Scientific Notation Calculator

Power of 10 Calculator

Use this power of 10 calculator to shift decimal places, convert between metric prefixes, and see how multiplying by 10^n scales any value across standard SI units.

Shift decimal by any power of 10SI metric prefix referenceOrder of magnitude conversion

Calculate powers of 10, shift decimals, and convert coefficient x 10^exponent forms with steps.

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Use fields directly or type expressions such as 4.2e5, 4.2 x 10^5, or 10^-3.

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Result Summary

Decimal result: 1000000
Engineering notation: 1 x 10^6

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Power of 10 Calculator

A power of 10 calculator multiplies or divides a value by 10 raised to any integer exponent, shifting the decimal point left or right by a precise number of places. Powers of 10 underlie the entire SI metric system: kilo means 10³, mega means 10⁶, and nano means 10⁻⁹. Understanding how to scale values by powers of 10 is essential for unit conversion, metric prefix navigation, and interpreting orders of magnitude in science and engineering.

What Is a Power of 10?

A power of 10 is an expression of the form 10^n, where n determines how many times 10 is multiplied (positive n) or divided (negative n) by itself. When n is positive, multiplying by 10^n moves the decimal point n places to the right, making the number larger. When n is negative, it moves the decimal n places to the left, making it smaller. This property makes powers of 10 a natural language for the metric system: 1 kilometer equals 10³ meters, 1 millimeter equals 10⁻³ meters, and 1 nanosecond equals 10⁻⁹ seconds. Every SI prefix corresponds directly to a specific power of 10.

How to Use the Power of 10 Calculator

Enter the value you want to scale and the exponent n you want to apply. For positive n, the result is the input multiplied by 10^n. For negative n, the result is the input divided by 10^|n|. The calculator accepts any real number as the base value and any integer as the exponent, including zero.

Click Calculate to see the scaled value, the decimal shift described step by step, and the corresponding SI prefix if one exists for the chosen exponent. The output also shows the value expressed in prefix notation where applicable, such as kilowatts or microseconds.

Worked Examples

Examples: 3.5 × 10^3 = 3500 (decimal shifts right 3 places); 7.2 × 10^(−4) = 0.00072 (shifts left 4 places); 1 × 10^6 matches the mega prefix; 5 × 10^(−9) matches the nano prefix; and 1000 × 10^(−3) = 1 (back to the base unit).

Common Power of 10 Problems

Common problems include converting between metric prefixes (milligrams to grams, kilowatts to watts), interpreting the scale of physical constants (electron radius ≈ 10^(−15) m), and applying unit analysis steps in chemistry and physics problem sets.

Powers of 10 and SI Prefix Reference

These tables cover the standard SI metric prefixes and the decimal shift rules for multiplying and dividing by powers of 10.

SI metric prefixes: large magnitudes

These prefixes multiply a base unit by increasingly large powers of 10, from kilo (thousands) upward to tera (trillions).

Prefix	Symbol	Power	Multiplier
kilo	k	10^3	1,000
mega	M	10^6	1,000,000
giga	G	10^9	1,000,000,000
tera	T	10^12	1,000,000,000,000

SI metric prefixes: small magnitudes

These prefixes divide a base unit by increasingly large powers of 10, from milli (thousandths) down to pico (trillionths).

Prefix	Symbol	Power	Fraction
milli	m	10^(−3)	0.001
micro	μ	10^(−6)	0.000001
nano	n	10^(−9)	0.000000001
pico	p	10^(−12)	0.000000000001

Decimal shift: positive exponents

Multiplying by 10^n with positive n moves the decimal point n places to the right, increasing the value.

Value	Exponent	Decimal shift	Result
3.57	10^2	2 places right	357
0.0081	10^4	4 places right	81

Decimal shift: negative exponents

Multiplying by 10^(−n) with positive n moves the decimal point n places to the left, decreasing the value.

Value	Exponent	Decimal shift	Result
1800	10^(−3)	3 places left	1.8
500	10^(−5)	5 places left	0.005

Orders of magnitude in science

An order of magnitude is a factor of 10. Comparing the orders of magnitude of two quantities shows how many times larger one is than the other.

Object or quantity	Approximate size	Power of 10	Unit
Hydrogen atom radius	5.3 × 10^(−11) m	10^(−11)	m
Earth radius	6.4 × 10^6 m	10^6	m
Distance to Sun	1.5 × 10^11 m	10^11	m

Converting between metric prefixes

To convert between prefixes, find the exponent difference and shift the decimal by that amount.

