By rounding to 1 significant figure, estimate the answers to these questions:
a) $76 \times 23$
b) $297 \times 589$
c) $715 \times 283$
Answer (2)
Round each number to 1 significant figure.
Multiply the rounded numbers to estimate the answer.
a) 76 × 23 ≈ 80 × 20 = 1600
b) 297 × 589 ≈ 300 × 600 = 180000
c) 715 × 283 ≈ 700 × 300 = 210000
b o x e d a ) 1600 , b ) 180000 , c ) 210000
Explanation
Problem Analysis We are asked to estimate the answers to the given multiplication problems by rounding each number to 1 significant figure. This means we need to identify the first non-zero digit in each number and round the number based on the digit that follows it. Then, we multiply the rounded numbers to get an estimate.
Estimating 76 x 23 a) For the first problem, we have 76 × 23 . We round 76 to 1 significant figure. The first digit is 7, and the next digit is 6, which is greater than or equal to 5, so we round 7 up to 8 and replace the 6 with 0, giving us 80. We round 23 to 1 significant figure. The first digit is 2, and the next digit is 3, which is less than 5, so we keep the 2 and replace the 3 with 0, giving us 20. Now we multiply the rounded numbers: 80 × 20 = 1600 .
Estimating 297 x 589 b) For the second problem, we have 297 × 589 . We round 297 to 1 significant figure. The first digit is 2, and the next digit is 9, which is greater than or equal to 5, so we round 2 up to 3 and replace the 9 and 7 with 0s, giving us 300. We round 589 to 1 significant figure. The first digit is 5, and the next digit is 8, which is greater than or equal to 5, so we round 5 up to 6 and replace the 8 and 9 with 0s, giving us 600. Now we multiply the rounded numbers: 300 × 600 = 180000 .
Estimating 715 x 283 c) For the third problem, we have 715 × 283 . We round 715 to 1 significant figure. The first digit is 7, and the next digit is 1, which is less than 5, so we keep the 7 and replace the 1 and 5 with 0s, giving us 700. We round 283 to 1 significant figure. The first digit is 2, and the next digit is 8, which is greater than or equal to 5, so we round 2 up to 3 and replace the 8 and 3 with 0s, giving us 300. Now we multiply the rounded numbers: 700 × 300 = 210000 .
Final Answer Therefore, the estimated answers are: a) 1600, b) 180000, and c) 210000.
Examples
Estimating calculations by rounding to one significant figure is useful in everyday situations. For example, when grocery shopping, you can quickly estimate the total cost of your items by rounding each price to the nearest dollar and then adding them up. This helps you stay within your budget without needing exact calculations on the go. Similarly, when planning a road trip, you can estimate the total distance by rounding each leg of the journey to the nearest hundred miles, giving you a rough idea of how far you'll travel.
The estimated answers by rounding to 1 significant figure are 1600 for 76 x 23, 180000 for 297 x 589, and 210000 for 715 x 283. Each original number is rounded to its nearest significant figure before multiplication. This method provides a quick way to estimate the result of large multiplications.
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