GCSE MATHS • HIGHER TIER

Converting Standard Form Made Simple

Convert very large and very small numbers into and out of standard form accurately.

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Converting Standard Form in Four Moves

1

Move the Decimal

Move the decimal point until the first number is between 1 and 10.

2

Circumference

Calculate the circumference of the full circle.

3

Choose the Power

Use a positive power for large numbers and a negative power for small numbers.

4

Check

Confirm that the first number satisfies 1 ≤ a < 10.

What You’ll Learn

Understand the structure a × 10ⁿ.

Convert large numbers into standard form.

Convert small numbers into standard form.

Convert standard form back into ordinary numbers.

Choose positive and negative powers correctly.

Check that the first number is between 1 and 10.

Key Rules

When writing a number in standard form, the first number must always be at least 1 but less than 10. If the first number is not between 1 and 10, the answer is not in standard form.

1 ≤ a < 10

Worked Proof: Converting Standard Form

Step-by-Step Method

  • 1. Decide whether you are converting
  • Move the decimal until the first number is between 1 and 10.
  • 3. Count how many places the decimal point moved.
  • 4. Choose the Correct Power
  • 5. If converting standard form back to an ordinary number:

More Worked Examples

1

Convert 45,000 into standard form.

Move the decimal point 4 places left.

45,000 = 4.5 × 10⁴
Answer : 4.5 × 10⁴

2

Convert 8,700,000 into standard form.

Move the decimal point 6 places left.

8.7 × 10⁶
Answer : 8.7 × 10⁶

3

Convert 0.005 into standard form.

Move the decimal point 3 places right.

5 × 10⁻³
Answer : 5 × 10⁻³

4

Convert 0.00042 into standard form.

Move the decimal point 4 places right.

4.2 × 10⁻⁴
Answer : 4.2 × 10⁻⁴
  • Common GCSE Mistakes
  • Using the wrong sign for the power of ten.
  • Forgetting that large numbers use positive powers.
  • Forgetting that small numbers use negative powers.
  • Writing a first number that is not between 1 and 10.
  • Exam Tips
  • Check whether the original number is large or smaller than 1.
  • Count decimal-place moves carefully.
  • Use positive powers when the decimal moves left to form a large-number conversion.
  • Use negative powers when the decimal moves right to form a small-number conversion.
  • Check that the first number is at least 1 but less than 10.
  • When converting back, use the sign of the power to choose the decimal direction.

Skills Used in Converting Standard Form

Standard Form

Powers of Ten

Positive Indices

Negative Indices

Decimal Place Value

Number Skills

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Exam-Style Questions

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Watch the Converting Standard Form Tutorial

Step-by-step walkthroughs of Converting Standard Form with clear methods and exam tips.

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Frequently Asked Questions

Standard form writes a number as a × 10ⁿ, where 1 ≤ a < 10 and n is an integer.

A positive power of ten is used when converting a large ordinary number into standard form.

A negative power of ten is used when converting a number smaller than 1 into standard form.

Move the decimal according to the power: right for positive powers and left for negative powers.

It must be greater than or equal to 1 and less than 10.

It makes extremely large and small numbers easier to read, compare and work with.