GCSE OCR Maths Indices: Nina estimates the value of \( \

Nina estimates the value of $ \sqrt{\frac{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

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Nina estimates the value of $ \sqrt{\frac{3.93 \times 393^3}{0.546 \times 220}} $ by rounding each number to 1 significant figure. (a) Show that Nina’s answer is ... show full transcript

Worked Solution & Example Answer:Nina estimates the value of $ \sqrt{\frac{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.

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Answer

To find Nina's estimated value, round each number in the expression to 1 significant figure:

Round 3.93 to 4
Round 393 to 400
Round 0.546 to 0.5
Round 220 to 200

Substituting the rounded values into the expression gives:

\sqrt{\frac{4 \times 400^3}{0.5 \times 200}}

Calculating the numerator:

4 \times 400^3 = 4 \times 64000000 = 256000000

Calculating the denominator:

0.5 \times 200 = 100

Now, substituting these values in:

\sqrt{\frac{256000000}{100}} = \sqrt{2560000} = 64

Thus, Nina’s estimated answer is indeed 64.

Step 2

(b) Calculate the error in her estimated answer as a percentage of the exact answer.

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Answer

To calculate the error in Nina's estimated answer, we first need the exact answer. We can evaluate the original expression:

\frac{3.93 \times 393^3}{0.546 \times 220}

Calculating the exact values:

Numerator: 3.93 \times 393^3 = 3.93 \times 61,865,097.897
Denominator: 0.546 \times 220 = 120.12

Now, divide the numerator by the denominator and find the square root:

Exact answer = $\sqrt{\frac{3.93 \times 61,865,097.897}{120.12}}$
Calculate the exact answer and denote it as $E$ .
Error = $|64 - E|$
Percentage error = ( \frac{|64 - E|}{E} \times 100 )%.

Insert the calculated exact answer to find the precise percentage error.

Nina estimates the value of \( \sqrt{\frac{3.93 \times 393^3}{0.546 \times 220}} \) by rounding each number to 1 significant figure - OCR - GCSE Maths - Question 4 - 2020 - Paper 6

Worked Solution & Example Answer:Nina estimates the value of \( \sqrt{\frac{3.93 \times 393^3}{0.546 \times 220}} \) by rounding each number to 1 significant figure - OCR - GCSE Maths - Question 4 - 2020 - Paper 6

(a) Show that Nina’s answer is 64.

(b) Calculate the error in her estimated answer as a percentage of the exact answer.

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