By rounding to one significant figure, estimate the answers to these questions:
a) $59 \div 25$
b) $\frac{682}{71}$
c) $\frac{91 \times 18}{58}$
Answer (2)
Round each number to one significant figure.
a) Divide the rounded numbers: 60 ÷ 30 = 2 .
b) Divide the rounded numbers: 70 700 = 10 .
c) Calculate the expression with the rounded numbers: 60 90 × 20 = 30 .
The estimated answers are 2 , 10 , 30 .
Explanation
Problem Analysis We need to estimate the answers to the given questions by rounding each number to one significant figure first.
Estimating a) a) We have 59 ÷ 25 . Rounding 59 to one significant figure gives 60, and rounding 25 to one significant figure gives 30. So, the estimated answer is 60 ÷ 30 = 2 .
Estimating b) b) We have 71 682 . Rounding 682 to one significant figure gives 700, and rounding 71 to one significant figure gives 70. So, the estimated answer is 70 700 = 10 .
Estimating c) c) We have 58 91 × 18 . Rounding 91 to one significant figure gives 90, rounding 18 to one significant figure gives 20, and rounding 58 to one significant figure gives 60. So, the estimated answer is 60 90 × 20 = 60 1800 = 30 .
Final Answer Therefore, the estimated answers are: a) 2 b) 10 c) 30
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 or estimating travel times. For example, if you're buying items priced at $59, $682, and $91 and want to quickly estimate the total cost, rounding to one significant figure ($60, $700, and $90) allows for a fast mental calculation of approximately $850. This method provides a reasonable estimate without needing exact calculations.
The estimated answers to the calculations by rounding to one significant figure are: a) 2, b) 10, and c) 30.
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