Browse Standard form

53 questions at your level

DifficultyAllLevel 1Level 2Level 3Level 4Level 5

Writing numbers in standard form

14 questions

LessonNot started
Write 30003000 in standard form.
●●●●●Level 11 markStart
Write 5.6×1025.6 \times 10^2 as an ordinary number.
●●●●●Level 11 markStart
6.4×10−36.4 \times 10^{-3} written as an ordinary number is

Circle your answer.
  • A 0.00640.0064
  • B 0.0640.064
  • C 640640
  • D 64006400
●●●●●Level 11 markStart
8.6×1038.6 \times 10^3 written as an ordinary number is

Circle your answer.
  • A 860860
  • B 86008600
  • C 86 00086\,000
  • D 0.00860.0086
●●●●●Level 11 markStart
(a) Write 45 000 000 in standard form.

(b) Write 0.00062 in standard form.

(c) Write 3.08×1053.08 \times 10^5 as an ordinary number.
●●●●●Level 33 marksStart
Write these numbers in order of size, starting with the smallest:

9.8×1031.2×1054.5×1042.1×1039.8 \times 10^3 \qquad 1.2 \times 10^5 \qquad 4.5 \times 10^4 \qquad 2.1 \times 10^3
●●●●●Level 32 marksStart
(a) Write 7 200 0007\,200\,000 in standard form.

(b) Write 0.0000580.000058 in standard form.
●●●●●Level 32 marksStart
(a) Write 6.04×10−36.04 \times 10^{-3} as an ordinary number.

(b) Write 2.5×1042.5 \times 10^4 as an ordinary number.
●●●●●Level 32 marksStart
Write 45×10645 \times 10^6 in standard form.
●●●●●Level 41 markStart
(a) Write 0.00306 in standard form.

(b) Explain why 30.6×10−430.6 \times 10^{-4} is not standard form, even though it equals 0.00306.
●●●●●Level 42 marksStart
p=8×105p = 8 \times 10^5. Write 2p2p in standard form.
●●●●●Level 42 marksStart
Write 0.35×1050.35 \times 10^5 in standard form.
●●●●●Level 42 marksStart
Write these numbers in order of size, starting with the smallest.

3.4×10−25.1×10−32.9×10−28×10−33.4 \times 10^{-2} \qquad 5.1 \times 10^{-3} \qquad 2.9 \times 10^{-2} \qquad 8 \times 10^{-3}
●●●●●Level 42 marksStart
q=3.6×107q = 3.6 \times 10^7

Write q9\dfrac{q}{9} in standard form.
●●●●●Level 42 marksStart

Calculating in standard form

20 questions

LessonNot started
Work out (2×103)×(4×102)(2 \times 10^3) \times (4 \times 10^2). Give your answer in standard form.
●●●●●Level 12 marksStart
Work out (6×104)÷(2×102)(6 \times 10^4) \div (2 \times 10^2). Give your answer in standard form.
●●●●●Level 12 marksStart
Work out (3×102)+(5×102)(3 \times 10^2) + (5 \times 10^2). Give your answer in standard form.
●●●●●Level 11 markStart
Work out (4×105)×(5×103)(4 \times 10^5) \times (5 \times 10^3). Give your answer in standard form.
●●●●●Level 22 marksStart
(a) Work out (3×104)×(5×10−2)(3 \times 10^4) \times (5 \times 10^{-2}) Give your answer in standard form. (2 marks)

(b) Work out (8×105)÷(2×102)(8 \times 10^5) \div (2 \times 10^2) Give your answer in standard form. (1 mark)
●●●●●Level 23 marksStart
(a) Work out (2.4×106)×(3×10−2)(2.4 \times 10^6) \times (3 \times 10^{-2}). Give your answer in standard form. [2]

(b) Work out (9×108)÷(1.5×103)(9 \times 10^8) \div (1.5 \times 10^3). Give your answer in standard form. [2]
●●●●●Level 24 marksStart
(a) Work out (4×105)×(6×10−2)(4 \times 10^5) \times (6 \times 10^{-2}). Give your answer in standard form. [2]

(b) Work out (3.6×107)÷(9×102)(3.6 \times 10^7) \div (9 \times 10^2). Give your answer in standard form. [2]
●●●●●Level 24 marksStart
Work out (3×104)×(2×105)(3 \times 10^4) \times (2 \times 10^5). Give your answer in standard form.
●●●●●Level 32 marksStart
Work out (2×103)×(4×106)(2 \times 10^3) \times (4 \times 10^6). Give your answer in standard form.
●●●●●Level 32 marksStart
(a) Work out (4.8×105)÷(1.2×10−2)(4.8 \times 10^5) \div (1.2 \times 10^{-2})

Give your answer in standard form. (2 marks)
(b) Work out (3×104)+(4×103)(3 \times 10^4) + (4 \times 10^3)

Give your answer in standard form. (1 mark)
●●●●●Level 33 marksStart
Work out 4.6×105+7.9×1034.6 \times 10^{5} + 7.9 \times 10^{3}

Give your answer in standard form.

