What standard form is
Standard form (also called scientific notation) writes very large or very small numbers neatly as A × 10ⁿ, where 1 ≤ A < 10 and n is a whole number. The digit A carries the significant figures; the power of 10 records the size.
Key idea
A × 10ⁿ with 1 ≤ A < 10. Move the decimal point so one non-zero digit sits in front of it, then count how many places you moved: right shift → negative n, left shift → positive n.
Converting numbers
For 3400, place the point after the 3 to get 3.4, which needed moving 3 places, so 3400 = 3.4 × 10³. For 0.00056, move the point to after the 5 to get 5.6, moving 4 places to the right, so 0.00056 = 5.6 × 10⁻⁴.
Worked example
Calculate (2 × 10³) × (3 × 10⁴). Multiply the numbers: 2 × 3 = 6. Add the indices of 10: 3 + 4 = 7. So the answer is 6 × 10⁷. Because 6 is between 1 and 10, this is already in standard form.
Calculating in standard form
To multiply, multiply the front numbers and add the powers of 10. To divide, divide the front numbers and subtract the powers. Always check the front number stays between 1 and 10, adjusting the index if needed.
Remember
- A must satisfy 1 ≤ A < 10 (34 × 10² is not standard form).
- Small numbers have negative powers of 10.
- Multiply → add powers; divide → subtract powers.