Scientific Notation Calculator
Accepts 12500, 0.00042, 1.25e4 or 1.25 x 10^4.
Scientific notation:
Engineering notation:
Standard (decimal) form:
Calculator (E) notation:
Significant figures:
SI prefix (engineering):
Calculation:
This calculator turns any number into scientific and engineering notation, and works the other way too: type 1.25e4 or 1.25 x 10^4 and you get 12500. It also adds, subtracts, multiplies and divides numbers in scientific notation with the steps on screen, counts significant figures and rounds. The drawing places your number on a powers-of-ten scale, from a proton to the observable universe.
Further down you will find the rules, worked examples, reference tables and the most common questions.
How to use the scientific notation calculator?
Step 1: Pick what you want to do from the list: convert a number, do arithmetic on two numbers, or count significant figures and round.
Step 2: Type the number. It accepts 12500, 0.00042, 1.25e4 and 1.25 x 10^4. A decimal point or comma both work.
Step 3: Press Calculate or the Enter key. The result updates as you type.
Step 4: Read the results, see where the number lands on the scale (read as a length in meters) and check the Calculation box.
Rules of scientific notation
A number in scientific notation is written as a coefficient between 1 and 10 times a power of 10:
| N = a × 10n, with 1 ≤ |a| < 10 and n an integer |
A large number has a positive exponent, and a number below 1 has a negative one. Engineering notation is similar, but the exponent is always a multiple of 3 and the coefficient runs from 1 to 999, which ties it to prefixes like kilo, mega and micro.
To multiply and divide, operate on the coefficients and add or subtract the exponents. To add and subtract, first make the exponents equal:
| (a × 10m) × (b × 10n) = (a × b) × 10m + n |
| (a × 10m) ÷ (b × 10n) = (a ÷ b) × 10m - n |
If the coefficient of the result falls outside 1 to 10, move the point and adjust the exponent. Significant figures are the digits that carry precision: count from the first nonzero digit. In a product or quotient the result keeps as many figures as the factor with the fewest. In a sum or difference you round to the place of the least precise number.
Examples of scientific notation
Example 1: Convert 45,600,000
The point moves 7 places to the left: 45600000 = 4.56 × 107
Engineering notation: the exponent 7 is not a multiple of 3, so use 6: 45.6 × 106
Example 2: Convert 0.000832
The point moves 4 places to the right: 0.000832 = 8.32 × 10-4
Engineering notation: 832 × 10-6, which is 832 micro (µ) of the unit.
Example 3: Multiply (3.2 × 10⁵) × (4.5 × 10⁻²)
(3.2 × 4.5) × 105 + (-2) = 14.4 × 103
The coefficient is above 10, so move the point: 1.44 × 104
Both factors have 2 significant figures, so the result keeps 2: 1.4 × 104
Example 4: Add (6.5 × 10⁴) + (3.2 × 10³)
Same power, 104: 6.5 × 104 + 0.32 × 104
(6.5 + 0.32) × 104 = 6.82 × 104
The least precise number ends at the 103 place, so the rounded result is 6.8 × 104
Table: the same number in three forms
| Standard form | Scientific | Engineering |
|---|---|---|
| 4500000 | 4.5 × 106 | 4.5 × 106 |
| 0.00032 | 3.2 × 10-4 | 320 × 10-6 |
| 602000000000000000000000 | 6.02 × 1023 | 602 × 1021 |
| 299792458 | 2.99792458 × 108 | 299.792458 × 106 |
| 0.0000000001 | 1 × 10-10 | 100 × 10-12 |
Table of SI prefixes and powers of 10
| Power | Prefix | Standard form |
|---|---|---|
| 10-9 | nano (n) | 0.000000001 |
| 10-6 | micro (µ) | 0.000001 |
| 10-3 | milli (m) | 0.001 |
| 103 | kilo (k) | 1000 |
| 106 | mega (M) | 1000000 |
| 109 | giga (G) | 1000000000 |
| 1012 | tera (T) | 1000000000000 |
Frequently asked questions
How do you write a number in scientific notation?
Move the decimal point until one nonzero digit is left of it, and the number of places moved is the exponent. For 45600000 the point moves 7 places: 4.56 × 107. Numbers below 1 get a negative exponent.
What is the difference between scientific and engineering notation?
In engineering notation the exponent is a multiple of 3. The same number 45600000 is 4.56 × 107 in scientific and 45.6 × 106 in engineering, which reads straight off as 45.6 mega.
How do you multiply and divide numbers in scientific notation?
Multiply (or divide) the coefficients and add (or subtract) the exponents. If the coefficient lands outside 1 to 10, adjust it: (3.2 × 10⁵) × (4.5 × 10⁻²) = 14.4 × 10³ = 1.44 × 104.
How do you add and subtract numbers in scientific notation?
First write them with the same exponent, then add or subtract the coefficients. For example, 6.5 × 10⁴ + 3.2 × 10³ is 6.5 × 10⁴ + 0.32 × 10⁴ = 6.82 × 104.
How many significant figures does a number have?
Count from the first nonzero digit, and trailing zeros after the decimal point count. 0.004500 has 4 figures. Zeros at the end of a whole number, as in 1200, are ambiguous: the calculator counts 2, and if you type 1.200e3 it counts 4.
Learn more
- Examples of scientific notation
- Laws of exponents: definition and examples
- Examples of negative exponents
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