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3 (a) Write 4.5 × 10² as an ordinary number - Edexcel - GCSE Maths - Question 4 - 2021 - Paper 3

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3 (a) Write 4.5 × 10² as an ordinary number. (b) Write 0.007 in standard form. (c) Work out 4.2 × 10² + 5.3 × 10¹ Give your answer in standard form.

Worked Solution & Example Answer:3 (a) Write 4.5 × 10² as an ordinary number - Edexcel - GCSE Maths - Question 4 - 2021 - Paper 3

Step 1

(a) Write 4.5 × 10² as an ordinary number.

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Answer

To convert 4.5 × 10² into an ordinary number, we need to multiply 4.5 by 100 (which is 10210²). This gives us:

4.5×100=450.4.5 × 100 = 450.

Thus, 4.5 × 10² as an ordinary number is 450.

Step 2

(b) Write 0.007 in standard form.

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Answer

To express 0.007 in standard form, we recognize that it can be written as:

7×10−37 × 10^{-3}

This shows 0.007 in standard form as 7×10−37 × 10^{-3}.

Step 3

(c) Work out 4.2 × 10² + 5.3 × 10¹ Give your answer in standard form.

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Answer

To sum the two values, we first align them in standard form:

  1. Convert 5.3 × 10¹ into a comparable format by rewriting it as 0.53 × 10²:

    5.3×101=0.53×1025.3 × 10^{1} = 0.53 × 10^{2}

  2. Now we can add:

    4.2×102+0.53×102=(4.2+0.53)×102=4.73×1024.2 × 10² + 0.53 × 10² = (4.2 + 0.53) × 10² = 4.73 × 10²

Thus, in standard form, the result of the addition is 4.73×1024.73 × 10².

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