From	To	Exponent change	Conversion
kilometers	meters	+3	1 km = 1000 m
milliseconds	seconds	−3	1 ms = 0.001 s
megawatts	kilowatts	+3 relative	1 MW = 1000 kW

Powers of 10 on a scale

Powers of 10 grow exponentially, not linearly. Each step multiplies or divides by 10, so adjacent powers differ by a factor of 10.

Exponent	Value	Comparison to 10^0	Example
10^3	1,000	1000× larger than 1	1 kilometer
10^0	1	reference point	1 meter
10^(−3)	0.001	1000× smaller than 1	1 millimeter

Process

Calculation Workflow

Enter value and exponent

Shift decimal point

Match SI prefix

Return scaled result

The calculator takes the input value and exponent, shifts the decimal left or right by the appropriate number of places, checks for a matching SI prefix, and returns the result in standard decimal notation with any applicable prefix form.

Input Formats

Supported Formats

Input style	Example
Value × 10^n	3.5 × 10^3
Negative exponent	1.2 × 10^(−6)
Metric prefix conversion	2.5 km to m
Order of magnitude	10^9 = giga

Reference

Common Scientific Constants

Back to calculator

Constant name	Symbol	Notation value	Unit
Speed of light	c	2.99792458 x 10^8	m/s
Gravitational constant	G	6.67430 x 10^-11	N m^2/kg^2
Avogadro constant	NA	6.02214076 x 10^23	mol^-1

Questions

Calculator FAQ

What is a power of 10?

A power of 10 is a number expressed as 10 raised to an integer exponent: 10^n. Positive exponents produce numbers greater than 1, negative exponents produce numbers less than 1, and 10^0 equals 1.

What does 10^3 equal?

10^3 equals 1,000. The exponent 3 means multiplying 10 by itself three times: 10 × 10 × 10 = 1,000. The SI prefix kilo represents this value.

What does 10^(−6) equal?

10^(−6) equals 0.000001, or one millionth. The SI prefix micro represents this value. For example, 1 micrometer = 10^(−6) meters.

How do I convert kilometers to meters using powers of 10?

Multiply by 10^3, because the prefix kilo = 10^3. Moving the decimal 3 places right: 2.5 km × 10^3 = 2500 m.

How do I convert nanoseconds to seconds?

Multiply by 10^(−9), because nano = 10^(−9). Move the decimal 9 places left: 250 ns = 250 × 10^(−9) s = 2.5 × 10^(−7) s.

What is an order of magnitude?

An order of magnitude is a factor of 10. If one value is 1,000 times larger than another, it is three orders of magnitude larger (10^3). Orders of magnitude help scientists compare very different-sized quantities quickly.

What are the SI prefixes for powers of 10?

The main SI prefixes from large to small are: tera (10^12), giga (10^9), mega (10^6), kilo (10^3), milli (10^−3), micro (10^−6), nano (10^−9), and pico (10^−12).

How does multiplying by a power of 10 affect the decimal point?

Multiplying by 10^n moves the decimal point n places to the right for positive n, and n places to the left for negative n. For example, 4.5 × 10^2 = 450 and 4.5 × 10^(−2) = 0.045.

What is 10^0?

10^0 = 1. Any non-zero number raised to the power zero equals 1. This is the reference point on the SI scale—the base unit itself with no prefix applied.

How many orders of magnitude is 1 km compared to 1 mm?

1 km = 10^3 m and 1 mm = 10^(−3) m. The difference in exponents is 3 − (−3) = 6, so they differ by 6 orders of magnitude, or a factor of 1,000,000.

What is the giga prefix?

Giga represents 10^9, or one billion. It is used in computing (gigabyte), networking (gigabit), and radio frequency (gigahertz).

How do powers of 10 relate to logarithms?

The base-10 logarithm of a power of 10 equals the exponent: log₁₀(10^n) = n. Taking log base-10 of a value gives its order of magnitude directly.

Why do scientists use powers of 10?

Powers of 10 compress extremely large or small quantities into compact notation. Writing the mass of an electron as 9.11 × 10^(−31) kg is far cleaner than writing 30 digits.

What is the difference between this calculator and a scientific notation calculator?

A power of 10 calculator focuses on scaling by 10^n—shifting decimal places and mapping to SI prefixes. A scientific notation calculator performs arithmetic on values already written in scientific notation format.

How do I convert megawatts to watts?

Multiply by 10^6 because mega = 10^6. For example, 3.5 MW × 10^6 = 3,500,000 W = 3.5 × 10^6 W.