Scientific Notation in Depth: From E Notation to SI Prefixes

By WhiteCalc · 2026-11-14

Why scientific notation exists

Some numbers are awkward to write in full. The speed of light is about 299,800,000 metres per second. The mass of an electron is 0.000000000000000000000000000000911 kilograms. Both are easy to get wrong when counting zeros, and neither fits on a small calculator screen.

Scientific notation solves this by writing every number in two parts: a coefficient between 1 and 10 (the "mantissa"), and a power of ten that says how far to move the decimal point.

Form: a × 10ⁿ, where 1 ≤ a < 10 and n is a whole number.

So the speed of light is 2.998 × 10⁸ m/s and the electron mass is 9.11 × 10⁻³¹ kg. Calculators and spreadsheets write the same thing as 2.998E8 and 9.11E-31. The letter E stands for "times ten to the power of". It is not the mathematical constant e (2.718...), even though it looks similar.

Reading and writing the exponent

The exponent tells you which way and how far to move the decimal point.

Positive exponent: the number is big. Move the decimal point to the right by n places. 4.5E3 = 4,500.
Negative exponent: the number is small. Move the decimal point to the left by n places. 4.5E-3 = 0.0045.
Zero exponent: no movement. 7.2E0 = 7.2, because 10 to the power 0 is 1.

To convert an ordinary number into scientific notation: move the decimal point until exactly one non-zero digit is left in front of it, count the moves, and use that count as the exponent.

Ordinary number	Scientific notation	E notation
7,800,000	7.8 × 10⁶	7.8E6
93,000	9.3 × 10⁴	9.3E4
0.00042	4.2 × 10⁻⁴	4.2E-4
0.0000000501	5.01 × 10⁻⁸	5.01E-8
602,200,000,000,000,000,000,000	6.022 × 10²³	6.022E23

For 7,800,000 the decimal point moved 6 places to the left, so the exponent is +6. For 0.00042 it moved 4 places to the right, so the exponent is −4. A quick check on sign: numbers greater than 10 get a positive exponent, and numbers smaller than 1 get a negative one.

Significant figures

The digits in the coefficient show how precisely a number is known. These digits are called significant figures. Scientific notation makes it clear which zeros count.

All non-zero digits count.
Zeros between non-zero digits count (the 0 in 4,005).
Leading zeros never count (0.0042 has two significant figures).
Trailing zeros count only if they come after a decimal point, or are shown explicitly in the coefficient.

The number 1,500 is ambiguous: it might have two, three or four significant figures. Written as 1.5E3 it clearly has two; as 1.500E3 it has four. That is a good reason to use the notation in reports and homework.

When you round, count the digits in the coefficient. Rounding 6.62607E-34 to 3 significant figures gives 6.63E-34. Rounding 299,792,458 to 4 significant figures gives 2.998E8. For a longer discussion of rounding rules, see the rounding guide.

When you combine measured values, the result should not claim more precision than the least precise input. If you multiply 3.2E5 (two significant figures) by 1.4142E-2 (five), report the answer with two significant figures. The raw product is 4.5254E3, which should be written as 4.5E3.

Exponent rules for multiplication and division

This is where scientific notation really helps. Instead of juggling many zeros, you work on the coefficients and exponents separately.

Multiply: multiply the coefficients and add the exponents.
Divide: divide the coefficients and subtract the exponents.
Power: raise the coefficient to the power and multiply the exponent by it.
Add or subtract: first make the exponents equal, then add the coefficients.

Afterwards, check that the coefficient is between 1 and 10. If it is not, shift the decimal point and adjust the exponent.

Multiplication: (4.2E5) × (3E-2). Coefficients: 4.2 × 3 = 12.6. Exponents: 5 + (−2) = 3. That gives 12.6E3, which becomes 1.26E4 = 12,600. Check by ordinary arithmetic: 420,000 × 0.03 = 12,600. ✔

Division: (9E6) ÷ (3E-2). Coefficients: 9 ÷ 3 = 3. Exponents: 6 − (−2) = 8. The result is 3E8 = 300,000,000. Watch the sign: subtracting a negative exponent is the same as adding.

Powers: (3E4)³. Coefficient: 3 × 3 × 3 = 27. Exponent: 4 × 3 = 12. That gives 27E12 = 2.7E13.

