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Scientific Notation Calculator
Very big and very small numbers are painful to write in full — the number of atoms in a gram of hydrogen has 24 digits, and the width of a hair in metres needs five zeros after the point. Scientific notation fixes this by writing a number as a short decimal times a power of ten. This scientific notation calculator converts plain numbers into scientific and engineering notation, and converts scientific or e-notation (like 3.2e8) back into plain numbers. It works on the digits themselves, so even an 18-digit number converts exactly, with no rounding surprises.
Plain modes accept long numbers like 123456789012345678 — they are handled digit by digit, so no digits are lost. The plain-number mode accepts 3.2e8, 1.5E6 or 1.5×10^-3.
How to use this tool
- Choose what you want to do in the top list: number to scientific, number to engineering, or notation back to a plain number.
- Type or paste your number. Long numbers are fine — commas and spaces are ignored.
- The big line is the answer. The line below shows the same number in the other two forms.
- For the third mode you can type 3.2e8, 1.5E6, or 1.5×10^-3 — all three styles are understood.
Scientific notation — common values
| Number | Scientific Notation | Engineering Notation |
|---|---|---|
| 1,000 | 1 × 10³ | 1 × 10³ |
| 45,000 | 4.5 × 10⁴ | 45 × 10³ |
| 1,234,567 | 1.234567 × 10⁶ | 1.234567 × 10⁶ |
| 0.001 | 1 × 10⁻³ | 1 × 10⁻³ |
| 0.00045 | 4.5 × 10⁻⁴ | 450 × 10⁻⁶ |
| 3.2e8 (typed form) | 320,000,000 as a plain number | |
| 602,200,000,000,000,000,000,000 | 6.022 × 10²³ | 602.2 × 10²¹ |
Avogadro's number in the last row — about 6.022 × 10²³ — is the count of particles in one mole, and it shows why this notation exists: nobody wants to write out 602,200,000,000,000,000,000,000 in a chemistry exam. Engineering notation in the same row keeps the exponent a multiple of 3, so the number reads as 602.2 × 10²¹, matching the kilo/mega/giga style prefixes.
How it works
Scientific notation writes a number as a × 10ⁿ, where a (the mantissa) is at least 1 and less than 10, and n (the exponent) is a whole number that can be negative. To convert, move the decimal point until exactly one non-zero digit sits in front of it, then count the moves: moving left makes a positive exponent, moving right makes a negative one. So 1,234,567 becomes 1.234567 × 10⁶ (six moves left), and 0.00045 becomes 4.5 × 10⁻⁴ (four moves right).
Engineering notation is a close cousin: the exponent is always a multiple of 3, and the mantissa can be up to just under 1,000. That matches the metric prefixes — 10³ is kilo, 10⁶ is mega, 10⁻³ is milli — which is why engineers and electricians prefer it: 450 × 10⁻⁶ metres is instantly "450 micrometres", while 4.5 × 10⁻⁴ needs a moment of thought. Calculators and programming languages use a third form, e-notation, where 3.2e8 means 3.2 × 10⁸.
Most calculators quietly round long numbers, because computers store numbers with about 15–17 reliable digits. Type 123456789012345678 into a normal calculator and the last digits may change. This tool is different: it moves the decimal point around in the digit string itself and never turns your number into a floating-point value, so every digit you type is a digit you get back.
Worked example
A student needs 1,234,567 in scientific notation for a physics answer, and also wants to check a tiny measurement, 0.00045 metres.
Step 1: For 1,234,567, move the point 6 places left: 1.234567.
Step 2: Six moves left means ×10⁶ — so 1.234567 × 10⁶. (Engineering agrees here, because 6 is already a multiple of 3.)
Step 3: For 0.00045, move the point 4 places right: 4.5, with ×10⁻⁴ — so 4.5 × 10⁻⁴.
Step 4: In engineering notation the exponent must be a multiple of 3, so it becomes 450 × 10⁻⁶.
And in reverse: type 3.2e8 in the third mode and the calculator gives the plain number 320,000,000.
FAQ
What is scientific notation?
Scientific notation writes a number as a short decimal multiplied by a power of ten, like 1.234567 × 10⁶ for 1,234,567. The first part (the mantissa) is always at least 1 and less than 10; the power of ten (the exponent) says how many places the decimal point moved.
What is the difference between scientific and engineering notation?
In scientific notation the mantissa is between 1 and 10. In engineering notation the exponent is always a multiple of 3 (…, -6, -3, 0, 3, 6, …) and the mantissa can go up to 999.99. So 0.00045 is 4.5 × 10⁻⁴ in scientific but 450 × 10⁻⁶ in engineering — the engineering version matches metric prefixes like micro (10⁻⁶).
How do I convert 3.2e8 to a normal number?
3.2e8 means 3.2 × 10⁸. Move the decimal point 8 places to the right, adding zeros: 320,000,000. The third mode of this calculator does it for you, including negative exponents like 1.5e-3 = 0.0015.
How do I write 0.00045 in scientific notation?
Move the decimal point right until one non-zero digit is in front: 4.5. You moved 4 places, and moving right gives a negative exponent, so 0.00045 = 4.5 × 10⁻⁴. In engineering notation it is 450 × 10⁻⁶.
Why does this calculator give exact digits for very long numbers?
Ordinary calculators store numbers as floating-point values with about 15–17 reliable digits, so 123456789012345678 can come back changed. This tool never stores your number that way — it works on the digit string itself, moving the point and counting, so the digits stay exact.
Can the exponent be zero?
Yes. Any number from 1 up to (but not including) 10 has an exponent of 0: 7.5 is 7.5 × 10⁰, which is usually just written as 7.5. Zero itself is written 0 × 10⁰, because no decimal point movement can give zero a leading digit.
Note: conversions are done on the digits you type, so long numbers stay exact. E-notation input (like 3.2e8) is read in the third mode only.