How do I write a number in scientific notation?

Move the decimal point until exactly one non-zero digit sits in front of it, then count the moves. Moving left gives a positive exponent, moving right a negative one. For 299,792,458 the point moves eight places left, giving 2.99792458 × 10⁸. For 0.0450 it moves two places right, giving 4.50 × 10⁻². The mantissa always ends up between 1 and 10 in size, which is what makes the form standard.

Why do scientists use it instead of ordinary decimals?

Mainly to make precision explicit. Written as 1200, a measurement gives no way to tell whether two, three or four digits were actually determined. Written as 1.2 × 10³ it says two, and 1.200 × 10³ says four. Ordinary decimal notation simply cannot express that distinction for numbers ending in zeros. The compactness for very large and very small values is a convenience; the removal of ambiguity is the reason.

How do I count significant figures?

Every non-zero digit counts, and so does any zero between non-zero digits — 1002 has four. Leading zeros never count, since they only locate the decimal point: 0.00123 has three. Trailing zeros count when there is a decimal point, so 1.200 has four, and are ambiguous without one, which is the case that scientific notation resolves.

What is the difference between the multiplying and adding rules?

They measure different things. Multiplying or dividing keeps the fewest significant figures, because a product can only be as reliable as the least reliable factor overall. Adding or subtracting keeps the fewest decimal places, because a sum is limited by where the coarsest measurement stopped, not by how many digits it had. On 100.0 + 0.002 the decimal-place rule gives 100.0; using the significant-figure rule would give 100 and discard a tenths digit that was genuinely measured.

What does the e in 6.022e23 mean?

It stands for exponent, and 6.022e23 means 6.022 × 10²³. It is the form calculators, spreadsheets and programming languages use because superscripts are awkward to type. It has nothing to do with Euler’s number, despite the shared letter — a genuine source of confusion when e also appears in the same expression as the base of natural logarithms. Some contexts write it E23 or ×10^23 instead.

What is engineering notation?

A variant where the exponent is always a multiple of three, which lines it up with the SI prefixes. So 45,000 is written 45 × 10³ rather than 4.5 × 10⁴, because 10³ is kilo and the answer reads directly as forty-five kilo-something. The mantissa can then be anywhere from 1 to 1000 rather than 1 to 10. Engineers prefer it because the result maps straight onto the units people actually say aloud — microseconds, megawatts, kilometres.

How do I add two numbers in scientific notation?

Make the exponents match first, then add the mantissas. You cannot simply add the fronts: 1.5 × 10³ plus 2.0 × 10² is not 3.5 of anything. Rewrite the second as 0.20 × 10³, add to get 1.7 × 10³, and renormalise if the result falls outside 1 to 10. Multiplying has no such requirement — the mantissas multiply and the exponents add, whatever they happen to be, which is why multiplication in this notation is so much easier than addition.

Is 1200 two, three or four significant figures?

Nobody can tell, and that is the honest answer. The trailing zeros might be measured digits or might be placeholders keeping the point in position, and plain decimal notation has no way to distinguish them. Some conventions add a bar over the last significant zero or write 1200. with a trailing point to mean four, but neither is universal. Writing it in scientific notation is the reliable fix, since the mantissa contains exactly the digits you mean to claim.

What does a negative exponent mean?

That the number is small, not that it is negative. 1.6 × 10⁻¹⁹ is a positive number a little larger than zero — the negative exponent says the decimal point moves nineteen places to the left. A negative number carries its sign on the mantissa instead: −1.5 × 10³ is negative and large. Both can happen at once, so −1.6 × 10⁻¹⁹ is a small negative quantity.

Why does my calculator show 0.30000000000000004 for 0.1 + 0.2?

Because it stores numbers in binary, and 0.1 has no exact binary representation any more than one third has an exact decimal one. The stored value is very slightly off, and adding two slightly-off values makes the error visible. This page avoids the problem by scaling both numbers to whole numbers, adding them as arbitrary-precision integers, and scaling back — so the answer is 0.3. On a page about precision it would be poor form to teach significant figures using arithmetic that invents digits.

Scientific Notation Calculator

Scientific notation writes a number as one digit, a decimal point, and a power of ten. The compactness is convenient, but it is not the reason the notation exists. The reason is that 1200 is ambiguous. It might be two significant figures, or three, or four — the written form cannot say, because the...

1200 might be two significant figures, or three, or four. Written plainly there is no way to tell, and that ambiguity is the actual reason scientific notation exists — 1.2 × 10³ is unmistakably two, and 1.200 × 10³ is four. This page keeps every digit you type rather than parsing to a decimal, so a trailing zero survives instead of quietly disappearing.

