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7 (a) Write the number 0.00008623 in standard form - Edexcel - GCSE Maths - Question 8 - 2018 - Paper 2

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7 (a) Write the number 0.00008623 in standard form. (b) Work out \[ \frac{3.2 \times 10^1 + 5.1 \times 10^{-2}}{4.3 \times 10^{10}} \] Give your answer in standar... show full transcript

Worked Solution & Example Answer:7 (a) Write the number 0.00008623 in standard form - Edexcel - GCSE Maths - Question 8 - 2018 - Paper 2

Step 1

Write the number 0.00008623 in standard form.

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Answer

To express the number 0.00008623 in standard form, we shift the decimal point to the right until we have a number between 1 and 10.

This yields:

[ 8.623 \times 10^{-5} ]

Thus, the answer is ( 8.623 \times 10^{-5} ).

Step 2

Work out \( \frac{3.2 \times 10^{1} + 5.1 \times 10^{-2}}{4.3 \times 10^{10}} \)

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Answer

First, we need to add the two terms in the numerator:

[ 3.2 \times 10^1 = 32 \quad \text{and} \quad 5.1 \times 10^{-2} = 0.051 ]

Adding these gives:

[ 32 + 0.051 = 32.051 ]

Next, we divide by the denominator:

[ \frac{32.051}{4.3 \times 10^{10}} \approx \frac{32.051}{43000000000} \approx 7.44 \times 10^{-10} ]

So, the answer in standard form, correct to 3 significant figures, is ( 7.44 \times 10^{-10} ).

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