By first rounding both numbers to 1 significant figure, estimate the answer to [tex]$13 \times 378$[/tex]
Answer (2)
Round 13 to one significant figure: 13 ≈ 10 .
Round 378 to one significant figure: 378 ≈ 400 .
Multiply the rounded numbers: 10 × 400 = 4000 .
The estimated answer is 4000 .
Explanation
Problem Analysis We are asked to estimate the product of 13 and 378 by first rounding each number to one significant figure. This means we need to round each number to the nearest multiple of ten or hundred, depending on the number.
Rounding 13 First, we round 13 to one significant figure. The first significant figure is 1 , and the digit to the right of it is 3 , which is less than 5 . Therefore, we round down to 10 .
Rounding 378 Next, we round 378 to one significant figure. The first significant figure is 3 , and the digit to the right of it is 7 , which is greater than or equal to 5 . Therefore, we round up to 400 .
Multiplication Now, we multiply the rounded numbers: 10 × 400 = 4000 .
Final Answer Therefore, the estimated answer is 4000 .
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 13 items that cost approximately $378 each, rounding these numbers to 10 and 400 respectively allows you to quickly estimate the total cost as $10 \times 400 = $4000. This provides a reasonable estimate without needing precise calculations.
To estimate 13 × 378 , first round each number to one significant figure, giving 10 and 400 respectively. Multiply these rounded figures to get an estimate of 4000 . Thus, the estimated answer is 4000 .
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