By rounding to 1 significant figure, estimate the answers to these questions:
a) $92 \times 98$
b) $49 \times 138$
c) $216 \times 876$
Answer (2)
Round 92 and 98 to one significant figure, resulting in 90 and 100, then multiply: 90 × 100 = 9000 .
Round 49 and 138 to one significant figure, resulting in 50 and 100, then multiply: 50 × 100 = 5000 .
Round 216 and 876 to one significant figure, resulting in 200 and 900, then multiply: 200 × 900 = 180000 .
The estimated answers are therefore 9000 , 5000 , 180000 .
Explanation
Understanding the Problem We're going to estimate the answers to the given multiplication problems by rounding each number to 1 significant figure first. This means we keep only the leftmost digit and replace the rest with zeros. Then, we'll multiply the rounded numbers to get our estimate.
Estimating 92 x 98 For part (a), we have 92 × 98 . Rounding 92 to 1 significant figure gives us 90. Rounding 98 to 1 significant figure gives us 100. Now we multiply these rounded numbers: 90 × 100 = 9000
Estimating 49 x 138 For part (b), we have 49 × 138 . Rounding 49 to 1 significant figure gives us 50. Rounding 138 to 1 significant figure gives us 100. Now we multiply these rounded numbers: 50 × 100 = 5000
Estimating 216 x 876 For part (c), we have 216 × 876 . Rounding 216 to 1 significant figure gives us 200. Rounding 876 to 1 significant figure gives us 900. Now we multiply these rounded numbers: 200 × 900 = 180000
Final Answer So, the estimated answers are: a) 9000 b) 5000 c) 180000
Examples
Estimating calculations by rounding to one significant figure is useful in everyday situations where you need a quick, approximate answer. For example, when grocery shopping, you might round the price of each item to the nearest dollar to quickly estimate the total cost. If you're buying items costing $2.95, $4.20, and $1.85, you can round these to $3, $4, and $2, respectively, to estimate a total cost of $9. This helps you ensure you have enough money or stay within a budget without needing exact calculations on the spot.
To estimate the products of the multiplication problems, we rounded each number to one significant figure before multiplying. This results in 9000 for 92 × 98 , 5000 for 49 × 138 , and 180000 for 216 × 876 . The estimated answers are 9000 , 5000 , and 180000 respectively.
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