(3 marks)
●●●●●Level 33 marksStart
Work out (4×105)×(5×103)(4 \times 10^5) \times (5 \times 10^3). Give your answer in standard form.
●●●●●Level 43 marksStart
Work out 8×1073.2×102\dfrac{8 \times 10^7}{3.2 \times 10^2}. Give your answer in standard form.
●●●●●Level 43 marksStart
Work out (3.4×105)+(2.7×104)(3.4 \times 10^5) + (2.7 \times 10^4). Give your answer in standard form.
●●●●●Level 43 marksStart
Work out 6×1081.5×10−3\dfrac{6 \times 10^8}{1.5 \times 10^{-3}}. Give your answer in standard form.
●●●●●Level 43 marksStart
Work out (6×104)×(7×105)(6 \times 10^4) \times (7 \times 10^5). Give your answer in standard form.
●●●●●Level 42 marksStart
Work out 9×1083×10−2\dfrac{9 \times 10^8}{3 \times 10^{-2}}. Give your answer in standard form.
●●●●●Level 42 marksStart
Work out (5.6×106)−(8×105)(5.6 \times 10^6) - (8 \times 10^5). Give your answer in standard form.
●●●●●Level 42 marksStart
M=ABM = \frac{A}{B}

A=7.26×105A = 7.26 \times 10^{5} correct to 33 significant figures.

B=4.8×102B = 4.8 \times 10^{2} correct to 22 significant figures.

Work out the upper bound for MM.

Give your answer as an ordinary number correct to the nearest integer.

You must show all your working.

(3 marks)
●●●●●Level 43 marksStart
(a) Work out (3×10−4)2(3 \times 10^{-4})^2. Give your answer in standard form.

(b) Work out (2.5×103)2(2.5 \times 10^3)^2. Give your answer in standard form.
●●●●●Level 53 marksStart

Standard form in context

19 questions

LessonNot started
The population of a city is 2.4×1062.4 \times 10^6. Write this as an ordinary number.
●●●●●Level 11 markStart
A grain of sand has mass 0.00040.0004 g. Write this mass in standard form.
●●●●●Level 11 markStart
Which is larger, 3.2×1043.2 \times 10^4 or 9.8×1039.8 \times 10^3? Explain how you know.
●●●●●Level 11 markStart
Write these in order of size, smallest first: 5×1032×1048×102\quad 5 \times 10^3 \qquad 2 \times 10^4 \qquad 8 \times 10^2
●●●●●Level 11 markStart
The distance from the Earth to the Moon is about 3.8×1053.8 \times 10^5 km. A rocket travels this distance in 44 days. How far does it travel each day, on average? Give your answer in standard form.
●●●●●Level 22 marksStart
A computer does 2×1092 \times 10^9 calculations per second. How many does it do in 3030 seconds? Give your answer in standard form.
●●●●●Level 22 marksStart
A country has a population of 6.8×1076.8 \times 10^7 and an area of 2.4×1052.4 \times 10^5 km2^2.

Work out the population density, in people per km2^2. Give your answer to the nearest whole number. (2 marks)
●●●●●Level 22 marksStart
Light travels at 3×1083 \times 10^8 metres per second.

The distance from the Sun to the Earth is 1.5×10111.5 \times 10^{11} metres.

Work out how long light takes to travel from the Sun to the Earth.

Give your answer in minutes, correct to the nearest minute. (3 marks)
●●●●●Level 23 marksStart
The mass of a hydrogen atom is 1.67×10−271.67 \times 10^{-27} kg.

(a) Work out the number of hydrogen atoms in 11 gram of hydrogen. Give your answer in standard form correct to 3 significant figures. [3]

(b) Write your answer to part (a) correct to 1 significant figure. [1]
●●●●●Level 34 marksStart
Light travels at 3×1083 \times 10^8 metres per second. Work out how far light travels in 5 minutes. Give your answer in metres, in standard form.
●●●●●Level 43 marksStart
The mass of the Earth is 5.97×10245.97 \times 10^{24} kg. The mass of the Moon is 7.35×10227.35 \times 10^{22} kg.

How many times greater is the mass of the Earth than the mass of the Moon? Give your answer to 1 decimal place.
●●●●●Level 43 marksStart
A country has a population of 6.8×1076.8 \times 10^7 people and an area of 2.4×1052.4 \times 10^5 km².

Work out the number of people per km². Give your answer to 3 significant figures.
●●●●●Level 43 marksStart
Sound travels at 3.4×1023.4 \times 10^2 metres per second.

Work out how far sound travels in 2×1032 \times 10^3 seconds. Give your answer in standard form.
●●●●●Level 42 marksStart
A=8×109A = 8 \times 10^9 and B=4×105B = 4 \times 10^5

How many times bigger is AA than BB? Give your answer in standard form.
●●●●●Level 42 marksStart
One bacterium has a mass of 9.5×10−139.5 \times 10^{-13} grams.

A colony contains 5×1085 \times 10^8 bacteria.

Work out the total mass of the colony. Give your answer in grams, in standard form.
●●●●●Level 43 marksStart
A grain of sand has a mass of 3.5×10−43.5 \times 10^{-4} grams. Work out the total mass of 2×1062 \times 10^6 grains of sand. Give your answer in kilograms, in standard form.
●●●●●Level 53 marksStart
A red blood cell has a diameter of 7×10−67 \times 10^{-6} m. A line of red blood cells, placed edge to edge, is 1.4 km long.

Work out the number of cells in the line. Give your answer in standard form.
●●●●●Level 53 marksStart
A country's national debt is £2.4×10122.4 \times 10^{12}.

The country's population is 6×1076 \times 10^7 people.

Work out the debt per person. Give your answer in standard form.
●●●●●Level 53 marksStart
A sheet of paper is 8×10−58 \times 10^{-5} m thick.

How many sheets make a pile exactly 22 m tall? Give your answer in standard form.
●●●●●Level 53 marksStart