lesson
Separate scale from significant digits
1 · Learn
Standard form writes a positive number as A × 10ⁿ with 1 <= A < 10 and integer n. The coefficient carries the significant digits; the power gives the scale. Very small positive numbers use negative exponents.
Check both conditions. 42 × 10³ represents a number but is not in standard form until rewritten with a coefficient between 1 and 10.
2 · Worked example
0.00072 = 7.2 × 10⁻⁴. Moving from 7.2 to the small value requires division by 10,000.
3 · Your turn
Write 560,000 and 0.0034 in standard form.
Check your answer
5.6 × 10⁵ and 3.4 × 10⁻³.
4 · Apply your learning
Convert in both directions and use an estimate to detect an exponent with the wrong sign.
Adult guidance and safety
Ask for the reasoning and a check, not only a numerical result. Supply accurate diagrams, coordinate grids and data displays where required. Use varied examples and revisit prerequisite gaps; these short teaching models are not a completed assessment programme.
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Check a calculation · Year 5 onward
Use this only when your teacher or adult allows a calculator for the task. Show your thinking first. It does not replace mental or written arithmetic and does not mark your lesson answer.
Powers, roots and trigonometry · Year 7 onward
Use only when the task allows a calculator. Choose one operation at a time and record your working. Trigonometry here always uses degrees (DEG), not radians. Inverse sine, cosine and tangent return an angle, not a reciprocal. Keep exact fractions and π in answers when requested.
Approximate numerical results use up to 12 significant digits. Inverse sine returns −90° to 90°, inverse cosine 0° to 180°, and inverse tangent −90° to 90°; these are principal values, not every possible solution of a trigonometric equation.
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