Standard Form summary

Key learning points

• Convert by moving the decimal point and counting powers of 10.
• Multiply: multiply $a$s and add indices; divide: divide $a$s and subtract indices; then renormalise.
• Calculator standard-form mode is useful for checks, not a substitute for method.

Worked example 1 — Convert

Write $45000$ in standard form.

Working

One non-zero digit before the point.

Worked example 2 — Ordinary number

Write $3.2\times10^{-3}$ ordinarily.

Working

Move the point 3 places left.

Worked example 3 — Multiply

$(2\times10^3)(3\times10^4)$.

Working

Multiply coefficients; add indices.

Scaffolded Learning Sheet and answers (PDFs)

This page is a short, searchable overview for revision and search engines. Use the Scaffolded Learning Sheet first, then the Answers PDF for a full written solution. The printable PDFs remain the main classroom resource.