Scientific Notation to Decimal Converter

What the scientific notation to decimal converter does

This takes a number written in scientific notation and expands it back into its full, ordinary form. Enter the scientific notation, press the button, and copy out the plain number.

It is the reverse of compressing a number into powers of ten. Where that hides the zeros away in an exponent, this brings them all back out so you can see the number written in full.

How to use it

1. Enter the scientific notation. Type it in, for example 1.23e8 or 1.23x10^8.
2. Press Convert. The full decimal number appears in the output box.
3. Click the result to copy it. Tap the output to send it to your clipboard.

Press Reset to clear both boxes.

Reading the two parts

A number in scientific notation has two parts: a coefficient and an exponent. In 1.23 times 10 to the 8th, the coefficient is 1.23 and the exponent is 8. The coefficient holds the actual digits, and the exponent is an instruction about scale, telling you how far and which way to shift the decimal point to restore the number to its everyday size.

How to expand it: move the point

Expanding is just following the exponent's instruction. You move the decimal point of the coefficient by the number of places the exponent says, filling any new gaps with zeros. A positive exponent moves the point to the right, making the number larger. A negative exponent moves it to the left, making the number smaller. The size of the exponent is exactly how many places to move.

A positive exponent

Take 1.23 times 10 to the 8th. The exponent is positive 8, so move the decimal point in 1.23 eight places to the right. After the 2 and the 3 you run out of digits, so you fill the rest with zeros, ending up with 123,000,000. The positive exponent grew the number into the hundreds of millions.

A negative exponent

Now take 4.5 times 10 to the minus 4. The exponent is negative 4, so move the point in 4.5 four places to the left instead. That carries it past the 4 and on, padding with zeros, to give 0.00045. The negative exponent shrank the number into a small fraction well below 1.

Ways to write the input

There is more than one common way to write scientific notation, and you can use whichever you have. The compact form uses the letter e for the power, so 1.23e8 means 1.23 times 10 to the 8th. The fuller form writes it out, like 1.23x10^8. Both say the same thing, a coefficient and a power of ten, so either will convert the same way.

Questions people ask

How do I expand scientific notation?

Move the decimal point of the coefficient by the exponent's value, filling new spaces with zeros. A positive exponent moves it right, a negative one moves it left.

Which way does a positive exponent move the point?

To the right, which makes the number larger. So 1.23 times 10 to the 8th becomes 123,000,000, with zeros filling the places past the given digits.

What about a negative exponent?

It moves the point to the left, making the number a small fraction. So 4.5 times 10 to the minus 4 becomes 0.00045.

What does the e mean in something like 1.23e8?

The e is shorthand for times 10 to the power of. So 1.23e8 is the same as 1.23 times 10 to the 8th, just written more compactly.

References

1. Scientific notation. Wikipedia, The Free Encyclopedia. https://en.wikipedia.org/wiki/Scientific_notation