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61 / 95 Marks
By rounding to 1 significant figure, estimate the answers to these questions:
a) $875 \times 894$
b) $257 \times 789$
c) $887 \times 394$
Answer (2)
Round each number to 1 significant figure.
Multiply the rounded numbers to estimate the answer for each problem.
a) 875 × 894 ≈ 900 × 900 = 810000
b) 257 × 789 ≈ 300 × 800 = 240000
c) 887 × 394 ≈ 900 × 400 = 360000
The estimated answers are: a) 810000 , b) 240000 , c) 360000 .
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 hundred or thousand, depending on the number, and then multiply the rounded numbers.
Estimating a) a) For the first problem, we have 875 × 894 . Rounding 875 to 1 significant figure gives 900. Rounding 894 to 1 significant figure also gives 900. Therefore, the estimated answer is 900 × 900 = 810000 .
Estimating b) b) For the second problem, we have 257 × 789 . Rounding 257 to 1 significant figure gives 300. Rounding 789 to 1 significant figure gives 800. Therefore, the estimated answer is 300 × 800 = 240000 .
Estimating c) c) For the third problem, we have 887 × 394 . Rounding 887 to 1 significant figure gives 900. Rounding 394 to 1 significant figure gives 400. Therefore, the estimated answer is 900 × 400 = 360000 .
Final Answer The estimated answers are: a) 810000 b) 240000 c) 360000
Examples
Estimating calculations by rounding to one significant figure is useful in everyday life for quick mental calculations. For example, when shopping, you can quickly estimate the total cost of several items by rounding their prices to the nearest dollar or ten dollars and then adding them up. This helps you to make sure you have enough money or to compare prices quickly without needing exact calculations. If you're buying items priced at $257 and $789, rounding to $300 and $800 respectively gives you an estimated total of $1100.
To estimate the answers for the multiplications, round each number to 1 significant figure, then multiply the rounded values. The estimated answers are: a) 810000, b) 240000, c) 360000.
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