Addition: 3.2E5 + 4E4. The exponents differ, so rewrite 4E4 as 0.4E5. Now add the coefficients: 3.2 + 0.4 = 3.6, so the sum is 3.6E5 = 360,000. You cannot simply add the coefficients and exponents separately here.

A real-world calculation: sunlight

The distance from the Earth to the Sun is about 1.496E11 metres, and light travels at about 2.998E8 metres per second. How long does sunlight take to reach us?

Time = distance ÷ speed. Coefficients: 1.496 ÷ 2.998 ≈ 0.499. Exponents: 11 − 8 = 3. So time ≈ 0.499E3 = 499 seconds, about 8.3 minutes. This agrees with the commonly quoted "light takes about 8 minutes from the Sun".

Here is another: Avogadro's constant is 6.022E23 particles per mole. How many particles are in 2 moles? 6.022 × 2 = 12.044, so the answer is 12.044E23 = 1.2044E24. You can type these values into the scientific calculator in E form and see the same result on screen.

SI prefixes: scientific notation with names

The metric system gives common powers of ten their own names, called SI prefixes. They make units shorter and easier to say. Prefixes are written in front of a unit: kilo + metre = kilometre.

Prefix	Symbol	Power of ten	Meaning
tera	T	10¹²	1,000,000,000,000
giga	G	10⁹	1,000,000,000
mega	M	10⁶	1,000,000
kilo	k	10³	1,000
(base unit)		10⁰	1
milli	m	10⁻³	0.001
micro	µ	10⁻⁶	0.000001
nano	n	10⁻⁹	0.000000001
pico	p	10⁻¹²	0.000000000001

Converting with prefixes: replace the prefix with its power of ten.

2.5 GB = 2.5E9 bytes. In megabytes: 2.5E9 ÷ 1E6 = 2.5E3 = 2,500 MB.
350 nm = 350E-9 m = 3.5E-7 m. In micrometres: 3.5E-7 ÷ 1E-6 = 0.35 µm.
70 µm (about the width of a human hair) = 70E-6 m = 7E-5 m = 0.07 mm.
4.7 kΩ = 4.7E3 Ω = 4,700 Ω.

A neat rule: when you move from a smaller prefix to a larger one (nano to micro), the number gets smaller by the ratio of the two prefixes. When you go the other way, it grows. Going from nano to micro divides by 1,000 (3.5E-7 m is 350 nm and 0.35 µm).

Common mistakes

Confusing E with the constant e. 2E3 means 2,000. It does not mean 2 × 2.718³.
Typing the exponent wrongly. To enter 6.674 × 10⁻¹¹, use the E key (or the keyboard E) and enter −11. Do not type 6.674 × 10 and then raise it to −11.
Moving the decimal point the wrong way. A negative exponent means a small number. If 3E-5 looks bigger than 3, something is off.
Forgetting to normalise. 12.6E3 is correct arithmetic but not proper scientific notation. Convert it to 1.26E4.
Adding exponents in a sum. The rule "add exponents" applies to multiplication only. For addition, match the exponents first.
Mixing mega (M) and milli (m). The capital M is one million; the small m is one thousandth. They differ by a factor of one billion.
Overstating precision. Writing 4.52540E3 when your inputs have two significant figures suggests accuracy you do not have.

FAQ

Is 0.5E1 a valid scientific notation number?
It equals 5, but the proper form is 5E0. A normalised coefficient must be at least 1 and less than 10.

How do I enter E notation on a calculator?
Type the coefficient, press the E (or EXP) key, then type the exponent. On a phone or computer keyboard, you can usually type a capital or lowercase e in the display field. Open the scientific calculator and try 6.674E-11 × 5.972E24; the answer is about 3.986E14.

Why do I sometimes see a large number turn into E notation?
Calculators switch to E notation when the number would not fit on the screen, such as 1.2E24. It is the same value, just shown in a compact form.

What is the difference between 1 kilobyte and 1 kibibyte?
Strictly, kilo means exactly 1,000. Computer memory is often counted in powers of 2, where 1 kibibyte (KiB) = 1,024 bytes. Storage makers usually use the decimal prefixes.

Where can I learn more about powers and logarithms?
See the scientific calculator guide for angle modes and order of operations, and the logarithm guide for the reverse operation of powers.

Open the calculator: Scientific Calculator →