Answer :
To determine whether Shaha's answer of 70.3 is reasonable for the calculation [tex]$218 \div 31$[/tex], let's use estimation and then verify with a calculator.
### Step 1: Estimate the Division
1. Round the Numbers:
- Round 218 to a nearby multiple of 10 for easier calculation. We'll round it to 210.
- Round 31 to a nearby multiple of 10. We'll round it to 30.
2. Perform the Estimated Division:
- Divide the rounded numbers: [tex]\( 210 \div 30 \)[/tex].
3. Calculate the Estimate:
- [tex]\( 210 \div 30 = 7 \)[/tex].
Based on our estimation, the approximate answer should be somewhere around 7.
### Step 2: Check with a Calculator
1. Actual Division:
- Use a calculator to find the actual result of [tex]\( 218 \div 31 \)[/tex].
2. Calculate:
- The calculator gives a result of approximately 7.032.
### Conclusion
- Comparison: The estimated result of 7 is very close to the actual calculated result of 7.032.
- Assessment: Shaha's calculator result of 70.3 is not reasonable given our estimation and the actual value. The correct answer is around 7, not 70.3.
This step-by-step process demonstrates how estimation can help verify the reasonableness of a calculator's result and shows that Shaha's initial result was incorrect.
### Step 1: Estimate the Division
1. Round the Numbers:
- Round 218 to a nearby multiple of 10 for easier calculation. We'll round it to 210.
- Round 31 to a nearby multiple of 10. We'll round it to 30.
2. Perform the Estimated Division:
- Divide the rounded numbers: [tex]\( 210 \div 30 \)[/tex].
3. Calculate the Estimate:
- [tex]\( 210 \div 30 = 7 \)[/tex].
Based on our estimation, the approximate answer should be somewhere around 7.
### Step 2: Check with a Calculator
1. Actual Division:
- Use a calculator to find the actual result of [tex]\( 218 \div 31 \)[/tex].
2. Calculate:
- The calculator gives a result of approximately 7.032.
### Conclusion
- Comparison: The estimated result of 7 is very close to the actual calculated result of 7.032.
- Assessment: Shaha's calculator result of 70.3 is not reasonable given our estimation and the actual value. The correct answer is around 7, not 70.3.
This step-by-step process demonstrates how estimation can help verify the reasonableness of a calculator's result and shows that Shaha's initial result was incorrect.
