Scientific Notation Calculator
Convert any number to scientific, E or engineering notation and back, or calculate with two numbers in scientific notation, with steps.
Type 45600000, 4.56e7, 4.56E7 or 4.56 × 10^7. Commas and spaces are ignored.
The decimal point moves 7 places to the left, so the exponent is positive.
Other ways to write it
The same value in each common format. All of them are equal.
| Format | Value |
|---|---|
| Standard form | 45,600,000 |
| E notation | 4.56E7 |
| Engineering notation | 45.6 × 10⁶ |
| With an SI prefix | 45.6 mega (M) |
Your calculation
The same steps the calculator runs, with your numbers.
- Start with 45,600,000.
- Move the decimal point 7 places to the left to get 4.56, a number at least 1 and less than 10.
- The point moved left, so the exponent is positive: 7.
- Trailing zeros in a whole number without a decimal point are treated as placeholders, so the number has 3 significant figures.
- Result: 4.56 × 10⁷
Your number with SI prefixes
Engineering notation uses powers of 10 in steps of 3, which match the metric prefixes. The highlighted row keeps the number between 1 and 1,000.
| Prefix | Power of 10 | Your number |
|---|---|---|
| None | 10⁰ | 45,600,000 |
| kilo (k) | 10³ | 45,600 |
| mega (M) | 10⁶ | 45.6 |
| giga (G) | 10⁹ | 0.0456 |
| tera (T) | 10¹² | 0.0000456 |
Digits are handled as exact decimals, not floating point, so long coefficients and exponents up to ±100,000 keep every digit. Rounding uses round half up.
What Is Scientific Notation?
Scientific notation writes a number as a coefficient multiplied by a power of 10, in the form a × 10ⁿ. The coefficient a is at least 1 and less than 10, and the exponent n is a whole number. OpenStax Prealgebra defines it this way: the first factor is greater than or equal to 1 but less than 10, and the second factor is a power of 10 in exponential form.
The format keeps very large and very small numbers short and easy to compare. The speed of light, 299,792,458 meters per second, becomes 2.99792458 × 10⁸, and the charge of one electron in coulombs, 0.0000000000000000001602176634, becomes 1.602176634 × 10⁻¹⁹. The exponent tells you the size at a glance: each step of 1 is a factor of 10.
A positive exponent means the number is 10 or more, a negative exponent means it is between 0 and 1, and an exponent of 0 means it is already between 1 and 10. Scientific notation is also called standard index form in some countries, while the ordinary written number is often called standard form or decimal notation.
How to Use the Scientific Notation Calculator
- Choose a mode. Convert a number changes one number between formats. Calculate multiplies, divides, adds or subtracts two numbers that can be in any format.
- Type the number. Ordinary numbers such as 45,600,000 or 0.000456 work, and so do 4.56e7, 4.56E7, 4.56 × 10^7, 4.56x10^7 and 4.56 × 10⁷ with superscript digits. Negative numbers and negative exponents both work, as in −3.2 × 10^−7.
- Pick the precision. Keep digits as entered shows every significant digit. Choose a number of significant figures to round, or pick significant figure rules in Calculate mode to round the answer the way a chemistry or physics class expects.
- Read the results. If you typed an ordinary number, the answer is its scientific notation. If you typed scientific notation, the answer is the standard form. The table below shows E notation, engineering notation and the SI prefix form, and the steps show how the decimal point moved.
The calculator works with exact decimal digits rather than the binary floating point numbers most calculators use, so 6.02214076 × 10²³ keeps all nine digits and divisions are correct to 15 significant figures.
How to Convert to Scientific Notation
OpenStax gives a four step method: move the decimal point so the first factor is at least 1 and less than 10, count the places moved, write the number as a product with a power of 10, and check. Moving left gives a positive exponent and moving right gives a negative one.
To check, multiply back: 4.56 × 10,000,000 = 45,600,000. The zeros at the end of a whole number and at the start of a small decimal disappear, because the exponent now records where the decimal point belongs.
Scientific Notation to Standard Form
To write a number in scientific notation as an ordinary number, move the decimal point the number of places shown by the exponent. Move right for a positive exponent and left for a negative one, and fill empty places with zeros.
A quick check on the last two: the Avogadro number has 24 digits before the decimal point, one more than its exponent of 23. The electron charge has 18 zeros after the decimal point before the first digit 1, one fewer than 19.
Multiplying and Dividing in Scientific Notation
Because powers of 10 multiply by adding exponents, you can handle the coefficients and the powers separately. Multiply or divide the coefficients, add or subtract the exponents, and then normalize so the coefficient is between 1 and 10 again.
