Standard form writes a number as A × 10ⁿ, with A from 1 up to (but not including) 10. The repair is to decide big or small first, then count the moves, then write the sign.
What is the small gap?
Students count the moves but guess the sign. A cleaner habit is to ask first: is the number 10 or more (n positive), or between 0 and 1 (n negative)?
How do you write it, step by step?
- Place the decimal point after the first non-zero digit. This gives A.
- Count how many places the point moved. That gives the size of n.
- If the original number is 10 or more, n is positive. If it is between 0 and 1, n is negative.
A scaffolded example
An original problem: write 6 300 000 and 0.00072 in standard form.
6 300 000. It is a big number, so n is positive. Place the point after the 6: 6.3. It moved 6 places from the end of 6 300 000, so the number is 6.3 × 10⁶.
0.00072. It is small, so n is negative. Place the point after the 7: 7.2. The point moved 4 places right, so the number is 7.2 × 10⁻⁴.
Check by expanding: 7.2 × 10⁻⁴ = 7.2 ÷ 10 000 = 0.00072. It matches.
What does the common mistake look like?
A student writes 6 300 000 = 63 × 10⁵. It equals the right number, but 63 is not between 1 and 10, so it is not standard form. The same happens with 0.72 × 10⁻³ for 0.00072.
The fix is one glance at A: if it is 10 or more, or below 1, the point has not been placed after the first non-zero digit.
Self-check
Write 480 000 000 and 0.0305 in standard form. Then write 2.9 × 10⁻³ as an ordinary number.
Answer
480 000 000: point after the 4 gives 4.8, and it moved 8 places, so 4.8 × 10⁸.
0.0305: point after the 3 gives 3.05, moved 2 places right, so 3.05 × 10⁻².
2.9 × 10⁻³: move the point 3 places left: 0.0029.
Where does this show up in SPM?
In SPM Mathematics, standard form appears in its own section and in rounding. In Physics and Science, it is how very large and very small measurements are reported.
The next step is calculating with scientific notation. The hub lists the sequence, and index rules support it.
One-to-one Mathematics tuition starts with a one-hour trial class (from RM50).