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#305

Using standard form with positive indices

Number · Grade 4–6

Strand: Number Substrand: Standard form Sparx code: U330 Sparx levels: 1, 2, 3, 4, 5

Key steps (method)

  • Write the number in the form a × 10^n where 1 ≤ a < 10.
  • Move the decimal point so the leading number is between 1 and 10.
  • Count how many places the decimal moved: left → positive power, right → negative power.
  • For calculations, multiply/divide the a parts and add/subtract the powers of 10.
  • Convert back to an ordinary number only at the end if asked.

Common mistakes

  • Using an a value not between 1 and 10 (e.g. 54 × 10^3).
  • Getting the sign of the power wrong (moving decimal left vs right).
  • Mixing up adding powers (×) with subtracting powers (÷).
  • Rounding too early when asked for a specific number of significant figures.

Quick notes

  • If you get stuck, try a simpler version of the problem first or plug in easy numbers to test your method.
  • For multi-step questions, label each step and keep intermediate results.
  • For exam questions, always aim to make your work “mark-scheme readable”.

Self-assessment

  • Can I define it? Write a one-sentence definition of Using standard form with positive indices (or the key term in the question).
  • Can I do it? Do 3 questions: one easy, one standard, one harder. Don’t look at notes until you’ve tried.
  • Can I explain it? In 2–3 sentences, explain why the method works (or what would go wrong with a common mistake).
  • Can I check it? State one quick check (estimate, units, sign, reasonableness).

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Notes