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By rounding to one significant figure, estimate the answers to these questions:
a) $98 \div 11$
b) $\frac{764}{19}$
c) $\frac{798}{8 \times 41}$
Answer (2)
Round each number to one significant figure.
a) Round 98 to 100 and 11 to 10, then 100 ÷ 10 = 10 .
b) Round 764 to 800 and 19 to 20, then 20 800 = 40 .
c) Round 798 to 800, 8 to 8, and 41 to 40, then 8 × 40 800 = 320 800 = 2.5 .
The estimated answers are a ) 10 , b ) 40 , c ) 2.5 .
Explanation
Problem Analysis We are asked to estimate the answers to the given questions by rounding each number to one significant figure. This means we keep only the leftmost digit and replace the rest with zeros.
Estimating a) For question a), we need to estimate 98 o b re ak ÷ 11 . First, we round 98 to one significant figure, which gives us 100. Then, we round 11 to one significant figure, which gives us 10. Now we divide 100 by 10: 100 o b re ak ÷ 10 = 10 .
Estimating b) For question b), we need to estimate 19 764 . First, we round 764 to one significant figure, which gives us 800. Then, we round 19 to one significant figure, which gives us 20. Now we divide 800 by 20: 20 800 = 40 .
Estimating c) For question c), we need to estimate 8 × 41 798 . First, we round 798 to one significant figure, which gives us 800. Then, we round 8 to one significant figure, which remains 8. Next, we round 41 to one significant figure, which gives us 40. Now we divide 800 by the product of 8 and 40: 8 × 40 800 = 320 800 = 2.5 .
Final Answer Therefore, the estimated answers are: a) 10 b) 40 c) 2.5
Examples
Estimating calculations by rounding to one significant figure is useful in everyday situations where a quick, approximate answer is needed. For example, when grocery shopping, you can quickly estimate the total cost of your items by rounding each price to one significant figure and adding them up. This allows you to have a rough idea of whether you have enough money or if you're staying within your budget without needing exact calculations.
By rounding each number to one significant figure, we can estimate the answers to the given mathematical problems as follows: a) 10, b) 40, c) 2.5. This method allows for simpler calculations and is useful in various real-life situations.
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