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Auralith Learning

Year 8 · Maths · Indices and standard form · Lesson 2

Standard form: large numbers

Write large numbers in standard form, convert back to ordinary numbers, order numbers in standard form and multiply them.

Whiteboard video lesson: Standard form: large numbers

28-minute video lesson

Teaching, worked examples and 20 practice questions solved step by step.

Watch free for a month

What your child will learn

  • Understand what standard form is
  • Write large numbers in standard form
  • Convert from standard form to ordinary numbers
  • Order numbers in standard form
  • Multiply and divide numbers in standard form

The method

  1. The first number must be at least 1 and less than 10.
  2. Count how many places the decimal point moves.
  3. Big number: positive power of 10.
  4. To convert back, move the point right that many places.

Key words: standard form, power of 10, index, ordinary number, place value.

Worked examples

The first three practice questions from the lesson, with every step.

Question 1

Write 7000 in standard form.

  1. Step 1: First number: 7
  2. Step 2: 7 to 7000: the point moves 3 places right
  3. Step 3: 7000 = 7 × 10³

Answer: 7 × 10³

Question 2

Write 52 000 in standard form.

  1. Step 1: First number: 5.2
  2. Step 2: 5.2 to 52 000: the point moves 4 places right
  3. Step 3: 52 000 = 5.2 × 10⁴

Answer: 5.2 × 10⁴

Question 3

Write 830 000 in standard form.

  1. Step 1: First number: 8.3
  2. Step 2: 8.3 to 830 000: the point moves 5 places right
  3. Step 3: 830 000 = 8.3 × 10⁵

Answer: 8.3 × 10⁵