Photo AI
Nina estimates the value of \( rac{\sqrt{3.93 \times 393^3}}{0.546 \times 220}\) by rounding each number to 1 significant figure - OCR - GCSE Maths - Question 4 - 2020 - Paper 6
Question 4
Nina estimates the value of \( rac{\sqrt{3.93 \times 393^3}}{0.546 \times 220}\) by rounding each number to 1 significant figure. (a) Show that Nina’s answer is 64... show full transcript
Worked Solution & Example Answer:Nina estimates the value of \( rac{\sqrt{3.93 \times 393^3}}{0.546 \times 220}\) by rounding each number to 1 significant figure - OCR - GCSE Maths - Question 4 - 2020 - Paper 6
Step 1
(a) Show that Nina’s answer is 64.
Answer
To estimate the expression, we need to round each number to 1 significant figure:
- Round 3.93 to 4
- Round 393 to 400
- Round 0.546 to 0.5
- Round 220 to 200
Now substituting these rounded values:
[ \frac{\sqrt{4 \times (400)^3}}{0.5 \times 200} = \frac{\sqrt{4 \times 64000000}}{100} = \frac{\sqrt{256000000}}{100} = \frac{16000}{100} = 160 ]
The estimated value for Nina’s calculation is:
[ \frac{160}{100} = 64 ]
Thus, Nina’s answer is confirmed to be 64.
Step 2
(b) Calculate the error in her estimated answer as a percentage of the exact answer.
Answer
To compute the error, we need to determine the exact value of the expression without rounding:
-
Calculate the exact value:
- Exact value = ( \frac{\sqrt{3.93 \times 393^3}}{0.546 \times 220} )
-
Compute the estimated value:
- Estimated Value = 64
-
Error Calculation:
- Error = Exact Value - Estimated Value
- Percentage Error = ( \frac{\text{Error}}{\text{Exact Value}} \times 100 %
-
Substitute the values to find the percentage error.
The final result will give the percentage error of the estimation compared to the exact value.