Scientific Notation Calculator

1. Enter any number, however large or small.
2. Read the scientific notation, a coefficient times a power of ten.
3. See the E notation used by calculators and code.
4. See the engineering notation, which uses exponents in steps of three.

Here is what each result means:

Scientific notation writes a number as a coefficient between 1 and 10 multiplied by a power of ten, such as 6.5 x 10^6. It is a compact way to handle very large or very small numbers without writing long strings of zeros. The exponent tells you the order of magnitude, how many places the decimal point has moved.

Scientists and engineers rely on it constantly. The speed of light, the size of an atom and the distance to a star are all far clearer in scientific notation than in full decimal form. It also makes multiplying and dividing such numbers straightforward, since you add or subtract the exponents.

It finds the power of ten equal to the order of magnitude, then divides to get the coefficient.

1. Find the exponent as the whole part of the base-ten logarithm.
2. Divide the number by ten to that power for the coefficient.
3. For engineering notation, round the exponent down to a multiple of three.

Powers of ten are just exponents, so the exponent calculator and logarithm calculator are close companions.

Write 6,500,000 and 0.00042 in scientific notation.

Calculation: for the large number, move the decimal point 6 places left to get 6.5 x 10^6. For the small one, move it 4 places right, giving a negative exponent, 4.2 x 10^-4. In engineering notation the small number is 420 x 10^-6.

The exponent is the order of magnitude, and its sign shows the size of the number.

A positive exponent means a number bigger than one; a negative exponent means a number between zero and one.

Three ways to write the same value differ in where the exponent can sit.

Engineering notation lines up with unit prefixes like kilo, mega and micro, which is why engineers prefer it.

The Size of the Number

Each factor of ten adds one to the exponent, so bigger numbers give larger positive exponents.

Numbers Below One

Values between zero and one give negative exponents, one for each leading zero after the point.

The Chosen Form

Engineering notation shifts the exponent to a multiple of three, so its coefficient can be up to three digits.

Science Homework

Convert measurements like mass, distance or charge into a compact, comparable form.

Engineering and Units

Use engineering notation to match kilo, mega and micro prefixes.

Reading Calculator Output

Translate E notation from a calculator or spreadsheet back into a clear power of ten.

1. a Coefficient Outside 1 to 10

Proper scientific notation keeps one nonzero digit before the point. 42 x 10^3 should be 4.2 x 10^4.

2. Wrong Sign on the Exponent

Small numbers below one have negative exponents. Moving the point right makes the exponent negative.

3. Miscounting Decimal Moves

Count every place the decimal point moves. A miscount changes the exponent.

4. Confusing E in E Notation

The e here means times ten to the power, not the number e from natural logs.

5. Dropping Significant Digits

Keep the meaningful digits in the coefficient; do not round away precision you need.

The conversion is exact; only a long coefficient is rounded for display.

It writes a number as a coefficient between 1 and 10 times a power of ten, such as 6.5 times 10 to the 6th for 6,500,000. It is a compact way to handle very large or very small numbers.

Move the decimal point until one nonzero digit is in front, then count the moves for the exponent. Moving left gives a positive exponent, moving right a negative one. This tool does it for you.

It is the order of magnitude, the number of places the decimal point moved. A positive exponent means a number bigger than one, and a negative exponent means a number between zero and one.

E notation writes the same value with an e in place of times ten to the power, so 4.5 times 10 to the 4th becomes 4.5e+4. Calculators and spreadsheets use it to fit numbers on a screen.

It is like scientific notation but the exponent is always a multiple of three, so it lines up with unit prefixes like kilo, mega and micro. So 45,000 is 45 times 10 to the 3rd.

A number between zero and one is less than a single unit, so it equals a coefficient times ten to a negative power. Each leading zero after the decimal point adds one to the negative exponent.

No. The e in E notation just means times ten to the power. It is not the mathematical constant e, about 2.718, used in natural logarithms.

To multiply, you multiply the coefficients and add the exponents; to divide, you subtract the exponents. That turns unwieldy numbers into simple steps.

No. The calculation runs in your browser and nothing you enter is stored or sent anywhere, unless you choose Save, which keeps the result only on this device.

• Scientific notation (Wikipedia).
• Scientific notation explained (Maths Is Fun).
• Engineering notation (Wikipedia).