By rounding to 1 significant figure, estimate the answers to these questions:
a) [tex]$426 \times 894$[/tex]
b) [tex]$657 \times 889$[/tex]
c) [tex]$287 \times 494$[/tex]
Answer (2)
Round each number to 1 significant figure.
Multiply the rounded numbers for each question.
a) 426 × 894 ≈ 400 × 900 = 360000
b) 657 × 889 ≈ 700 × 900 = 630000
c) 287 × 494 ≈ 300 × 500 = 150000
The estimated answers are 360000 , 630000 , 150000 .
Explanation
Problem Analysis We're going to estimate the answers to the given multiplication problems by rounding each number to one significant figure. This means we keep only the leftmost digit and replace the rest with zeros.
Estimating a) a) For 426 × 894 , we first round 426 to 400 and 894 to 900. Then we multiply these rounded numbers: 400 × 900 = 360000 .
Estimating b) b) For 657 × 889 , we round 657 to 700 and 889 to 900. Multiplying these gives us: 700 × 900 = 630000 .
Estimating c) c) For 287 × 494 , we round 287 to 300 and 494 to 500. The product is: 300 × 500 = 150000 .
Final Answer So, the estimated answers are: a) 360000, b) 630000, and c) 150000.
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're buying 3 items that cost $2.95, $6.20, and $9.40, you can quickly estimate the total cost by rounding each price to the nearest dollar: $3 + $6 + $9 = $18. This gives you a rough idea of the total amount you'll spend without needing exact calculations.
To estimate the products of the given multiplications by rounding to one significant figure, the estimated answers are 360000 for a), 630000 for b), and 150000 for c).
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