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Standard form practice questions with answers

Foundation and Higher · Grade 5

A second set of standard form questions for GCSE Maths. They are different from the ones on the topic page, so work through both. Try each question, then open the answer to check your working.

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Question 1 Easy

Work out (5×10^3)×(2×10^2). Give your answer in standard form.

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Answer: 1×10^6

  1. Multiply fronts: 5 × 2 = 10, powers: 3 + 2 = 5.
  2. Adjust to standard form: 10 × 10^5 = 1×10^6.
  • Method (1): Multiply fronts: 5 × 2 = 10, powers: 3 + 2 = 5.
  • Accuracy (1): Adjust to standard form: 10 × 10^5 = 1×10^6.

Question 2 Easy

Work out (3×10^6)×(3×10^2). Give your answer in standard form.

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Answer: 9×10^8

  1. Multiply fronts: 3 × 3 = 9.
  2. Add powers: 6 + 2 = 8, giving 9×10^8.
  • Method (1): Multiply fronts: 3 × 3 = 9.
  • Accuracy (1): Add powers: 6 + 2 = 8, giving 9×10^8.

Question 3 Medium

Work out (6×10^5)÷(2×10^3). Give your answer in standard form.

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Answer: 3×10^2

  1. Divide fronts: 6 / 2 = 3.
  2. Subtract powers: 5 - 3 = 2, giving 3×10^2.
  • Method (1): Divide fronts: 6 / 2 = 3.
  • Accuracy (1): Subtract powers: 5 - 3 = 2, giving 3×10^2.

Question 4 Medium

Work out (4×10^3)+(2×10^3). Give your answer in standard form.

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Answer: 6×10^3

  1. Powers match (10^3), so add fronts: 4 + 2 = 6.
  2. Keep power: 6×10^3.
  • Method (1): Powers match (10^3), so add fronts: 4 + 2 = 6.
  • Accuracy (1): Keep power: 6×10^3.

Question 5 Hard

Write 600 in standard form.

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Answer: 6×10^2

  1. Place decimal: 6.
  2. Count moves: 2 places right, so 6×10^2.
  • Method (1): Place decimal: 6.
  • Accuracy (1): Count moves: 2 places right, so 6×10^2.

Question 6 Hard

Work out (6×10^4)+(3×10^4). Give your answer in standard form.

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Answer: 9×10^4

  1. Powers match (10^4), so add fronts: 6 + 3 = 9.
  2. Keep power: 9×10^4.
  • Method (1): Powers match (10^4), so add fronts: 6 + 3 = 9.
  • Accuracy (1): Keep power: 9×10^4.

Exam-style question

A longer question with marks, in the style of a written paper. This is a Yumio practice question, not a past paper question.

Exam-style question 11 marks

Write 480000 in standard form.

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Answer: 4.8×10^5

  1. Identify front number: 4.8.
  2. Count places decimal moved: 5 places to the left.
  3. Write power of 10: 10^5, giving 4.8×10^5.
  • Mark (1): 4.8×10^5

Quick checks

Short one-step questions. Pick an option before you open the answer.

Check 1

How do you multiply two numbers in standard form?

  1. Multiply fronts and add powers
  2. Add fronts and multiply powers
  3. Multiply fronts and multiply powers
Show answer

Multiply fronts and add powers Multiply front numbers and add the index powers of 10.

Check 2

What is (3×10^4)×(2×10^3)?

  1. 6×10^7
  2. 5×10^7
  3. 6×10^12
Show answer

6×10^7 3×2 = 6 and 4+3 = 7, so 6×10^7.

Check 3

What is (2×10^5)×(4×10^1)?

  1. 8×10^6
  2. 8×10^5
  3. 6×10^6
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8×10^6 2×4 = 8 and 5+1 = 6, so 8×10^6.

Check 4

How do you divide two numbers in standard form?

  1. Divide fronts and subtract powers
  2. Subtract fronts and divide powers
  3. Divide fronts and add powers
Show answer

Divide fronts and subtract powers Divide front numbers and subtract index powers of 10.

Check 5

What is (8×10^6)÷(2×10^2)?

  1. 4×10^4
  2. 4×10^8
  3. 6×10^4
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4×10^4 8÷2 = 4 and 6−2 = 4, so 4×10^4.

Check 6

What is (6×10^5)÷(2×10^3)?

  1. 3×10^2
  2. 3×10^8
  3. 4×10^2
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3×10^2 6÷2 = 3 and 5−3 = 2, so 3×10^2.

Check 7

When can you add standard form numbers directly by adding front numbers?

  1. When the powers of 10 match
  2. Whenever fronts are integers
  3. When powers are consecutive
Show answer

When the powers of 10 match You can factorise out the power of 10 only when powers match.

Check 8

What is (4×10^3)+(2×10^3)?

  1. 6×10^3
  2. 6×10^6
  3. 8×10^3
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6×10^3 Same power, so (4+2)×10^3 = 6×10^3.

Check 9

What is (6×10^4)+(3×10^4)?

  1. 9×10^4
  2. 9×10^8
  3. 18×10^4
Show answer

9×10^4 Same power, so (6+3)×10^4 = 9×10^4.

Check 10

What is 3400 written in standard form?

  1. 3.4×10^3
  2. 34×10^2
  3. 3.4×10^4
Show answer

3.4×10^3 3.4 × 1000 = 3.4 × 10^3.

Check 11

What is 25000 written in standard form?

  1. 2.5×10^4
  2. 25×10^3
  3. 2.5×10^5
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2.5×10^4 2.5 × 10000 = 2.5 × 10^4.

Check 12

What is 600 written in standard form?

  1. 6×10^2
  2. 60×10^1
  3. 6×10^3
Show answer

6×10^2 6 × 100 = 6 × 10^2.

Check 13

In standard form A × 10^n, what range must A be in?

  1. 1 ≤ A < 10
  2. 0 < A < 10
  3. 1 ≤ A ≤ 10
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1 ≤ A < 10 A must have exactly one non-zero digit before the decimal point.

Check 14

How is 12 × 10^5 adjusted to proper standard form?

  1. 1.2×10^6
  2. 1.2×10^4
  3. 120×10^4
Show answer

1.2×10^6 12 = 1.2 × 10, so 1.2 × 10 × 10^5 = 1.2 × 10^6.

Check 15

Why is 34 × 10^2 not in standard form?

  1. 34 is not less than 10
  2. Power 2 is too small
  3. Multiplication sign is missing
Show answer

34 is not less than 10 The front number must be strictly less than 10.

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