By rounding to one significant figure, estimate the answers to these questions:
a) [tex]\frac{53 \times 17}{42}=142[/tex]
b) [tex]\frac{43 \times 19}{41}=\square[/tex]
Answer (2)
Round 43 to one significant figure: 40.
Round 19 to one significant figure: 20.
Round 41 to one significant figure: 40.
Calculate the estimated value: 40 40 × 20 = 20 . The estimated answer is 20 .
Explanation
Understanding the Problem We need to estimate the value of the expression 41 43 × 19 by rounding each number to one significant figure. This means we will round each number to the nearest multiple of 10.
Rounding 43 First, let's round 43 to one significant figure. Since the digit in the ones place (3) is less than 5, we round down to 40.
Rounding 19 Next, let's round 19 to one significant figure. Since the digit in the ones place (9) is greater than or equal to 5, we round up to 20.
Rounding 41 Now, let's round 41 to one significant figure. Since the digit in the ones place (1) is less than 5, we round down to 40.
Substituting Rounded Values Now we substitute the rounded values into the expression: 41 43 × 19 ≈ 40 40 × 20
Simplifying the Expression Finally, we simplify the expression and calculate the result: 40 40 × 20 = 40 800 = 20
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 or estimating travel time based on distance and speed. For example, if you are buying 4 items that cost $22, $18, $39, and $21, you can quickly estimate the total cost by rounding each amount to the nearest ten ($20, $20, $40, and $20) and adding them up: $20 + $20 + $40 + $20 = $100. This gives you a reasonable estimate of the total cost without needing exact calculations.
The estimated answer for part (a) is 25, and for part (b) it is 20, achieved by rounding the numbers to one significant figure before performing the calculations.
;
