IGCSE Mathematics | Practice Test | 25 Questions
Write down the general form of a number written in standard form.
State the two conditions that the value of $A$ must satisfy in standard form $A \times 10^n$.
What type of number must $n$ be in $A \times 10^n$?
Is $25 \times 10^3$ written in standard form? Give a reason for your answer.
Is $0.3 \times 10^7$ written in standard form? Give a reason for your answer.
Write 70 000 in standard form.
Write 0.008 in standard form.
Write $6 \times 10^5$ as an ordinary number.
Write $4 \times 10^{-3}$ as an ordinary number.
A number is written in standard form with a negative power of 10. Is this number greater than 1 or less than 1? Give a reason.
Write 840 000 in standard form.
Write 0.000056 in standard form.
Write $1.25 \times 10^4$ as an ordinary number.
Write $3.7 \times 10^{-5}$ as an ordinary number.
Calculate $(4 \times 10^3) \times (2 \times 10^5)$. Give your answer in standard form.
Calculate $(9 \times 10^8) \div (3 \times 10^4)$. Give your answer in standard form.
Calculate $(7 \times 10^4) + (3 \times 10^4)$. Give your answer in standard form.
Calculate $(5 \times 10^6) \times (4 \times 10^3)$. Give your answer in standard form.
Write the following numbers in order from smallest to largest.
$$2.7 \times 10^4 \qquad 8.1 \times 10^3 \qquad 5 \times 10^4 \qquad 1.4 \times 10^5$$
Which is the larger number: $5.1 \times 10^{-3}$ or $9.8 \times 10^{-4}$? Show your working and explain your reasoning.
(a) Write 4 700 000 in standard form.
(b) Write $8.05 \times 10^{-3}$ as an ordinary number.
(c) State which of your two answers is the larger number. Explain how you know.
(a) Calculate $(5 \times 10^4) \times (6 \times 10^3)$. Give your answer in standard form.
(b) Calculate $(9 \times 10^6) \div (3 \times 10^2)$. Give your answer in standard form.
(c) Add together your answers to (a) and (b). Give your answer in standard form.
The distance from the Earth to the Sun is approximately $1.5 \times 10^8$ km. Light travels at $3 \times 10^5$ km per second.
(a) Calculate how long it takes light to travel from the Sun to the Earth. Give your answer in standard form.
(b) Write your answer to (a) as an ordinary number.
(c) Convert your answer to (b) into minutes. Give your answer to the nearest minute.
A factory produces $2.4 \times 10^4$ items per day.
(a) Write $2.4 \times 10^4$ as an ordinary number.
(b) Calculate the total number of items produced in 5 days. Give your answer in standard form.
(c) Each item has a mass of $3 \times 10^{-2}$ kg. Calculate the total mass of all items produced in one day. Give your answer in standard form.
(a) Calculate $(7 \times 10^4) + (5 \times 10^3)$. Give your answer in standard form.
(b) Calculate $(8 \times 10^5) – (3 \times 10^4)$. Give your answer in standard form.
(c) Explain why adding or subtracting standard form numbers requires a different method compared to multiplying or dividing them.
