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Auralith Learning

Year 8 · Maths · Indices and standard form · Lesson 3

Standard form: small numbers

Write small numbers in standard form using negative powers of 10, convert back, order them, and calculate with them.

Whiteboard video lesson: Standard form: small 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 negative powers of 10
  • Write small numbers in standard form
  • Convert small numbers back 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. Number less than 1: negative power of 10.
  4. To convert back, move the point left that many places.

Key words: standard form, negative power, power of 10, decimal, place value.

Worked examples

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

Question 1

Write 0.04 in standard form.

  1. Step 1: First number: 4
  2. Step 2: 4 to 0.04: the point moves 2 places left
  3. Step 3: 0.04 = 4 × 10⁻²

Answer: 4 × 10⁻²

Question 2

Write 0.0062 in standard form.

  1. Step 1: First number: 6.2
  2. Step 2: 6.2 to 0.0062: the point moves 3 places left
  3. Step 3: 0.0062 = 6.2 × 10⁻³

Answer: 6.2 × 10⁻³

Question 3

Write 0.000315 in standard form.

  1. Step 1: First number: 3.15
  2. Step 2: 3.15 to 0.000315: the point moves 4 places left
  3. Step 3: 0.000315 = 3.15 × 10⁻⁴

Answer: 3.15 × 10⁻⁴