Decimal to Scientific Notation Converter

What the decimal to scientific notation converter does

This rewrites an ordinary number in scientific notation, the compact form built around powers of ten. Enter your number, press the button, and copy the result.

Scientific notation is how you tame numbers that are awkwardly large or awkwardly small. Instead of a long parade of zeros, you get one tidy digit, a decimal part, and a power of ten that records the scale.

How to use it

1. Enter your number. Type any number, large or small, for example 123000000.
2. Press Convert. The scientific notation form 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.

What scientific notation is

Scientific notation writes a number as a coefficient times a power of ten, in the shape a times 10 to the power n. The coefficient a is always kept between 1 and 10, meaning it has exactly one nonzero digit in front of the decimal point. The exponent n is a whole number that records how big or small the value is. So 1.23 times 10 to the 8th, often written 1.23e8, is one compact way of saying 123 million.

How to find it: move the point

The method is simply to slide the decimal point until just one nonzero digit sits in front of it, and to count how many places you moved. That count is the exponent. If you moved the point to the left, because the number was large, the exponent is positive. If you moved it to the right, because the number was a small fraction, the exponent is negative. The digits you are left with, trimmed of trailing zeros, become the coefficient.

A large number

Take 123,000,000. The decimal point sits at the far right, after the last zero. Slide it left until it sits just after the 1, and you will have moved it 8 places. So the coefficient is 1.23 and the exponent is 8, giving 1.23 times 10 to the 8th. The eight zeros collapsed into a single small number, 8, in the exponent.

A small number

Now take 0.00045. Here you slide the point the other way, to the right, until one nonzero digit stands in front of it. Moving it past the three zeros and the 4 takes 4 places, landing you at 4.5. Because you moved right, the exponent is negative, so the number is 4.5 times 10 to the minus 4. A negative exponent is the signal that the original was a small fraction rather than a large number.

Why it is worth using

Scientific notation pays off whenever the plain number is unwieldy. It saves you from writing and miscounting long runs of zeros, and it makes the scale of a value obvious at a glance, since the exponent tells you the size directly. It also shows clearly how many meaningful digits a measurement has. This is why it is the everyday language of science, where quantities like the number of atoms in a sample or the size of a cell would otherwise be hopeless to write out.

Questions people ask

What is scientific notation?

A way of writing a number as a coefficient between 1 and 10 times a power of ten, like 1.23 times 10 to the 8th. The power records the scale of the number.

How do I convert a number to it?

Slide the decimal point until one nonzero digit is in front of it, and count the places moved. That count is the exponent, positive if you moved left, negative if you moved right.

What does a negative exponent mean?

It means the number is a small fraction, less than 1. You had to move the point to the right to normalize it, so the exponent comes out negative, as in 4.5 times 10 to the minus 4.

Why must the coefficient be between 1 and 10?

So every number has one standard form. Keeping exactly one nonzero digit before the point means the same value is always written the same way, which is what makes the notation easy to compare.

References

1. Weisstein, Eric W. "Scientific Notation." From MathWorld, A Wolfram Resource. https://mathworld.wolfram.com/ScientificNotation.html