Standard Form Calculator

Standard form at a glance#

A standard form calculator writes a number as a × 10ⁿ, where a is at least 1 and less than 10 and n is a whole-number exponent. Standard form is the UK name for scientific notation, so the two mean the same thing. Move the decimal point until one non-zero digit sits in front of it, then count the moves: left gives a positive exponent, right gives a negative one. So 4500 becomes 4.5 × 10³.

For 4500, the decimal moves 3 places left to sit after the 4, giving 4.5 and an exponent of 3: 4.5 × 10³ = 4.5 × 1000 = 4500. For a small number such as 0.00065, the decimal moves 4 places right, giving 6.5 and an exponent of −4: 6.5 × 10⁻⁴ = 6.5 ÷ 10000 = 0.00065.

The speed of light, about 300,000,000 metres per second, is 3 × 10⁸ in standard form. Because standard form and scientific notation are identical, a number written one way is correct in the other. Enter your number in the calculator above for the exact standard form, with the decimal placement and exponent worked out for you.

Converting standard form back to a plain number#

To undo standard form, move the decimal by the exponent: right for a positive power, left for a negative one. So 4.5 × 10³ means move the decimal 3 places right, giving 4500. And 6.5 × 10⁻⁴ means move it 4 places left, giving 0.00065. The sign of the exponent tells you the direction every time.

Positive and negative powers#

A positive power means the number is 10 or larger, and the power counts how many places the decimal sat to the right of the coefficient. A negative power means the number is below 1. The power is never the count of zeros: 0.00065 has three zeros after the point but a power of −4, because the decimal moves 4 places to reach 6.5.

What the calculator accepts#

The calculator above takes plain decimals, e-notation such as 2.4e7, and engineering notation, but not fractions. A standard-form coefficient always has exactly one non-zero digit before the decimal point, so 0.045 is wrong as a coefficient and 4.5 × 10⁻² is right.

Standard form FAQ#

Is standard form the same as scientific notation?#

Yes. Standard form is the UK and international name; scientific notation is the US name. Both write a number as a coefficient from 1 up to 10 times a power of 10, so 45000 is 4.5 × 10⁴ in either system.

How do you write a small number in standard form?#

Move the decimal right until one non-zero digit leads, then make the power negative and equal to the number of moves. So 0.000408 becomes 4.08 × 10⁻⁴, because the decimal moves 4 places right.

How do you write a large number in standard form?#

Move the decimal left until one non-zero digit leads, then make the power positive and equal to the number of moves. So 72000 becomes 7.2 × 10⁴, and 4500 becomes 4.5 × 10³.

What is the power of 10 in standard form?#

It is the number of places the decimal point shifts to turn the standard form back into the plain number, signed for direction: positive when the number is 10 or more, negative when it is below 1. It is not the count of zeros in the original number.