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1 (a) Write these numbers in standard form - OCR - GCSE Maths - Question 1 - 2020 - Paper 1

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1 (a) Write these numbers in standard form. (i) 6500 (ii) 0.0584 (b) Work out (4.2 × 10^5) × (1.8 × 10^-2), giving your answer in standard form.

Worked Solution & Example Answer:1 (a) Write these numbers in standard form - OCR - GCSE Maths - Question 1 - 2020 - Paper 1

Step 1

(i) 6500

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Answer

To express 6500 in standard form, we identify it as follows:

  1. Move the decimal point to the left until only one non-zero digit remains before it:
    • 6.5
  2. Count the number of places moved (3 places) and apply the exponent:
    • Thus, 6500 can be written as 6.5×1036.5 \times 10^3.

Step 2

(ii) 0.0584

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Answer

To express 0.0584 in standard form, we perform the following steps:

  1. Move the decimal point to the right until only one non-zero digit is left:
    • 5.84
  2. Count the number of places moved (2 places) which will be negative since we are moving right:
    • Therefore, 0.0584 can be expressed as 5.84×10−25.84 \times 10^{-2}.

Step 3

(b) Work out (4.2 × 10^5) × (1.8 × 10^-2)

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Answer

To solve this multiplication in standard form, follow these steps:

  1. Multiply the coefficients: 4.2×1.8=7.564.2 \times 1.8 = 7.56.
  2. Add the exponents of the powers of ten:
    • 105×10−2=105+(−2)=10310^5 \times 10^{-2} = 10^{5 + (-2)} = 10^{3}.
  3. Combine the results to express the answer in standard form:
    • The final answer is 7.56×1037.56 \times 10^3.

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