Scientific notation

Writing very large and very small numbers as a × 10ⁿ.

Indices & Logarithms · O/L Maths

Level 1: What is standard form?

Read and write a × 10ⁿ (1 ≤ a < 10)

Standard form (scientific notation) writes very large or small numbers compactly: a × 10ⁿ.

The number a must always be between 1 and 10 (1 ≤ a < 10), and n is a whole number.

• 6.2 × 10³
• 10³ = 1000
• 6.2 × 1000 = 6200

Level 2: Writing large numbers

Write large numbers as a × 10ⁿ

Move the decimal point left to get a between 1 and 10. The number of places moved is n.

• 45 000
• Put the point after the 4: 4.5000 (moved 4 places)
• 45 000 = 4.5 × 10⁴

Level 3: Writing small numbers

Write small numbers as a × 10⁻ⁿ

For numbers smaller than 1, move the point right; the index is negative.

0.0045 = 4.5 × 10⁻³

• 0.00032
• Move the point right to just after the 3: 4 places
• 0.00032 = 3.2 × 10⁻⁴

Level 4: Calculating in standard form

Multiply, divide and add

Multiplying: multiply the numbers and add the powers of 10. Dividing: divide the numbers and subtract the powers of 10.

At the end, if a is not between 1 and 10, rewrite the answer in standard form.

• (4 × 10³) × (5 × 10²)
• Multiply the numbers: 4 × 5 = 20; add the powers: 10⁵
• 20 × 10⁵
• 20 = 2 × 10, so the answer is 2 × 10⁶