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MathidiaMathematics Academy
Number fluency, bounds and accuracy
Lesson 4 of 75
Challenge

Standard form operations

Objective. Calculate with standard form and normalise answers correctly.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

Standard form writes numbers as a × 10ⁿ where 1 ≤ a < 10, and this topic covers multiplying, dividing and adding numbers given in that form. To multiply, multiply the coefficients and add the powers of 10; to divide, divide the coefficients and subtract the powers. For example, (3 × 10⁴) × (2 × 10³) = 6 × 10⁷. After the calculation, the coefficient must be renormalised to lie between 1 and 10, adjusting the power accordingly if it is not. Addition and subtraction require converting both numbers to the same power of 10 first.

Worked example

Calculate (5 × 10⁶) × (6 × 10⁻²), giving your answer in standard form.

Array of 5 rows by 10 columns
  1. 1Multiply coefficients: 5 × 6 = 30.
  2. 2Add the powers of 10: 6 + (−2) = 4.
  3. 3This gives 30 × 10⁴, which is not in standard form.
  4. 4Renormalise: 30 × 10⁴ = 3 × 10⁵.

Answer: 3 × 10⁵

Concept mastery

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Practice

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Common mistake. Pupils leave an answer like 48 × 10⁶ instead of converting it to proper standard form 4.8 × 10⁷. Always check the coefficient is between 1 and 10 and adjust the power if needed.

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