Question: Express in standard form: (a) $123\,000$, (b) $0.028$, (c) $50.62$ terametres, in metres. [Tera $= 10^{12}$]

Step 1. Standard form is $A \times 10^n$ with $1 \le A < 10$. For a big number, count how many places the point moves left:

Step 2. For a small number the point moves right, so the power is negative:

Step 3. For the prefixed value, substitute the prefix first:

This is not yet standard form — $50.62$ is too big.

Step 4. Shift one more place and compensate in the power:

Check. Each $A$ sits in $[1, 10)$: $1.23$ ✓, $2.8$ ✓, $5.062$ ✓.

⚠ Watch out: $50.62 \times 10^{12}$ looks finished but fails the $1 \le A < 10$ test — prefix conversions almost always need that final one-place adjustment. Making $A$ ten times smaller makes the power one bigger, and vice versa.

Question: The distance between the Sun and the Earth is $1.5 \times 10^8$ km. Light travels at $3.0 \times 10^5$ km/s. Find the time, in seconds, for light to travel from the Sun to the Earth, giving your answer in standard form.

Step 1. Pick the formula from the D–S–T triangle:

Step 2. Divide the number parts and the powers of ten separately:

Step 3. Combine:

Step 4. Adjust into standard form ($0.5$ is below 1):

⚠ Watch out: The units already match (km with km/s), so no conversion was needed — check that before dividing, not after. And $0.5 \times 10^3$ loses the final mark: standard form demands $1 \le A < 10$, so shift to $5 \times 10^2$.