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Standard Form: O-Level / IGCSE Maths (0580)

Syllabus C1.8, E1.8 · Strand 1 Number

Questions
4
Total marks
16
Tier mix
2 Core · 2 Extended

Standard form (also called scientific notation) writes a number as

a×10n,1≤a<10, n∈Z.a \times 10^{n}, \qquad 1 \le a < 10,\ n \in \mathbb{Z}.

It is the compact way to handle very large or very small quantities: the kind that turn up constantly in science and finance questions on the 0580 paper. The skill has three parts: writing a number in standard form, converting back to an ordinary number, and calculating (multiplying, dividing, adding) with values already in standard form using the index laws.

The worked questions below are original and written from the syllabus objective, not taken from any past paper. When you want exam-condition practice, use Cambridge’s own official past papers, linked at the bottom of the page.

Question 1

Structured Core 3 marks

A single grain of a particular variety of rice has a mass of about 0.000021 kg0.000021\ \text{kg}. A small sack holds 30 00030\,000 of these grains.

(a) Write 0.0000210.000021 in standard form. [1]

(b) Work out the total mass of rice in the sack. Give your answer in standard form. [2]

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Question 2

Structured Extended 6 marks

A space probe travels in a straight line from a relay station to a distant asteroid.

The distance between the relay station and the asteroid is 7.2×10117.2 \times 10^{11} metres.

The probe travels at a constant speed of 1.6×1041.6 \times 10^{4} metres per second.

(a) Calculate the time taken, in seconds, for the probe to travel from the relay station to the asteroid.

Give your answer in standard form. [2]

(b) A radio signal travels at a speed of 3.0×1083.0 \times 10^{8} metres per second.

Calculate the time taken, in seconds, for a radio signal to travel the same distance of 7.2×10117.2 \times 10^{11} metres.

Give your answer in standard form. [2]

(c) Find how many times longer the probe takes to make the journey than the radio signal.

Give your answer in standard form. [2]

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Question 3

Multiple choice Extended 1 mark

A laboratory sample contains 6×1056 \times 10^{5} identical microscopic beads. Each bead has a mass of 8×10−98 \times 10^{-9} grams.

Work out the total mass of all the beads in the sample, giving your answer in standard form.

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Question 4

Structured Core 6 marks

The distance from a space probe to a distant moon is 5 040 000 km5\,040\,000\text{ km}.

(a) Write 5 040 0005\,040\,000 in standard form. [1]

(b) The width of a grain of pollen is 3.7×10−4 m3.7 \times 10^{-4}\text{ m}. Write this number as an ordinary (decimal) number. [1]

(c) Work out (6×108)×(1.5×10−3)(6 \times 10^{8}) \times (1.5 \times 10^{-3}). Give your answer in standard form. [2]

(d) Write down which is larger, 8×1058 \times 10^{5} or 2×1062 \times 10^{6}, and explain your answer. [2]

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