Math
Standard Form Calculator
Standard form, as used in UK schools and GCSE maths, writes a number as A × 10^n where A is at least 1 and less than 10 and n is an integer.
Type an ordinary number such as 0.00042 or 3,450,000 to get its standard form, with the number of places the decimal point moved; or enter A and n to get the ordinary number back. Everything is exact, so 40-digit numbers convert without rounding.
Any decimal, up to 60 digits. Commas are fine.
Try an example
Result
Result
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- Standard form
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- Ordinary number
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- Power of ten n
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- Decimal point moves
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What the standard form calculator solves
Standard form (also called standard index form, and Writing a number as one digit, a decimal part, and a power of ten. in the US) writes any number as A × 10^n, where A is between 1 and 10 and n is a whole number. It keeps very large and very small numbers readable: the distance to the Sun is 1.5 × 10^11 m rather than 150,000,000,000 m, and a red blood cell is about 7 × 10^-6 m across. This calculator converts in both directions exactly.
| Ordinary number | Standard form | Point moves |
|---|---|---|
| 7 | 7 × 10^0 | none |
| 250 | 2.5 × 10^2 | 2 left |
| 3,450,000 | 3.45 × 10^6 | 6 left |
| 0.5 | 5 × 10^-1 | 1 right |
| 0.00042 | 4.2 × 10^-4 | 4 right |
| -0.0000071 | -7.1 × 10^-6 | 6 right |
How to write a number in standard form
- Move the decimal point until exactly one non-zero digit is in front of it. That number is A.
- Count how many places the point moved. That is n: positive if the original number was 10 or bigger (the point moved left), negative if it was less than 1 (the point moved right).
- Write A × 10^n. Check by multiplying back.
Standard form vs scientific notation vs 'standard form' in the US
In the UK, standard form means A × 10^n. In the US the same thing is called scientific notation, while 'standard form' there means the ordinary way of writing a number (3,450,000) as opposed to expanded form or word form. This page follows the UK meaning; the ordinary-number output is what a US textbook would call standard form.
How to use it
- Choose the direction: ordinary number to standard form, or A and n to an ordinary number.
- Type the number (or A and n) and read the result with the count of decimal-point moves.
- Open Show the work to see A chosen, n counted, and the multiplication check.
How to read the answer
In standard form, n tells you the size at a glance: n = 6 means millions, n = -4 means ten-thousandths. A carries the significant digits. Converting back, a positive n moves the point right (bigger number) and a negative n moves it left (smaller number). The conversion is exact; no rounding is applied, so A shows every non-zero digit of the input.
Common mistakes and edge cases
- Letting A be 10 or more, or less than 1: 34.5 × 10^5 must become 3.45 × 10^6.
- Getting the sign of n backwards: small numbers (less than 1) have negative n.
- Counting the moves wrongly with leading zeros: 0.00042 has n = -4 (the point moves four places), not -5.
- Confusing the UK meaning (A × 10^n) with the US meaning of 'standard form' (the ordinary number).
- Trying to write 0 in standard form; there is no A between 1 and 10 that works.
Worked examples
0.00042
4.2 × 10^-4.
Result
4.2 × 10^-4
3,450,000
3.45 × 10^6.
Result
3.45 × 10^6
Single digit
7 = 7 × 10^0.
Result
7 × 10^0
Negative number
-0.0000071 = -7.1 × 10^-6.
Result
-7.1 × 10^-6
40-digit number
Exact conversion.
Result
1.23456789012345678901234567890123456789 × 10^39
Back to ordinary
4.2 × 10^-4 = 0.00042.
Result
0.00042
Large power
1.5 × 10^11 = 150,000,000,000.
Result
150,000,000,000
Improper A
34.5 × 10^5 is renormalised to 3.45 × 10^6.
Result
3,450,000
Zero
No standard form.
Result
Error
Frequently asked questions
What is standard form in maths?+
A way of writing numbers as A × 10^n with 1 ≤ A < 10 and n a whole number, used for very large or very small values. 3,450,000 = 3.45 × 10^6.
Is standard form the same as scientific notation?+
Yes. Standard form is the UK term; scientific notation is the US term for the same A × 10^n format.
How do I write 0.00042 in standard form?+
Move the point four places right to get 4.2, so n = -4: 0.00042 = 4.2 × 10^-4.
How do I convert standard form back to an ordinary number?+
Move the decimal point n places: right for positive n, left for negative n, filling with zeros. 1.5 × 10^11 = 150,000,000,000.
Why must A be between 1 and 10?+
So every number has exactly one standard form and sizes can be compared by n alone. 34.5 × 10^5 and 3.45 × 10^6 are equal, but only the second is standard form.
Can 0 be written in standard form?+
No. There is no A with 1 ≤ A < 10 such that A × 10^n = 0. Zero is just written as 0.
What does 'standard form' mean in the US?+
In US classrooms, standard form usually means the ordinary numeral (3,450,000) as opposed to expanded form (3,000,000 + 400,000 + 50,000) or word form.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- September 4, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
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Last updated: September 4, 2026