O Level MathematicsC1.8 Standard form ($A \times 10^n$, conversion and calculation).

🚀 Mastering Standard Form: Tiny to Colossal Numbers Made Easy!

Edudent Academy
3 Dec 25

Ever struggled to write very large or incredibly small numbers neatly? Standard form, also called scientific notation, is the mathematician’s **power-tool** for expressing such numbers quickly and accurately—vital in exams, science experiments and everyday calculations.

What Is Standard Form?

A number is in **standard form** when it is written as A×10nA \times 10^n, where **1≤A<101 \le A < 10** and **nn is an integer**. This compact style makes comparisons, multiplications, and divisions far simpler, especially on a non-calculator paper.

  • Shift the decimal to make the first digit non-zero (1–9).
  • Count the places moved: left gives positive nn, right gives negative nn.

Worked Example: Converting & Calculating

Problem: Write 0.0004560.000456 in standard form and then multiply it by 3.2×1033.2 \times 10^3.

  • Step 1: Convert 0.0004560.000456 →
    0.000456=4.56×10−40.000456 = 4.56 \times 10^{-4}
  • Step 2: Multiply: (4.56×10−4)(3.2×103)=14.592×10−1(4.56 \times 10^{-4}) (3.2 \times 10^3) = 14.592 \times 10^{-1}
  • Step 3: Adjust to standard form:
    14.592×10−1=1.4592×100  (=1.4592)14.592 \times 10^{-1} = 1.4592 \times 10^{0} \; (= 1.4592)

Practice converting both gigantic and minuscule numbers until the decimal shift feels natural, and always tidy the final answer into true standard form. **Consistent rehearsal is the key to exam confidence!**