THE NUMBER

SCIENTIFIC NOTATION

2.99792458 × 10⁸

9 significant figures, and standard form shows all of them.

E NOTATION

2.99792458e8

what calculators and code use

ENGINEERING

299.792458 × 10^6

the mega range

WRITTEN OUT

299,792,458

every digit, no exponent

SIGNIFICANT FIGURES

unambiguous

WHAT IS HAPPENING

The exponent is a count, not a size. It records how many places the point moved to leave exactly one non-zero digit in front. Moving left gives a positive exponent and moving right a negative one, which is why a negative exponent means a small number rather than a negative one.

Read from your digits directly · no floating point anywhere

Created with❤️byeaglecalculator.com

HOW TO USE

1
Type the number exactly as you have it, including any trailing zeros. Those zeros carry the precision, and this page keeps them rather than parsing them away.
2
Read the significant figure count alongside the answer. If it comes back as a range, the number is ambiguous as written and standard form is what resolves it.
3
Switch to arithmetic for calculations. The page applies the correct rounding rule for the operation and shows you what the other rule would have given, since mixing them up is the usual error.
4
Use engineering notation when the answer needs a unit prefix. Its exponent is always a multiple of three, which is exactly how kilo, mega, milli and micro are spaced.

REFERENCE FORMULAS

Rule	Formula	What it is for
Standard form	a × 10ⁿ with 1 ≤ \|a\| < 10	Exactly one non-zero digit before the point. This is what makes it standard.
Moving the point	left n places → ×10ⁿ; right → ×10⁻ⁿ	The exponent counts the moves. Bigger number, bigger exponent.
E notation	1.5e3 means 1.5 × 10³	What calculators and code use. The e is not Euler’s number.
Engineering form	exponent a multiple of 3	Matches the SI prefixes, so 45,000 is 45 × 10³ — forty-five kilo-something.
Multiply	(a×10ᵐ)(b×10ⁿ) = ab × 10ᵐ⁺ⁿ	Multiply the fronts, add the exponents, then renormalise if needed.
Divide	(a×10ᵐ)÷(b×10ⁿ) = a/b × 10ᵐ⁻ⁿ	Divide the fronts, subtract the exponents.
Add or subtract	match the exponents first	You cannot add the fronts directly. 1.5×10³ + 2.0×10² needs converting first.
Sig figs: × ÷	keep the fewest significant figures	Three sig figs times two sig figs gives two.
Sig figs: + −	keep the fewest decimal places	A different rule. Using the sig-fig one here discards measured digits.
Leading zeros	never significant	0.00123 has three. They only locate the point.
Trailing zeros	significant after a decimal point	1.200 has four. Without a point, 1200 is ambiguous.
Zero itself	has no standard form	No choice of exponent gives a mantissa between 1 and 10.
Negatives	the sign sits on the mantissa	−1.5 × 10³. A negative exponent means small, not negative.
Order of magnitude	the exponent alone	Two numbers three exponents apart differ by a factor of a thousand.

FREQUENTLY ASKED QUESTIONS

RELATED CALCULATORS

5 to the Power of 8

Calculate instantly →

5 to the Power of 10

Calculate instantly →

2 to the Power of 2

Calculate instantly →

4 to the Power of 8

Calculate instantly →

MORE ALGEBRA CALCULATORS

24 Times Table

Calculate instantly →

Quadratic Equation Solver

Calculate instantly →

Logarithm Calculator

Calculate instantly →

Fraction Calculator

Calculate instantly →

Fraction Simplifier

Calculate instantly →

Linear Equation Solver

Calculate instantly →

25 Times Table

Calculate instantly →

26 Times Table

Calculate instantly →

27 Times Table

Calculate instantly →

Simultaneous Equations Solver (2×2)

Calculate instantly →

28 Times Table

Calculate instantly →

Exponent Calculator

Calculate instantly →

29 Times Table

Calculate instantly →

30 Times Table

Calculate instantly →

Times Tables Mega Calculator

Calculate instantly →

Square Root of 10

Calculate instantly →

Square Root of 1

Calculate instantly →

Square Root Mega

Calculate instantly →

Square Root of 2

Calculate instantly →

23 Times Table

Calculate instantly →

Was this calculator helpful?

Last updated: August 4, 2026 · Every digit you type is kept — no parseFloat anywhere · Multiply keeps the fewest significant figures; add keeps the fewest decimal places.