Scientific Notation Calculator

About Scientific Notation Calculator

Convert numbers between standard form and scientific notation, perform arithmetic on numbers in scientific notation, and see engineering notation with SI prefixes. Every conversion shows step-by-step working in both directions.

What Is Scientific Notation?

Scientific notation expresses a number as a coefficient between 1 and 10 multiplied by a power of 10:

a × 10^n where 1 ≤ a < 10

How to convert: Move the decimal point until you have a number between 1 and 10. The number of places you moved is the exponent. Moving left gives a positive exponent (large numbers); moving right gives a negative exponent (small numbers).

Worked example: Convert 6,370,000 to scientific notation

1. Place the decimal after the first digit: 6.370000
2. Count how many places the decimal moved: 6 places to the left
3. Result: 6.37 × 10^6

Worked example: Convert 0.0000042 to scientific notation

1. Place the decimal after the first non-zero digit: 4.2
2. Count how many places the decimal moved: 6 places to the right
3. Result: 4.2 × 10^(-6)

Conversion Reference Table

Standard Form	Scientific Notation	Name
1,000,000,000	1 × 10^9	One billion
1,000,000	1 × 10^6	One million
1,000	1 × 10^3	One thousand
1	1 × 10^0	One
0.001	1 × 10^(-3)	One thousandth
0.000001	1 × 10^(-6)	One millionth
0.000000001	1 × 10^(-9)	One billionth

How to Do Arithmetic in Scientific Notation

The rules differ for multiplication/division vs addition/subtraction:

Multiplication: Multiply coefficients, add exponents

• (3 × 10^4) × (2 × 10^5) = 6 × 10^9

Division: Divide coefficients, subtract exponents

• (8 × 10^7) / (4 × 10^3) = 2 × 10^4

Addition/Subtraction: First make the exponents the same, then add or subtract the coefficients

• (3.5 × 10^4) + (2.1 × 10^3) = (3.5 × 10^4) + (0.21 × 10^4) = 3.71 × 10^4

Detailed worked example (multiplication): Calculate (4.2 × 10^3) × (3.0 × 10^(-5))

1. Multiply coefficients: 4.2 × 3.0 = 12.6
2. Add exponents: 3 + (-5) = -2
3. Intermediate: 12.6 × 10^(-2)
4. Normalise (coefficient must be 1-10): 1.26 × 10^(-1)
5. Standard form: 0.126

Engineering Notation and SI Prefixes

Engineering notation restricts the exponent to multiples of 3, which maps directly to SI prefixes:

SI Prefix	Symbol	Power of 10	Example
Tera	T	10^12	1 TB = 1 × 10^12 bytes
Giga	G	10^9	2.4 GHz = 2.4 × 10^9 Hz
Mega	M	10^6	5 MW = 5 × 10^6 watts
Kilo	k	10^3	47 kΩ = 4.7 × 10^4 ohms
Milli	m	10^(-3)	250 mL = 2.5 × 10^(-1) litres
Micro	μ	10^(-6)	10 μF = 1 × 10^(-5) farads
Nano	n	10^(-9)	5 nm = 5 × 10^(-9) metres
Pico	p	10^(-12)	22 pF = 2.2 × 10^(-11) farads

Engineering notation is standard practice in electronics, physics, and engineering because the prefixes are immediately meaningful. "4.7 × 10^3 ohms" becomes "4.7 kΩ" at a glance.

Famous Constants in Scientific Notation

Constant	Value	Scientific Notation
Speed of light	299,792,458 m/s	2.998 × 10^8 m/s
Avogadro's number	602,214,076,000,000,000,000,000	6.022 × 10^23
Planck's constant	0.000000000000000000000000000000000663	6.63 × 10^(-34) J·s
Electron mass	0.000000000000000000000000000000911	9.11 × 10^(-31) kg
Boltzmann constant	0.0000000000000000000000138	1.38 × 10^(-23) J/K
Earth's mass	5,972,000,000,000,000,000,000,000 kg	5.972 × 10^24 kg

Without scientific notation, numbers at these extremes are nearly impossible to read, compare, or compute with.

Scientific Notation and Significant Figures

One major advantage of scientific notation is that it removes ambiguity about significant figures. The number 4500 could have 2, 3, or 4 sig figs. But 4.5 × 10^3 clearly has 2, while 4.500 × 10^3 clearly has 4. For counting and rounding significant figures, the sig figs calculator handles any number.

Orders of Magnitude

The exponent in scientific notation gives the "order of magnitude" - a rough measure of size. Two numbers are said to differ by one order of magnitude if one is about 10 times the other.

Object/Distance	Size	Order of Magnitude (m)
Proton diameter	~1 fm	10^(-15)
Atom diameter	~0.1 nm	10^(-10)
Human hair width	~75 μm	10^(-5)
Human height	~1.7 m	10^0
Earth diameter	~12,742 km	10^7
Sun diameter	~1.39 million km	10^9
Light-year	~9.46 trillion km	10^16

For exponent calculations directly, the exponent calculator computes any base raised to any power. For handling error in scientific measurements, the percent error calculator compares experimental to theoretical values.

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