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§ Algebra

Scientific Notation

CCSS.8.EE3 min read

Scientific notation transforms unwieldy numbers like 93,000,000 miles (Earth to Sun) into the elegant 9.3 × 10⁷. Year 8 students often struggle with this GCSE foundation skill, particularly when moving decimal points and determining positive versus negative exponents.

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§ 01

Why it matters

Scientific notation becomes essential across GCSE sciences and beyond. In physics, students encounter Planck's constant (6.63 × 10⁻³⁴ J·s) and the speed of light (3.0 × 10⁸ m/s). Chemistry requires expressing Avogadro's number (6.02 × 10²³) and atomic masses. Biology uses scientific notation for cell sizes (typical bacteria: 2 × 10⁻⁶ m) and population genetics. Computing students work with data storage—a terabyte equals 10¹² bytes. Without scientific notation, calculations involving very large or small quantities become unmanageable. Students who master this skill find A-level maths, physics, and chemistry significantly more accessible, as scientific calculators display results in this format by default for extreme values.

§ 02

How to solve scientific notation

Scientific Notation

  • Write as c × 10n where 1 ≤ c < 10.
  • Count decimal places moved = exponent.
  • Right = negative exponent, left = positive.

Example: 45000 = 4.5 × 10⁴.

§ 03

Worked examples

Beginner§ 01

Write 300 in scientific notation.

Answer: 3 × 102

  1. Move the decimal point → 300 = 3 × 10^2 — Move decimal 2 places left to get 3.
Easy§ 02

Write 660000 in scientific notation.

Answer: 6.6 × 105

  1. Find coefficient (1 ≤ c < 10) → 660000 = 6.6 × 10^5 — Coefficient is 6.6, exponent is 5.
Medium§ 03

(6 × 105) × (5 × 101) = _______

Answer: 3 × 107

  1. Multiply coefficients, add exponents → 6 × 5 = 30, 10^5 × 10^1 = 10^6 — Coefficients multiply normally, exponents add.
  2. Normalize → 3 × 10^7 — Adjust so coefficient is between 1 and 10.
§ 04

Common mistakes

  • Students write 4500 as 45 × 10² instead of 4.5 × 10³, forgetting the coefficient must be between 1 and 10.
  • When converting 0.0032, students often write 32 × 10⁻⁴ rather than 3.2 × 10⁻³, miscounting decimal places moved.
  • Multiplying (2 × 10³) × (3 × 10²), students calculate 6 × 10⁶ instead of 6 × 10⁵, incorrectly multiplying exponents rather than adding them.
  • Converting large numbers like 850,000, students write 8.5 × 10⁴ instead of 8.5 × 10⁵, moving the decimal point the wrong number of places.
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§ 05

Frequently asked questions

How do I know whether the exponent is positive or negative?
If the original number is greater than 10, the exponent is positive. If it's between 0 and 1, the exponent is negative. For 45,000, you get 4.5 × 10⁴ (positive). For 0.045, you get 4.5 × 10⁻² (negative).
What's the quickest way to count decimal places?
Count how many positions the decimal point moves to create a coefficient between 1 and 10. For 67,000, the decimal moves 4 places left (6.7000 → 6.7), giving 6.7 × 10⁴. Always double-check your coefficient falls between 1 and 10.
How do I multiply numbers in scientific notation?
Multiply the coefficients normally, then add the exponents. For (3 × 10²) × (4 × 10⁵), calculate 3 × 4 = 12 and 10² × 10⁵ = 10⁷. This gives 12 × 10⁷, which normalizes to 1.2 × 10⁸.
Why does my calculator show 2.5E+04?
This is calculator notation for scientific notation. The 'E' means '× 10^', so 2.5E+04 equals 2.5 × 10⁴ or 25,000. Negative exponents appear as 2.5E-04 for 2.5 × 10⁻⁴ or 0.00025.
When should students start using scientific notation?
Introduce scientific notation in Year 8 as part of the National Curriculum. Students typically encounter it first in science lessons with very large or small measurements, then develop fluency through maths lessons before applying it extensively in GCSE sciences.
§ 06

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