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By rounding to one significant figure, estimate the answers to these questions:
a) $\frac{634}{3 \times 17}=$ $\square$
b) $\frac{827}{4 \times 18}=$ $\square$
Answer (2)
Round 634 to 600, 3 remains 3, and 17 rounds to 20, then calculate 3 × 20 600 = 60 600 = 10 .
Round 827 to 800, 4 remains 4, and 18 rounds to 20, then calculate 4 × 20 800 = 80 800 = 10 .
The estimated answer for a) is 10.
The estimated answer for b) is 10. Therefore, the answers are 10 .
Explanation
Problem Analysis We need to estimate the answers to the given expressions by rounding each number to one significant figure.
Rounding for Expression a) First, let's round the numbers in expression a) to one significant figure:
634 rounded to one significant figure is 600.
3 remains as 3 since it is already a single digit.
17 rounded to one significant figure is 20.
Substitution Now, let's substitute these rounded values into the expression: 3 × 17 634 ≈ 3 × 20 600
Calculating the Denominator Next, we calculate the denominator: 3 × 20 = 60
Calculating the Estimated Value of a) Now, we can calculate the estimated value of expression a): 60 600 = 10
Rounding for Expression b) Now, let's round the numbers in expression b) to one significant figure:
827 rounded to one significant figure is 800.
4 remains as 4 since it is already a single digit.
18 rounded to one significant figure is 20.
Substitution Now, let's substitute these rounded values into the expression: 4 × 18 827 ≈ 4 × 20 800
Calculating the Denominator Next, we calculate the denominator: 4 × 20 = 80
Calculating the Estimated Value of b) Now, we can calculate the estimated value of expression b): 80 800 = 10
Final Answer Therefore, the estimated answer for expression a) is 10, and the estimated answer for expression b) is 10.
Examples
Estimating calculations by rounding to one significant figure is useful in everyday situations, such as quickly calculating the approximate cost of multiple items at a store. For instance, if you're buying 3 items priced at $17, $634, and $827, you can quickly estimate the total cost by rounding to one significant figure: $20 + $600 + $800 = $1420. This provides a reasonable estimate without needing precise calculations.
By rounding to one significant figure, the estimated answer for expression a) is 10, and the estimated answer for expression b) is also 10.
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