Standard form is used to write very large or very small numbers compactly. A number is in standard form if it is written as \(a \times 10^n\), where \(1 \le a < 10\) and \(n\) is an integer.

A quick validity check: if the front number \(a\) is not between \(1\) (inclusive) and \(10\) (exclusive), then it is not in standard form.

To compare or order numbers in standard form, compare the powers of ten first:

• If \(n\) is larger, the number is larger.
• If the powers are the same, compare the values of \(a\).

$$
4.6 \times 10^{5} > 7.2 \times 10^{4}
$$

If you need to interpret size, remember: multiplying by \(10^n\) moves the decimal point \(n\) places (right if \(n\) is positive, left if \(n\) is negative). This helps you estimate quickly and check that answers are sensible.

Always keep track of units in worded questions (for example, metres, grams, seconds) because standard form changes how the number is written, not what it means.

Topic Revision Checklist