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13 (a) Write 0.00316 in standard form - OCR - GCSE Maths - Question 13 - 2018 - Paper 2

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13 (a) Write 0.00316 in standard form. (b) Work out. 2 × 10² × 4 × 10⁵ Give your answer in standard form.

Worked Solution & Example Answer:13 (a) Write 0.00316 in standard form - OCR - GCSE Maths - Question 13 - 2018 - Paper 2

Step 1

(a) Write 0.00316 in standard form.

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Answer

To convert 0.00316 into standard form, we first move the decimal point three places to the right, which gives us 3.16. Since we moved the decimal point three places to the right, we multiply by 10 raised to the power of -3. Therefore, the answer in standard form is:

3.16×10−33.16 \times 10^{-3}

Step 2

(b) Work out. 2 × 10² × 4 × 10⁵ Give your answer in standard form.

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Answer

To solve the expression, we first multiply the coefficients (2 and 4):

2×4=82 \times 4 = 8

Next, we apply the laws of exponents to combine the powers of 10:

102×105=10(2+5)=10710^2 \times 10^5 = 10^{(2 + 5)} = 10^7

Now, combining the coefficient and the power of ten gives us:

8×1078 \times 10^7

Thus, the answer in standard form is:

8×1078 \times 10^7

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