Scientific Notation Calculator
Type a number in either form and get the other. 45000 becomes 4.5 × 10⁴, and 3.2e5 becomes 320000, with the decimal point moved one place at a time and the reason for the exponent's sign stated.
How it works
How the Scientific Notation Calculator works
the part a result on its own leaves out
What scientific notation is for
It writes a number as a × 10ⁿ, where a is at least 1 and under 10. Very large and very small numbers become short: 602,200,000,000,000,000,000,000 is 6.022 × 10²³. The exponent n counts how many places the decimal point moved.
Why the exponent's sign carries the meaning
A positive exponent means the original number was 10 or more, so the point moved left to get there. A negative exponent means the original was below 1, so the point moved right. The size of the exponent is how many places, never how many zeros the number happens to print with.
Why this calculator works on digits, not decimals
A computer's ordinary number type loses digits after about 15 of them. This calculator moves the point on the digits themselves, so a long number keeps every digit it was given.
Common mistakes
Common mistakes with scientific notation
the errors that actually show up, not every possible slip
Leaving the front number outside the range of 1 to 10
45 × 10³ is a correct value but not scientific notation, because 45 is not below 10. Move one more place: 4.5 × 10⁴.
Getting the sign of the exponent backwards
0.00032 is 3.2 × 10⁻⁴, not 3.2 × 10⁴. A small number needs a negative exponent: the point moves right to reach the front digit.
Counting zeros instead of places moved
45000 has three zeros but the exponent is 4, because the point moves four places, past the 4 and three zeros. Count the moves, not the zeros.
Questions
Asked often enough to answer here
answers that change how you work
How do I write a number in scientific notation?
Move the decimal point until one non-zero digit is in front of it, then multiply by 10 raised to the number of places you moved. Moving left is a positive exponent; moving right is negative. 45000 → 4.5 × 10⁴.
How do I convert scientific notation back to a normal number?
Move the decimal point the number of places the exponent says: right for a positive exponent, left for a negative one, filling with zeros. 3.2 × 10⁵ → 320000.
What does e mean, as in 3.2e5?
It is calculator shorthand for × 10 to the power. 3.2e5 means 3.2 × 10⁵. This calculator reads that, 3.2x10^5 and 3.2 × 10^5 equally.
Can scientific notation be negative?
Yes in two separate ways. A negative front number means a negative value: −4.5 × 10³ is −4500. A negative exponent means a small value: 4.5 × 10⁻³ is 0.0045.
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