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 expression.
a) 30 × 80 = 2400
b) 30 × 600 = 18000
c) 800 × 300 = 240000
2400 , 18000 , 240000
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 identify the first non-zero digit in each number and round the number based on the digit that follows it.
Estimating a) For part a), we have 31 × 75 . Rounding 31 to 1 significant figure gives us 30. Rounding 75 to 1 significant figure gives us 80. Therefore, the estimated answer is 30 × 80 = 2400 .
Estimating b) For part b), we have 29 × 564 . Rounding 29 to 1 significant figure gives us 30. Rounding 564 to 1 significant figure gives us 600. Therefore, the estimated answer is 30 × 600 = 18000 .
Estimating c) For part c), we have 765 × 273 . Rounding 765 to 1 significant figure gives us 800. Rounding 273 to 1 significant figure gives us 300. Therefore, the estimated answer is 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 quickly calculating the approximate cost of multiple items while shopping. For example, if you are buying 4 items that cost $28, $52, $93, and 11 , you can quickly estimate the total cost by rounding each price to one significant figure: $30 + 50 + 90 + 10 = $180. This gives you a rough idea of the total amount you will spend without needing exact calculations.
By rounding each number to 1 significant figure and then multiplying, the estimated results are: 2400 for 31 × 75 , 18000 for 29 × 564 , and 240000 for 765 × 273 .
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