Standard Form

Topic

Edexcel

AQA

Foundation June 2025 Paper 1 Q23

EdexcelCurrent spec3 marksStandard Form

23 Work out \(5.7 \times 10^2 + 9.8 \times 10^3\)
Give your answer in standard form. (3)

Mark scheme

Answer	Mark	Mark scheme
\(1.037 \times 10^4\)	M1	for 570 or 9800 or \(0.57 \times 10^3\) or \(98 \times 10^2\)
	A1	for 10370 oe eg \(10.37 \times 10^3\) or \(103.7 \times 10^2\)
	A1	for \(1.037 \times 10^4\)

Higher June 2025 Paper 3 Q9

EdexcelCurrent spec2 marksStandard Form

(a) Write \(5.73 \times 10^6\) as an ordinary number. (1)

(b) Write 0.035 in standard form. (1)

Answer	Mark	Mark scheme
5 730 000	B1	cao

Answer	Mark	Mark scheme
\(3.5 \times 10^{-2}\)	B1	cao

Higher June 2025 Paper 1 Q5

EdexcelCurrent spec3 marksStandard Form

5 Work out \(5.7 \times 10^2 + 9.8 \times 10^3\)
Give your answer in standard form. (3)

Mark scheme

Answer	Mark	Mark scheme
\(1.037 \times 10^4\)	M1	for 570 or 9800 or \(0.57 \times 10^3\) or \(98 \times 10^2\)
	A1	for 10370 oe eg \(10.37 \times 10^3\) or \(103.7 \times 10^2\)
	A1	for \(1.037 \times 10^4\)

Foundation November 2024 Paper 2 Q27

EdexcelCurrent spec2 marksStandard Form

27 \(1.25 \times 10^{-12} = k \times (4 \times 10^{-20})\)

Work out the value of \(k\).
Give your answer in standard form. (2)

Mark scheme

Answer	Mark	Mark scheme
\(3.125 \times 10^7\)	M1	for \((k =)\ (1.25 \times 10^{-12}) \div (4 \times 10^{-20})\) or for the digits 3125
\(3.125 \times 10^7\)	A1	cao

Additional guidance

Condone missing brackets on division
\(3.1 \times 10^7\) or \(3.12 \times 10^7\) or \(3.13 \times 10^7\) will score M1A0

Foundation November 2024 Paper 3 Q18

EdexcelCurrent spec2 marksStandard Form

(a) Write \(3.402 \times 10^5\) as an ordinary number. (1)

(b) Write 0.8026 in standard form. (1)

Answer	Mark	Mark scheme
340 200	B1	cao

Answer	Mark	Mark scheme
\(8.026 \times 10^{-1}\)	B1	cao

Higher November 2024 Paper 2 Q8

EdexcelCurrent spec2 marksStandard Form

8 \(1.25 \times 10^{-12} = k \times (4 \times 10^{-20})\)

Work out the value of \(k\).
Give your answer in standard form. (2)

Mark scheme

Answer	Mark	Mark scheme
\(3.125 \times 10^7\)	M1	for \((k =)\ (1.25 \times 10^{-12}) \div (4 \times 10^{-20})\) or for the digits 3125
\(3.125 \times 10^7\)	A1	cao

Additional guidance

Can condone missing brackets on division
\(3.1 \times 10^7\) or \(3.12 \times 10^7\) or \(3.13 \times 10^7\) will score M1A0

Higher November 2024 Paper 3 Q2

EdexcelCurrent spec2 marksStandard Form

(a) Write \(3.402 \times 10^5\) as an ordinary number. (1)

(b) Write 0.8026 in standard form. (1)

Answer	Mark	Mark scheme
340 200	B1	cao

Answer	Mark	Mark scheme
\(8.026 \times 10^{-1}\)	B1	cao

Foundation June 2023 Paper 3 Q28

EdexcelCurrent spec4 marksStandard Form

(a) Write \(\quad (9 \times 10^4) : (4.5 \times 10^6) \quad\) in the form \(1 : n\) where \(n\) is an integer. (2)

(b) Write the following numbers in order of size.
Start with the smallest number.\[5.625 \times 10^4 \qquad 5625 \qquad 56\,250 \times 10^{-3} \qquad 0.005\,625 \times 10^5\] (2)

Mark scheme (a)

Answer	Mark	Mark scheme
1 : 50	M1	for an equivalent ratio eg 9 : 450 or \(9 : 4.5 \times 10^2\) or 90000 : 4500000 oe or for \(4500000 \div 90000\) or \(\dfrac{4500000}{90000}\ (=50)\)
1 : 50	A1	For 1 : 50, accept \(n = 50\)

Mark scheme (b)

Answer	Mark	Mark scheme
\(56250 \times 10^{-3}\) \(0.005625 \times 10^5\) 5625 \(5.625 \times 10^4\)	M1	for writing numbers correctly in a common format eg 56250, 56.25, 562.5 or a correct list with one error or correct list but in reverse order
	A1	for correct list

Additional guidance

Count an omission as one error.

