Home / iGCSE Mathematics (0580) – C1.8 Standard form- Exam Style Questions Paper 1

iGCSE Mathematics (0580) - C1.8 Standard form- Exam Style Questions Paper 1- New Syllabus

Question

Write \(1.753 \times 10^{8}\) as an ordinary number.

Most-appropriate topic codes (Cambridge IGCSE Mathematics 0580):

TOPIC C1.8 Standard form: Convert numbers into and out of standard form \(A \times 10^n\) where \(n\) is a positive or negative integer and \(1 \leqslant A < 10\) (Core)
▶️ Answer/Explanation
Multiplying by \(10^8\) moves the decimal point 8 places to the right.
\(1.753\) becomes \(175{,}300{,}000\) (insert zeros as needed after the significant figures).
\[1.753 \times 10^8 = 175\,300\,000\]
Answer: \(175\,300\,000\)

Question

Sam writes \(851\,000\) in standard form as \(85.1 \times 10^4\).
Explain why \(85.1 \times 10^4\) is not a number in standard form.

Most-appropriate topic codes (Cambridge IGCSE Mathematics 0580):

Topic C1.8 Standard form: Use the standard form \(A \times 10^n\) where \(n\) is a positive or negative integer, and \(1 \le A < 10\) (Core)
▶️ Answer/Explanation

Standard form requires a number to be written as \(A \times 10^n\), where the value of \(A\) must be between \(1\) and \(10\) (specifically \(1 \le A < 10\)).
In Sam’s answer, the number \(85.1\) is greater than \(10\), so it violates the rule for standard form.
Answer: In standard form, the value \(A\) is written as \(A \times 10^n\) where \(1 \le A < 10\), and \(85.1\) is greater than \(10\).

Question

The table shows the population and area of three countries in 2020.

(a) Calculate the difference in population between Nigeria and Vietnam.

(b) Which of Comoros or Vietnam has the greater population density? Show your working. 
[Population density = \(\frac{population}{area(km^{2})}\)]

▶️ Answer/Explanation
Solution

Ans (a): 1.087 × 10⁸ or 108,700,000

Difference = Nigeria population (2.06×10⁸) – Vietnam population (9.73×10⁷) = 1.087×10⁸

Ans (b): Comoros

Comoros density = 8.70×10⁵ ÷ 1.86×10³ ≈ 468/km²

Vietnam density = 9.73×10⁷ ÷ 3.10×10⁵ ≈ 314/km²

Comoros has higher population density.

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