Answer :
Sure! Let's go through each part of the question step by step.
### Part a:
Estimate the value of [tex]\(97.9 \times 17\)[/tex]
1. Round the numbers for estimation:
- [tex]\(97.9\)[/tex] rounds to [tex]\(100\)[/tex] (since [tex]\(97.9\)[/tex] is close to [tex]\(100\)[/tex])
- [tex]\(17\)[/tex] rounds to [tex]\(20\)[/tex] (as it is the nearest multiple of [tex]\(10\)[/tex])
2. Calculate the estimated value:
[tex]\[
100 \times 20 = 2000
\][/tex]
So, the estimated value of [tex]\(97.9 \times 17\)[/tex] is [tex]\(2000\)[/tex].
3. Compare with the actual calculation:
The actual value (given from the calculations) is approximately [tex]\(1664.3\)[/tex].
### Part b:
Estimate the value of [tex]\(100.7 \div 1.8\)[/tex]
1. Round the numbers for estimation:
- [tex]\(100.7\)[/tex] rounds to [tex]\(100\)[/tex] (since [tex]\(100.7\)[/tex] is close to [tex]\(100\)[/tex])
- [tex]\(1.8\)[/tex] rounds to [tex]\(2\)[/tex] (as it is the nearest whole number)
2. Calculate the estimated value:
[tex]\[
100 \div 2 = 50
\][/tex]
So, the estimated value of [tex]\(100.7 \div 1.8\)[/tex] is [tex]\(50\)[/tex].
3. Compare with the actual calculation:
The actual value (given from the calculations) is approximately [tex]\(55.94\)[/tex].
### Summary:
- The estimate for [tex]\(97.9 \times 17\)[/tex] is [tex]\(2000\)[/tex] (actual value: [tex]\(1664.3\)[/tex]).
- The estimate for [tex]\(100.7 \div 1.8\)[/tex] is [tex]\(50\)[/tex] (actual value: [tex]\(55.94\)[/tex]).
By rounding the numbers in each case, we simplify the arithmetic, making it easier to quickly estimate the result.
### Part a:
Estimate the value of [tex]\(97.9 \times 17\)[/tex]
1. Round the numbers for estimation:
- [tex]\(97.9\)[/tex] rounds to [tex]\(100\)[/tex] (since [tex]\(97.9\)[/tex] is close to [tex]\(100\)[/tex])
- [tex]\(17\)[/tex] rounds to [tex]\(20\)[/tex] (as it is the nearest multiple of [tex]\(10\)[/tex])
2. Calculate the estimated value:
[tex]\[
100 \times 20 = 2000
\][/tex]
So, the estimated value of [tex]\(97.9 \times 17\)[/tex] is [tex]\(2000\)[/tex].
3. Compare with the actual calculation:
The actual value (given from the calculations) is approximately [tex]\(1664.3\)[/tex].
### Part b:
Estimate the value of [tex]\(100.7 \div 1.8\)[/tex]
1. Round the numbers for estimation:
- [tex]\(100.7\)[/tex] rounds to [tex]\(100\)[/tex] (since [tex]\(100.7\)[/tex] is close to [tex]\(100\)[/tex])
- [tex]\(1.8\)[/tex] rounds to [tex]\(2\)[/tex] (as it is the nearest whole number)
2. Calculate the estimated value:
[tex]\[
100 \div 2 = 50
\][/tex]
So, the estimated value of [tex]\(100.7 \div 1.8\)[/tex] is [tex]\(50\)[/tex].
3. Compare with the actual calculation:
The actual value (given from the calculations) is approximately [tex]\(55.94\)[/tex].
### Summary:
- The estimate for [tex]\(97.9 \times 17\)[/tex] is [tex]\(2000\)[/tex] (actual value: [tex]\(1664.3\)[/tex]).
- The estimate for [tex]\(100.7 \div 1.8\)[/tex] is [tex]\(50\)[/tex] (actual value: [tex]\(55.94\)[/tex]).
By rounding the numbers in each case, we simplify the arithmetic, making it easier to quickly estimate the result.
