Year 9 - Maths
Writing small numbers in standard form
Standard form
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This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
Unit Summary
In this unit pupils learn to recognise, interpret and write in standard form. Pupils then extend this knowledge so that they can order numbers written in standard form.
Lesson Summary
You will learn to write very small numbers in the form A × 10^n, (where 1 ≤ A < 10) and appreciate the real-life contexts where this format is usefully used.
Key Notes
- It is difficult to read very small numbers, due to the number of digits involved.
- It can be more efficient to write these very small numbers in standard form.
- There is a convention for standard form.
Vocabulary To Learn
- Exponential form: When a number is multiplied by itself multiple times, it can be written more simply in exponential form.
- Associative law: The associative law states that a repeated application of the operation produces the same result regardless of how pairs of values are grouped. We can group using brackets.
- Standard form: Standard form is when a number is written in the form A × 10^n, (where 1 ≤ A < 10 and n is an integer).
Common Mistakes To Avoid
- Pupils can incorrectly write a number in standard form or use a number in incorrect standard form whereby the number A does not satisfy 1 ≤ A < 10 or pupils use division of positive powers of 10.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
It is difficult to read very small numbers, due to the number of digits involved. It can be more efficient to write these very small numbers in standard form.
2. Use this key word in a maths sentence and explain it clearly. 'Exponential form'
When a number is multiplied by itself multiple times, it can be written more simply in exponential form. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Pupils can incorrectly write a number in standard form or use a number in incorrect standard form whereby the number A does not satisfy 1 ≤ A < 10 or pupils use division of positive powers of 10. Correction: Standard form represents a multiplicative relationship, so there should always be a multiplication. Embedding the understanding that negative exponents refer to 1/10^n is important. Using the place value chart with fractional and exponent form helps.
More Lessons In This Unit
- Checking and further securing understanding of the commutative law Study Guide
- Checking and securing understanding of multiples of 10 Study Guide
- Multiples of 10 involving negative exponents Study Guide
- Ordering numbers in standard form Study Guide
- Problem solving with standard form Study Guide
- Writing large numbers in standard form Study Guide
Browse all guides in the Year 9 Maths guide library.