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By rounding to 1 significant figure, estimate the answers to these questions:
a) $\quad 426 \times 894$
b) $657 \times 889$
c) $287 \times 494$
Answer (2)
Round each number to 1 significant figure.
Multiply the rounded numbers to estimate the answer.
a) 426 × 894 ≈ 400 × 900 = 360000
b) 657 × 889 ≈ 700 × 900 = 630000
c) 287 × 494 ≈ 300 × 500 = 150000
360000 , 630000 , 150000
Explanation
Problem Analysis We are asked to estimate the answers to the given multiplication problems by rounding each number to 1 significant figure. Let's start with problem a) 426 × 894 .
Estimating a) First, we round 426 to 1 significant figure. The first significant figure is 4, and the next digit is 2, which is less than 5, so we round down to 400. Next, we round 894 to 1 significant figure. The first significant figure is 8, and the next digit is 9, which is greater than or equal to 5, so we round up to 900. Now we multiply the rounded numbers: 400 × 900 = 360000 .
Estimating b) Now let's move on to problem b) 657 × 889 . First, we round 657 to 1 significant figure. The first significant figure is 6, and the next digit is 5, which is equal to 5, so we round up to 700. Next, we round 889 to 1 significant figure. The first significant figure is 8, and the next digit is 8, which is greater than or equal to 5, so we round up to 900. Now we multiply the rounded numbers: 700 × 900 = 630000 .
Estimating c) Finally, let's solve problem c) 287 × 494 . First, we round 287 to 1 significant figure. The first significant figure is 2, and the next digit is 8, which is greater than or equal to 5, so we round up to 300. Next, we round 494 to 1 significant figure. The first significant figure is 4, and the next digit is 9, which is greater than or equal to 5, so we round up to 500. Now we multiply the rounded numbers: 300 × 500 = 150000 .
Final Answer Therefore, the estimated answers are: a) 426 × 894 ≈ 360000 b) 657 × 889 ≈ 630000 c) 287 × 494 ≈ 150000
Examples
Estimating calculations by rounding to one significant figure is useful in everyday situations. For instance, 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. 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 the overall travel distance.
By rounding each number to one significant figure, we estimate:
a) 426 × 894 ≈ 360000 ,
b) 657 × 889 ≈ 630000 ,
c) 287 × 494 ≈ 150000 .
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