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Write these numbers in order, starting with the smallest - OCR - GCSE Maths - Question 16 - 2023 - Paper 3

Question 16

Write these numbers in order, starting with the smallest. 2.4 × 10² 1.3 × 10³ 4.9 × 10⁻¹ 9.5 × 10¹ (b) Work out. 5 × 10² + 4 × 10³ Give your answer in standard fo... show full transcript

Worked Solution & Example Answer:Write these numbers in order, starting with the smallest - OCR - GCSE Maths - Question 16 - 2023 - Paper 3

Step 1

Write these numbers in order, starting with the smallest.

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Answer

To compare the numbers in standard form, convert them to decimal form:

$2.4 \times 10^{2} = 240$
$1.3 \times 10^{3} = 1300$
$4.9 \times 10^{-1} = 0.49$
$9.5 \times 10^{1} = 95$

Now, ordering these from smallest to largest:

$4.9 \times 10^{-1}$ (0.49)
$9.5 \times 10^{1}$ (95)
$2.4 \times 10^{2}$ (240)
$1.3 \times 10^{3}$ (1300)

Thus, the order is:

4.9 × 10⁻¹, 9.5 × 10¹, 2.4 × 10², 1.3 × 10³

Step 2

Work out. 5 × 10² + 4 × 10³

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Answer

Convert both numbers to decimal form:

$5 \times 10^{2} = 500$
$4 \times 10^{3} = 4000$

Now, add them together:

$500 + 4000 = 4500$

To express this in standard form: $4500 = 4.5 \times 10^{3}$

Therefore, the answer is: 4.5 × 10³

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