Accept alternative indications of the correct order.

Foundation November 2022 Paper 3 Q29

EdexcelCurrent spec3 marksStandard Form

(a) Write \(\;6.75 \times 10^{-4}\;\) as an ordinary number. (1)

(b) Work out \(\quad \dfrac{2.56 \times 10^{6} \times 4.12 \times 10^{-3}}{1.6 \times 10^{-2}}\)
Give your answer in standard form. (2)

Answer	Mark	Mark scheme
0.000675	B1	cao

Mark scheme (b)

Answer	Mark	Mark scheme
\(6.592 \times 10^5\)	M1	for \(10.5472 \times 10^3\) oe or \(1.6 \times 10^8\) oe or \(2.575 \times 10^{-1}\) oe or for \(6.592 \times 10^n\) where \(n \neq 5\) or for \(6.59 \times 10^5\) or for \(6.6 \times 10^5\) or for 659200 oe
\(6.592 \times 10^5\)	A1	cao

Additional guidance

If the answer (for 2 marks) is seen in working and then rounded or truncated, award full marks.

Foundation June 2022 Paper 1 Q26

EdexcelCurrent spec4 marksStandard Form

(a) Write \(1.63 \times 10^{-3}\) as an ordinary number. (1)

(b) Write 438 000 in standard form. (1)

Answer	Mark	Mark scheme
0.00163	B1	cao

Answer	Mark	Mark scheme
\(4.38 \times 10^5\)	B1	cao

Answer	Mark	Mark scheme
\(2.4 \times 10^{-1}\)	M1	for \(4 \times 6 \times 10^{3-5}\) or 0.24 oe eg \(24 \times 10^{-2}\) or \(2.4 \times 10^{n}\) where \(n \neq -1\)
A1	cao

Foundation November 2021 Paper 3 Q23

EdexcelCurrent spec4 marksStandard Form

(a) Write \(4.5 \times 10^5\) as an ordinary number. (1)

(b) Write 0.007 in standard form. (1)

Answer	Mark	Mark scheme
450 000	B1	cao

Answer	Mark	Mark scheme
\(7 \times 10^{-3}\)	B1	cao

Answer	Mark	Mark scheme
\(4.73 \times 10^3\)	M1	for 4730 oe or for \(4.73 \times 10^n\) where \(n \ne 3\)
A1	cao

Foundation June 2025 Paper 1 Q20

AQACurrent spec4 marksStandard Form

(a) Work out \(\quad 0.6 \div 100\)

Give your answer in standard form. [2 marks]

(b) Work out \(\quad 40 \times 30 \times 10^5\)

Give your answer in standard form. [2 marks]

Mark scheme (a)

Answer	Mark	Comments
\(6 \times 10^{-3}\)	B2	condone extra zeros which do not affect the value eg \(6.0 \times 10^{-3}\) B1 correct value not in standard form (allow value written as \(a \times 10^n\)) eg 0.006 or \(0.6 \times 10^{-2}\) or given calculation with 0.6 written as \(6 \times 10^{-1}\) eg \(6 \times 10^{-1} \div 100\) or value whose only non-zero digit is 6 correctly converted to standard form answer eg \(0.0006 = 6 \times 10^{-4}\)

Additional guidance

\(6 \times 10^{-1} \div 10^2\)

Mark scheme (b)

Answer	Mark	Comments
\(1.2 \times 10^8\)	B2	condone extra zeros which do not affect the value eg \(1.20 \times 10^8\) B1 120 000 000 or 120 million or \(12 \times 10^7\) or \(120 \times 10^6\) or \(1.2 \times 10^a \times 10^b\) where \(a + b = 8\) or value whose only non-zero digits are 12 correctly converted to standard form answer eg \(12\,000\,000 = 1.2 \times 10^7\)

Foundation June 2024 Paper 2 Q20

AQACurrent spec3 marksPercentages Standard Form

20 The mass of an iceberg is 2 200 000 kg

This value is a 12% reduction from the original mass of the iceberg.

Work out the original mass of the iceberg.

Give your answer in standard form. [3 marks]

Mark scheme

Answer	Mark	Comments
88(%) or 0.88	M1	oe eg \(1 - 0.12\)
\(2\,200\,000 \div 88\) (\(\times\) 100) or 25 000 (\(\times\) 100)	M1dep	oe eg \(2.2 \times 10^6 \div (100 - 12)\) (\(\times\) 100) or \(2\,200\,000 \times [1.136, 1.14]\) or 2 500 000
\(2.5 \times 10^6\)	A1	oe standard form eg \(2.500\,000 \times 10^6\) SC1 \(2.2 \times 10^6\) oe standard form seen SC1 any value seen converted to standard form