In the first example, 12.8 is not between 1 and 10, so the decimal point moves one place left and the exponent goes up by 1, from 8 to 9. If a division gives a coefficient below 1, such as 0.5 × 10⁶, move the point one place right and subtract 1 from the exponent: 5 × 10⁵. Watch the signs when subtracting a negative exponent: 8 − (−2) = 10.
Adding and Subtracting in Scientific Notation
Addition and subtraction need matching powers of 10 first. Rewrite the number with the smaller exponent so it uses the larger exponent, add or subtract the coefficients, and keep the shared power.
To rewrite 4.5 × 10³ with 10⁵, the exponent goes up by 2, so the decimal point in the coefficient moves 2 places left to keep the value the same: 0.045. When the exponents are far apart, the smaller number barely changes the larger one, which is why 3.2 × 10⁵ + 4.5 × 10³ is still close to 3.2 × 10⁵.
Significant Figures in Scientific Notation
Every digit in the coefficient is significant, and the power of 10 only locates the decimal point. OpenStax Chemistry explains that leading zeros are never significant, while trailing zeros to the left of the decimal point are ambiguous. Scientific notation removes the doubt: 1,300 could have 2, 3 or 4 significant figures, but 1.3 × 10³, 1.30 × 10³ and 1.300 × 10³ each state their precision.
When you type a whole number without a decimal point, this calculator treats trailing zeros as placeholders, so 45,600,000 has 3 significant figures. Type 45,600,000. with a final decimal point, or 4.5600 × 10^7, to keep the zeros. Trailing zeros after a decimal point always count: 0.0004560 has 4.
Rounding a calculation
| Operation | Rule | Example |
|---|---|---|
| × and ÷ | Keep the fewest significant figures of any input | 0.6238 × 6.6 = 4.11708 → 4.1 |
| × and ÷ | Keep the fewest significant figures of any input | 421.23 ÷ 486 = 0.866728… → 0.867 |
| + and − | Round to the least precise decimal place | 1.0023 + 4.383 = 5.3853 → 5.385 |
| + and − | Round to the least precise decimal place | 486 − 421.23 = 64.77 → 65 |
E Notation and Engineering Notation
E notation is how calculators, spreadsheets and programming languages display scientific notation. The letter E means times 10 to the power that follows, so 4.56E7 is 4.56 × 10⁷ and 1.6E-19 is 1.6 × 10⁻¹⁹. Many languages accept a lowercase e, as in 4.56e7.
Engineering notation restricts the exponent to multiples of 3 and lets the coefficient run from 1 up to 1,000. That matches the metric prefixes, so 0.000456 = 456 × 10⁻⁶, which reads directly as 456 micro, for example 456 μm. Likewise 45,600,000 watts is 45.6 × 10⁶ W, or 45.6 MW.
SI Prefixes and Powers of Ten
NIST lists 24 SI prefixes from quecto (10⁻³⁰) to quetta (10³⁰). The four newest, ronna, quetta, ronto and quecto, were added in 2022. These are the common ones:
| Prefix | Symbol | Power | Name |
|---|---|---|---|
| tera | T | 10¹² | trillion |
| giga | G | 10⁹ | billion |
| mega | M | 10⁶ | million |
| kilo | k | 10³ | thousand |
| none | 10⁰ | one | |
| milli | m | 10⁻³ | thousandth |
| micro | μ | 10⁻⁶ | millionth |
| nano | n | 10⁻⁹ | billionth |
| pico | p | 10⁻¹² | trillionth |
Common Numbers in Scientific Notation
These values come up often in homework and science. The physical constants are exact by definition in the SI, according to the 2022 CODATA values published by NIST.
| Quantity | Standard form | Scientific notation |
|---|---|---|
| One thousand | 1,000 | 1 × 10³ |
| One million | 1,000,000 | 1 × 10⁶ |
| One billion | 1,000,000,000 | 1 × 10⁹ |
| One trillion | 1,000,000,000,000 | 1 × 10¹² |
| One millionth | 0.000001 | 1 × 10⁻⁶ |
| Speed of light (m/s) | 299,792,458 | 2.99792458 × 10⁸ |
| Avogadro constant (per mol) | 602,214,076,000,000,000,000,000 | 6.02214076 × 10²³ |
| Elementary charge (C) | 0.0000000000000000001602176634 | 1.602176634 × 10⁻¹⁹ |
Common Mistakes
- Leaving the coefficient at 10 or more. 45.6 × 10⁶ equals 4.56 × 10⁷, but only the second is in scientific notation.
- Getting the exponent sign backward. Numbers below 1 have negative exponents. 0.0052 is 5.2 × 10⁻³, not 5.2 × 10³.
- Confusing a negative number with a negative exponent. −5.2 × 10³ is −5,200, while 5.2 × 10⁻³ is 0.0052.
