Standard form converter (scientific notation)
Type an ordinary number to see it in standard form, or type a standard-form value to expand it. The converter keeps the mantissa between 1 and 10 exactly as GCSE and IGCSE mark schemes require, and shows the power of ten so you can see which way the decimal point moved.
Enter your number
Type an ordinary number such as 0.00042 or 4 500 000, or a standard-form value such as 4.2e-4 or 4.2 x 10^-4. The converter shows both forms.
4.2 × 10⁻⁴
Ordinary number: 0.000420000000000000017417
Mantissa: 4.2 (between 1 and 10) · Power: 10⁻⁴
The decimal point moves 4 places right to reach standard form.
The method behind it
- Standard form is a × 10ⁿ with 1 ≤ a < 10 and n an integer.
- Large numbers give a positive power; numbers below 1 give a negative power.
- The power equals the number of places the decimal point moves.
How to use this tool
1. Choose a direction
Switch between ordinary number → standard form and standard form → ordinary number.
2. Enter your value
Type the number, for example 0.00042 or 4.2e-4. Very large and very small values are both supported.
3. Copy the answer
The result is shown as a × 10ⁿ with 1 ≤ a < 10, which is the only form that earns full marks.
Frequently asked questions
What is standard form in maths?
Standard form writes a number as a × 10ⁿ where a is at least 1 and less than 10, and n is an integer. For example 4 500 000 is 4.5 × 10⁶ and 0.00032 is 3.2 × 10⁻⁴.
How do you convert a small number to standard form?
Move the decimal point right until exactly one non-zero digit sits in front of it, then make the power of ten negative and equal to the number of places you moved. 0.00042 becomes 4.2 × 10⁻⁴.
Is 12 × 10³ in standard form?
No. The number in front must be between 1 and 10, so 12 × 10³ must be rewritten as 1.2 × 10⁴. Losing this mark is one of the most common standard-form errors in GCSE papers.
How do I enter standard form on a calculator?
Use the ×10ˣ or EXP key rather than typing '× 10 ^'. Pressing 4.2, then ×10ˣ, then (−)4 gives 4.2 × 10⁻⁴ and avoids bracket errors.
Practise this properly, not just once
A solver gives you the answer; exam marks come from the working. MathsGradeUp pairs exam-board questions with step-by-step feedback and revision notes on the exact topics you keep dropping marks on.