Standard Form Calculator

What this calculator does

So, you have a number and you want it written in standard form. This tool converts it. Enter a number and it rewrites it as a value between 1 and 10 multiplied by a power of 10.

One input, and your number comes back in the compact standard form used in maths and science.

How to use it

1. Enter your number.
2. Press Calculate.

What standard form is

Standard form is a way of writing a number as a value between 1 and 10 multiplied by a power of 10. So 12,345 becomes 1.2345 times 10 to the power 4, and 300,000 becomes 3 times 10 to the power 5. The first part, always at least 1 but less than 10, carries the significant digits of the number. The power of 10 records its size, how many places the decimal point sits from where it would be in the plain number. Writing numbers this way keeps them tidy no matter how big they get.

Standard form and scientific notation

It is worth clearing up a point that confuses people: standard form and scientific notation are two names for exactly the same thing. Standard form is the term used most often in British schools, while scientific notation is more common elsewhere, but they mean an identical way of writing numbers, a value between 1 and 10 times a power of 10. So if you have seen one name and not the other, do not worry that they are different techniques. This tool even labels its answer as scientific notation, which is precisely the standard form of the number you entered.

How the conversion works

To convert a number, you work out how far the decimal point has to move to leave a single non-zero digit in front of it. For 12,345, the decimal point currently sits after the final 5; sliding it left until it sits just after the 1 moves it four places, which gives the number 1.2345 and a power of 10 to the fourth. The tool does this by finding how many digits the number has and using that to set the power of 10, then dividing the number down to a value between 1 and 10. The count of places the point moved is the exponent.

A worked example

Enter 12,345. The number has five digits, so the decimal point moves four places to the left to sit after the first digit, giving 1.2345. The four places become the power, so the standard form is 1.2345 times 10 to the power 4. As a simpler case, 300,000 becomes 3 times 10 to the power 5, since the point moves five places to land after the 3.

Why write numbers this way

Standard form earns its keep whenever numbers get large or unwieldy. It replaces long strings of zeros with a short power of 10, which is easier to read, write, and compare, and it makes the size of a number obvious at a glance from its exponent. Scientists, engineers, and mathematicians use it constantly for exactly this reason. Once numbers are in this form, doing arithmetic with them is its own small skill, and the scientific notation calculator will add, subtract, multiply, or divide two numbers written this way.

Questions people ask

What is standard form?

A way of writing a number as a value between 1 and 10 multiplied by a power of 10, such as 1.2345 times 10 to the power 4 for 12,345.

Is standard form the same as scientific notation?

Yes. They are two names for the identical way of writing numbers, standard form being the more common British term.

What does the power of 10 tell me?

It records the size of the number, how many places the decimal point has moved from the plain number.

Why must the first part be between 1 and 10?

So that exactly one non-zero digit sits in front of the decimal point, giving each number a single standard way to be written.

How do I do arithmetic in this form?

Use the scientific notation calculator, which adds, subtracts, multiplies, and divides numbers written this way.

References

On standard form. Standard form, also called scientific notation, writes a number as a value between 1 and 10 multiplied by a power of 10.

1. Christopher Stover and Eric W. Weisstein, "Scientific Notation," from MathWorld, a Wolfram resource, on writing a number as a value between 1 and 10 times a power of 10.
2. Eric W. Weisstein, "Power," from MathWorld, a Wolfram resource, on powers, including the powers of 10 that standard form relies on.