Year 10 - Maths
Multiplying numbers in standard form
Standard form calculations
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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 will learn how to add, subtract, multiply and divide numbers written in standard form.
Lesson Summary
You will learn to appreciate the mathematical structures that underpin multiplication of numbers represented in standard form.
Key Notes
- The commutative law allows the product of two numbers represented in standard form to be easily calculated.
- Using your knowledge of the index laws, you can combine powers with the same base.
- Standard form calculations can be done using a calculator.
Vocabulary To Learn
- Standard form: Standard form is when a number is written in the form A × 10n, (where 1 ≤ A < 10 and n is an integer).
- Exponential form: When a number is multiplied by itself multiple times, it can be written more simply in exponential form.
- Commutative: The commutative law states you can write the values of a calculation in a different order without changing the calculation; the result is still the same. It applies in addition and multiplication.
- Associative: The associative law states that it doesn't matter how you group or pair values (i.e. which we calculate first), the result is still the same. It applies for addition and multiplication.
Common Mistakes To Avoid
- When multiplying terms with coefficients, pupils also add the coefficients as well as the exponents.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
The commutative law allows the product of two numbers represented in standard form to be easily calculated. Using your knowledge of the index laws, you can combine powers with the same base.
2. Use this key word in a maths sentence and explain it clearly. 'Standard form'
Standard form is when a number is written in the form A × 10n, (where 1 ≤ A < 10 and n is an integer). Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: When multiplying terms with coefficients, pupils also add the coefficients as well as the exponents. Correction: Pupils should be encouraged to rewrite their expression using the associative and commutative laws, with the number parts grouped and powers grouped. This hopefully avoids this error as they can see it is the product of the numbers.
More Lessons In This Unit
- Adding numbers in standard form Study Guide
- Checking and securing understanding of writing large numbers in standard form Study Guide
- Checking and securing understanding of writing small numbers in standard form Study Guide
- Dividing numbers in standard form Study Guide
- Problem solving with standard form calculations Study Guide
- Subtracting numbers in standard form Study Guide
Browse all guides in the Year 10 Maths guide library.