Year 8 · Revision Notes

Standard Form — Year 8 Revision Notes

Q: Is 45 × 10⁵ in standard form?

No. The front number must be between 1 and 10, and 45 is too big. Rewrite it as 4.5 × 10⁶, which is the correct standard form.

These notes cover writing large numbers in standard form, converting back to ordinary numbers, and comparing numbers in standard form — all at Year 8 (Stage 8) level.

What standard form means

A number in standard form is written as A × 10ⁿ, where A is a number from 1 up to (but not including) 10, and n is a whole number. For large numbers, n is positive. For example, 3 × 10⁴ = 3 × 10 000 = 30 000. The power of 10 tells you the place value of the first digit.

Key Facts & Formulas

A × 10ⁿ, with 1 ≤ A < 10
3 × 10⁴ = 30 000

Tips

Always check that A is between 1 and 10.
A positive power of 10 means a large number.

Writing a large number in standard form

Put a decimal point after the first non-zero digit to make A, then count how many places the point has moved from its original position — that count is the power of 10. For 6 200 000, A = 6.2 and the point has moved 6 places, so it is 6.2 × 10⁶.

Key Facts & Formulas

6 200 000 = 6.2 × 10⁶

Tips

Count place-value shifts, not the number of zeros.
Drop trailing zeros from A, so 6.2 not 6.200.

Converting back and comparing

To turn standard form back into an ordinary number, move the decimal point to the right by the power of 10, filling with zeros. To compare two numbers in standard form, look at the power of 10 first; the larger power means the larger number, and only if the powers are equal do you compare the values of A.