Math calculator
Scientific Notation Calculator
Convert numbers to and from normalized scientific notation or perform basic arithmetic.
Use e notation for powers of ten, such as 4.5e-3.
Scientific notation
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Convert mode and Calculate mode
Convert mode takes one number, typed either as an ordinary decimal or in e-notation like 1.23e5, and returns four things at once: the normalized scientific notation, the plain decimal, the coefficient on its own, and the power of ten on its own. Calculate mode instead takes two numbers and an operation — add, subtract, multiply, or divide — runs the arithmetic on the ordinary values, and then converts that answer into scientific notation.
Division by zero is blocked outright; picking ÷ with a second value of 0 leaves the result blank rather than showing Infinity. Zero itself is handled as a special case everywhere else in the tool and is always displayed as 0 × 10^0, since the exponent formula (which relies on a logarithm) has no defined answer for zero.
The coefficient is rounded to 12 significant figures before display, so extremely long repeating decimals get trimmed rather than shown in full — a number like 1 ÷ 3 in scientific notation shows as 3.33333333333 × 10^-1, not an endless string of 3s.
Normalized form
Normalized scientific notation always keeps exactly one nonzero digit to the left of the decimal point in the coefficient. To convert 6,370,000 (roughly Earth's radius in meters), count how many places the decimal point moves to land after the first digit: it moves 6 places, so the exponent is 6 and the coefficient is 6.37, giving 6.37 × 10^6.
Small numbers work the same way but the exponent goes negative. Converting 0.00072 means moving the decimal point 4 places to the right to reach 7.2, so the result is 7.2 × 10^-4. As a sanity check, multiplying 7.2 × 10^-4 back out — 7.2 × 0.0001 — returns 0.00072.
The exponent rule people get backwards
When multiplying two numbers already in scientific notation, the exponents add — they do not multiply. (3 × 10^4) × (2 × 10^3) works out to (3 × 2) × 10^(4+3) = 6 × 10^7, not 6 × 10^12. Run the same numbers through Calculate mode and it confirms this: 30,000 × 2,000 = 60,000,000, which converts back to 6 × 10^7.
Division works the opposite way: exponents subtract. (8 × 10^5) ÷ (2 × 10^2) is (8 ÷ 2) × 10^(5−2) = 4 × 10^3, which is 4,000 — and 800,000 ÷ 200 does equal 4,000. A second common mix-up is skipping normalization after arithmetic, for instance leaving an answer as 65 × 10^4 instead of shifting the decimal to get 6.5 × 10^5; the calculator always returns the normalized form for you.
Where powers of ten show up
Scientific notation exists because plenty of real quantities are too large or too small to write comfortably in full:
- Astronomy – the average Earth–Sun distance, about 149,600,000 km, is written 1.496 × 10^8 km
- Chemistry – Avogadro's number, 602,200,000,000,000,000,000,000, is written 6.022 × 10^23
- Microelectronics – a transistor gate around 0.000000007 m wide is written 7 × 10^-9 m
- Computing – 1 terabyte, 1,000,000,000,000 bytes, is written 1 × 10^12 bytes
- National finance – a $2,700,000,000,000 budget figure is written 2.7 × 10^12
- Biology – a typical virus particle around 0.0000001 m across is written 1 × 10^-7 m
Frequently asked questions
How do I convert 45,000 to scientific notation?
Move the decimal point left until one nonzero digit remains before it — from 45,000. to 4.5, a move of 4 places — so 45,000 = 4.5 × 10^4. Type 45000 into Convert mode to see the same result along with the coefficient and exponent shown separately.
Why is my exponent negative?
Any number smaller than 1 gets a negative exponent, because the decimal point has to move right, not left, to reach the normalized form. Converting 0.00072 gives an exponent of −4, since the point moves 4 places rightward to land after the 7.
What does entering 0 give me?
Exactly 0 × 10^0. Zero has no meaningful power-of-ten exponent because log10(0) is undefined, so the calculator returns this fixed convention instead of an error.
Can I type e-notation directly instead of a full decimal?
Yes, in both modes. Typing 1.23e5 is read the same as typing 123000, and the Calculate mode's two number fields also accept values like 4.5e-3 directly.
How do I add two numbers written in scientific notation?
You can't add the coefficients directly unless the exponents match — 3 × 10^4 plus 2 × 10^3 is not 5 × 10^4. Switch to Calculate mode and enter the ordinary values (30000 and 2000, operation +) and the tool handles the exponent alignment for you, returning 3.2 × 10^4.
Why does my coefficient get cut off after so many digits?
The coefficient is rounded to 12 significant figures for display. A value like 100 ÷ 3 converts to 3.33333333333 × 10^1 rather than showing an infinite run of 3s.