figure, which gives us 800. Now we multiply the rounded values: 400 × 800 = 320000 .
Final Answer Therefore, the estimated answers are: a) 78 × 92 ≈ 7200 b) 615 × 38 ≈ 24000 c) 423 × 764 ≈ 320000
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 $$29 each, you can round $29 to $30 and easily estimate the total cost as $8 \times 30 = $240. This method provides a quick way to check if you have enough money or to compare prices without needing exact calculations.
To estimate the products of the multiplications, we round each number to one significant figure before multiplying. The estimated results are: a) 7200, b) 24000, and c) 320000. This approach simplifies calculations and provides approximate answers efficiently.
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