- Adding exponents when adding numbers. Exponents add only in multiplication. For addition, match the exponents first.
- Dropping significant zeros. 1.30 × 10³ and 1.3 × 10³ are equal in value but state different precision.
Related Calculations
For powers with any base, including negative and fractional exponents, use the Exponent Calculator. To find the exponent itself, such as the power of 10 that gives a number, use the Log Calculator.
To round a result to a set number of decimal places or significant figures, use the Rounding Calculator. For full expressions with E notation, use the Scientific Calculator, and for converting units that differ by powers of 10, use the Conversion Calculator.
Frequently Asked Questions
How do you write a number in scientific notation?
Move the decimal point until exactly one nonzero digit sits to its left, then count how many places it moved. That count is the exponent of 10. If the original number is 10 or more, the exponent is positive, and if it is between 0 and 1, the exponent is negative. For example, 37,000 becomes 3.7 × 10⁴ because the point moves 4 places left, and 0.0052 becomes 5.2 × 10⁻³ because it moves 3 places right. The first factor must be at least 1 and less than 10.
How do you convert scientific notation to standard form?
Look at the exponent and move the decimal point that many places. A positive exponent moves it to the right and makes the number larger, and a negative exponent moves it to the left and makes it smaller. Fill any empty places with zeros. For example, 6.02214076 × 10²³ becomes 602,214,076,000,000,000,000,000, and 4.56 × 10⁻⁴ becomes 0.000456. An exponent of 0 means the number stays the same, because 10⁰ equals 1.
How do you multiply numbers in scientific notation?
Multiply the two coefficients and add the exponents, then rewrite the result so the coefficient is between 1 and 10. For (3.2 × 10⁵) × (4 × 10³), multiply 3.2 × 4 = 12.8 and add 5 + 3 = 8 to get 12.8 × 10⁸. Because 12.8 is 10 or more, move the decimal point one place left and add 1 to the exponent: 1.28 × 10⁹. To divide, divide the coefficients and subtract the exponents, so (9 × 10⁸) ÷ (3 × 10⁻²) = 3 × 10¹⁰.
How do you add numbers in scientific notation?
First rewrite the numbers so they have the same power of 10, then add or subtract the coefficients and keep that power. For 3.2 × 10⁵ + 4.5 × 10³, rewrite 4.5 × 10³ as 0.045 × 10⁵. Then 3.2 + 0.045 = 3.245, so the sum is 3.245 × 10⁵, which is 324,500. Subtraction works the same way: 5.0 × 10⁴ − 2.5 × 10³ = 5.0 × 10⁴ − 0.25 × 10⁴ = 4.75 × 10⁴. Normalize the answer if the coefficient ends up below 1 or at 10 or more.
How many significant figures are in scientific notation?
Every digit in the coefficient is significant, and the power of 10 only places the decimal point. So 4.56 × 10⁻⁴ has 3 significant figures and 1.30 × 10³ has 3, because the written trailing zero counts. This is why scientific notation removes the doubt in numbers like 1,300, which could have 2, 3 or 4 significant figures. Written as 1.3 × 10³, 1.30 × 10³ or 1.300 × 10³, the precision is clear. Leading zeros, as in 0.000456, are never significant.
What does E mean on a calculator?
E stands for exponent and means times 10 to the power that follows. A calculator showing 4.56E7 means 4.56 × 10⁷, or 45,600,000, and 1.6E-19 means 1.6 × 10⁻¹⁹. Spreadsheets and programming languages use the same format, often with a lowercase e. When you type a number this way on a calculator, the EE or EXP key already supplies the times 10 part, so enter 4.56 EE 7, not 4.56 × 10 EE 7, which would give a number 10 times too large.
Sources & References
- OpenStax. Prealgebra 2e, 10.5 Integer Exponents and Scientific Notation (definition of scientific notation, converting to and from decimal notation, multiplying and dividing). openstax.org
- OpenStax. Chemistry 2e, 1.5 Measurement Uncertainty, Accuracy, and Precision (significant figures, trailing zero ambiguity, rounding rules for calculations). openstax.org
- NIST Office of Weights and Measures. Metric (SI) Prefixes (24 prefixes from 10⁻³⁰ to 10³⁰, symbols, 2022 additions). nist.gov
- NIST. CODATA Value: speed of light in vacuum (2022 CODATA, exact). physics.nist.gov
- NIST. CODATA Value: Avogadro constant (2022 CODATA, exact). physics.nist.gov
- NIST. CODATA Value: elementary charge (2022 CODATA, exact). physics.nist.gov
Results are for educational purposes. Every number on this page was recomputed with the same code the calculator uses. Methodology reviewed: 2026.