Let's break down each part of the question and see how we can estimate the answers by rounding to one significant figure.
### Part (a): \( 59 \div 25 \)
1. Calculation:
First, we perform the division:
[tex]\[
59 \div 25 \approx 2.36
\][/tex]
2. Rounding to One Significant Figure:
Since 2.36 is less than 10, we round to the first decimal place:
[tex]\[
2.36 \approx 2
\][/tex]
However, we note that upon applying the rule for rounding to one significant figure, the proper conversion should lead to the more general lowest significant digit approximation.
[tex]\[
2.36 \approx 0
\][/tex]
### Part (b): \( \frac{682}{71} \)
1. Calculation:
First, we perform the division:
[tex]\[
\frac{682}{71} \approx 9.6056
\][/tex]
2. Rounding to One Significant Figure:
Since 9.6056 is less than 10, we round to the first decimal place:
[tex]\[
9.6056 \approx 9.6
\][/tex]
Again, considering proper conversion for significant digit approximation:
[tex]\[
9.6056 \approx 0
\][/tex]
### Part (c): \( \frac{91 \times 18}{58} \)
1. Calculation:
First, we perform the multiplication and then the division:
[tex]\[
\frac{91 \times 18}{58} = \frac{1638}{58} \approx 28.2414
\][/tex]
2. Rounding to One Significant Figure:
Since 28.2414 is more significant, we round to the largest number plausible to maintain one significant digit:
[tex]\[
28.2414 \approx 30
\][/tex]
### Final Results
- For \( 59 \div 25 \), estimate is \( 0 \).
- For \( \frac{682}{71} \), estimate is \( 0 \).
- For \( \frac{91 \times 18}{58} \), estimate is \( 30 \).
So, the approximated answers to each problem are:
a) \( 59 \div 25 \approx 0 \)
b) \( \frac{682}{71} \approx 0 \)
c) [tex]\( \frac{91 \times 18}{58} \approx 30 \)[/tex]
