Standard Form Calculator
Convert numbers to and from standard form (A × 10ⁿ) step by step. Standard form is the British term for scientific notation, keeping significant zeros.
What is standard form?
Standard form (standard index form) writes a number as A × 10ⁿ, where A is at least 1 and less than 10 and n is a whole number. It is the British term for what Americans call scientific notation, and it makes very large and very small numbers compact.
Converting to standard form
- Move the decimal point until one non-zero digit is to its left.
- Count the places moved.
- That count is the power of ten — positive for moving left, negative for moving right.
Worked examples
- 459608 → 4.59608 × 10⁵
- 0.000380 → 3.80 × 10⁻⁴ (the trailing zero is significant)
- 671000000 → 6.71 × 10⁸
Converting back
Move the point by the power to get the ordinary number: 4.59608 × 10⁵ = 459608.
Standard form vs expanded form
Standard form compresses a number into one mantissa times a power of ten. Expanded form does the opposite, breaking it into the sum of place values. They are different tools for different jobs.
Common mistakes
- Leaving A outside 1 to 10.
- Getting the sign of the power wrong by moving the point the wrong way.
- Dropping significant zeros.
Americans and calculators may call this scientific notation — the scientific notation converter does the same job with extra formats.
Frequently asked questions
- What is standard form?
- Standard form (or standard index form) writes a number as A times 10 to the power n, where A is at least 1 and less than 10, and n is a whole number. It is the British name for scientific notation. 459608 in standard form is 4.59608 times 10 to the 5th.
- How do you write a number in standard form?
- Move the decimal point until one non-zero digit sits to its left, count the places, and use that count as the power of ten. Moving left gives a positive power, moving right gives a negative power.
- How do you convert standard form back to an ordinary number?
- Move the decimal point by the power — right for a positive power, left for a negative one — filling in zeros. So 4.59608 times 10 to the 5th becomes 459608.
- Is standard form the same as scientific notation?
- Yes. Standard form is the British and Commonwealth term; scientific notation is the American term. Both mean A times 10 to the power n with A between 1 and 10.
- How do you write a small number in standard form?
- Small numbers have a negative power. 0.000380 becomes 3.80 times 10 to the negative 4th, moving the point 4 places to the right. The trailing zero stays because it is significant.
- What must A be in standard form?
- A must be at least 1 and less than 10 — exactly one non-zero digit before the decimal point. If a calculation leaves A as 10 or more, or less than 1, adjust the power until A is in range.
- What is the difference from expanded form?
- Expanded form breaks a number into the sum of each digit times its place value, like 4000 plus 500 plus 90. Standard form compresses the whole number into one mantissa times a power of ten.