Additional guidance

M1 or SC1 may be awarded for correct work with no answer or incorrect answer, even if this is seen amongst multiple attempts
M1 may be seen in a trial or incorrect working eg \(3\,000\,000 \times 0.88\) or 88% of 2 200 000	M1
\(2\,200\,000 \div 88\%\) not recovered	M1M0
\(2\,200\,000 \times 1.12 = 2\,464\,000\) \(2.464 \times 10^6 = 2.5 \times 10^6\)	SC1

Foundation November 2023 Paper 1 Q29

AQACurrent spec3 marksRatio & Basic Proportion Standard Form

(a) Write \(\quad 2 \times 10^3 \quad\) as an ordinary number. [1 mark]

(b) Simplify \(\quad (2 \times 10^3) : (5 \times 10^{-1})\)

Give your answer in the form \(\quad n : 1\) [2 marks]

Answer	Mark	Comments
2000	B1

Mark scheme (b)

Answer	Mark	Comments
0.5 or \(\dfrac{2 \times 10^3}{5 \times 10^{-1}}\) or \(\dfrac{\text{their } 2000}{5 \times 10^{-1}}\) or \(0.4 \times 10^{3 - (-1)}\) or \(0.4 \times 10^4\)	M1	oe their 2000 from part (a)
4000 or \(4 \times 10^3\)	A1ft	ft \(2 \times\) their 2000 in part (a)

Foundation June 2017 Paper 2 Q27

AQACurrent spec2 marksStandard Form

27 Write these numbers in descending order.

\[9563 \qquad\qquad 9.56 \times 10^3 \qquad\qquad 9.56 \times 3^{10}\]

[2 marks]

Mark scheme

Answer	Mark	Comments
\(9.56 \times 3^{10} \quad 9563 \quad 9.56 \times 10^3\) or 564 508 (.44) \(\quad\) 9563 \(\quad\) 9560 with no incorrect evaluations seen	B2	B1 \(9.563 \times 10^3\) or 9560 or 564 508 (.44) or \(5.6(450844) \times 10^5\) SC1 \(9.56 \times 10^3 \quad 9563 \quad 9.56 \times 3^{10}\) with no incorrect evaluations seen

Additional guidance

Allow numbers to be written in original or converted form or as a mixture for B2 or SC1

Incorrect evaluation seen scores a maximum of B1

Foundation June 2017 Paper 1 Q18

AQACurrent spec2 marksStandard Form

18 Write the number six million five thousand two hundred in standard form. [2 marks]

Mark scheme

Answer	Mark	Comments
\(6.005\,2(00) \times 10^6\)	B2	B1 for their 6 005 200 written normally and correctly converted to standard form or no number written normally and answer \(6.(\ldots) \times 10^6\)

Additional guidance

(6 500 200 and) \(6.500\,2(00) \times 10^6\)	B1
65 200 and \(6.52 \times 10^4\)	B1
\(10^6 \times 6.005\,2(00)\)	B2
Correct value of 6 005 200 with no conversion to standard form	B0
\(6 \times 10^6\) with no number written normally	B1

Higher June 2017 Paper 1 Q13

AQACurrent spec2 marksStandard Form

13 Write the number \(\quad\) six million five thousand two hundred \(\quad\) in standard form. [2 marks]

Mark scheme

Answer	Mark	Comments
\(6.005\,2(00) \times 10^6\)	B2	B1 for their 6 005 200 written normally and correctly converted to standard form or no number written normally and answer \(6.(\ldots) \times 10^6\)

Additional guidance

(6 500 200 and) \(6.500\,2(00) \times 10^6\)	B1
65 200 and \(6.52 \times 10^4\)	B1
\(10^6 \times 6.005\,2(00)\)	B2
Correct value of 6 005 200 with no conversion to standard form	B0
\(6 \times 10^6\) with no number written normally	B1

Higher June 2017 Paper 2 Q11

AQACurrent spec2 marksStandard Form

11 Write these numbers in descending order.

\[9563 \qquad\qquad 9.56 \times 10^3 \qquad\qquad 9.56 \times 3^{10}\]

[2 marks]

Mark scheme

Answer	Mark	Comments
\(9.56 \times 3^{10} \quad 9563 \quad 9.56 \times 10^3\) or 564 508 (.44) \(\quad\) 9563 \(\quad\) 9560 with no incorrect evaluations seen	B2	B1 \(9.563 \times 10^3\) or 9560 or 564 508 (.44) or \(5.6(450844) \times 10^5\) SC1 \(9.56 \times 10^3 \quad 9563 \quad 9.56 \times 3^{10}\) with no incorrect evaluations seen

Additional guidance

Allow numbers to be written in original or converted form or as a mixture for B2 or SC1

Incorrect evaluation seen scores a maximum of B1

Higher June 2017 Paper 3 Q2

AQACurrent spec1 markStandard Form

2 Which of these values of \(n\) makes \(\;2.7 \times 10^n\;\) a cube number?

Circle your answer. [1 mark]