1.11 Standard form
9 exam questions worth 15 marks. Write your answer, open the mark scheme, then give yourself the marks you earned. Your answers are saved on this device.
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What is 5 600 000 in standard form?
Choose one answer.
Correct Not quite: the answer is \( 5.6 \times 10^6 \)
Mark scheme
C: 5.6 \times 10^6
Model answer
5.6 \times 10^6 (C). Move the decimal point 6 places left to get 5.6.
Write 0.000 34 in standard form.
Mark scheme
B1: 3.4 × 10⁻⁴
Model answer
3.4 × 10⁻⁴.
Write these as ordinary numbers. (a) 4.7 \times 10^3 (b) 6.1 \times 10^{-2}
Mark scheme
B1: 4700; B1: 0.061
Model answer
(a) 4700 (b) 0.061.
Write 640 \times 10^4 in standard form.
Mark scheme
B1: 6.4; B1: × 10⁶
Model answer
640 = 6.4 × 10², so 640 × 10⁴ = 6.4 × 10⁶.
Write these numbers in order, smallest first. 3.2 \times 10^4 4.5 \times 10^3 2.9 \times 10^4 8 \times 10^{-1}
Mark scheme
M1: compares powers of 10; A1: 8 × 10⁻¹, 4.5 × 10³, 2.9 × 10⁴, 3.2 × 10⁴
Model answer
Smallest first: 8 × 10⁻¹, 4.5 × 10³, 2.9 × 10⁴, 3.2 × 10⁴.
The distance from the Earth to the Sun is 150 000 000 km. Write this distance in standard form.
Mark scheme
B1: 1.5 × 10⁸
Model answer
1.5 × 10⁸ km.
Explain why 45 \times 10^5 is not in standard form, and write it in standard form.
Mark scheme
B1: 45 is not between 1 and 10; B1: 4.5 × 10⁶
Model answer
In standard form the first number must be at least 1 and less than 10, but 45 is bigger than 10. 45 × 10⁵ = 4.5 × 10 × 10⁵ = 4.5 × 10⁶.
Which of these numbers is the greatest?
Choose one answer.
Correct Not quite: the answer is \( 4.1 \times 10^{-2} \)
Mark scheme
B: 4.1 \times 10^{-2}
Model answer
4.1 \times 10^{-2} (B). The largest power of 10 is -2, so 4.1 × 10⁻² = 0.041 is the greatest.
The width of a human hair is 0.000 07 m. The width of a red blood cell is 7 \times 10^{-6} m. (a) Write 0.000 07 in standard form. (b) Which is wider and how many times wider is it?
Mark scheme
B1: 7 × 10⁻⁵; B1: the hair is wider (10⁻⁵ > 10⁻⁶); B1: 10 times wider
Model answer
(a) 7 × 10⁻⁵. (b) The hair is wider, because 10⁻⁵ is bigger than 10⁻⁶. 7 × 10⁻⁵ ÷ 7 × 10⁻⁶ = 10, so the hair is 10 times wider.
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