Scientific Notation Calculator
Scientific Notation Calculator
Convert very large and very small numbers into scientific notation. Enter a number to express it in the form a × 10ⁿ, making values easier to read, compare and calculate.
Enter your number
Enter a number and select Calculate.
Free Scientific Notation Calculator
Use this free scientific notation calculator to convert ordinary decimal numbers into scientific notation quickly and accurately. Scientific notation, also called standard form or exponential notation, represents a number as a coefficient multiplied by a power of 10. It is especially useful when working with extremely large values, very small decimals, measurements and numbers containing many zeros.
Enter any valid number in the calculator to express it in the standard scientific notation format a × 10ⁿ. The coefficient (also called the significand or mantissa) is adjusted so that its absolute value is at least 1 and less than 10. The exponent shows how many places the decimal point has moved.
How to use this scientific notation converter
- Enter the number you want to convert in the Number field. You can enter a whole number, decimal or negative value.
- Select Calculate to convert the value into scientific notation.
- Read the coefficient and the power-of-10 exponent in the result.
- Use Clear to remove the current input and start a new conversion.
Scientific notation formula
Scientific notation: N = a × 10ⁿ
For a non-zero number, 1 ≤ |a| < 10 and n is an integer. The coefficient a retains the sign of the original number, while the exponent n indicates the decimal-point shift.
When converting a number greater than or equal to 10, the decimal point is moved to the left and the exponent is positive. For a non-zero number with an absolute value less than 1, the decimal point is moved to the right and the exponent is negative. The number zero is written as 0 and does not need a power-of-ten exponent.
Scientific notation examples
Example 1: Large number
45,000 = 4.5 × 10⁴
The decimal point moves four places to the left, so the exponent is positive four.
Example 2: Small decimal
0.00072 = 7.2 × 10⁻⁴
The decimal point moves four places to the right, so the exponent is negative four.
Example 3: Negative number
−6,300,000 = −6.3 × 10⁶
The coefficient remains negative, and the exponent is positive six.
Where is scientific notation used?
- Science and chemistry: expressing very small measurements, atomic-scale quantities and large particle counts.
- Physics and astronomy: writing distances, masses, energy values and other measurements that span a wide range.
- Mathematics: simplifying calculations with powers of ten and comparing numbers with different magnitudes.
- Engineering and computing: communicating large or tiny measurements and numerical values in a compact form.
Scientific notation, standard form and significant figures
Scientific notation and standard form are commonly used to describe the same coefficient-times-power-of-ten representation. The coefficient communicates the digits of the value, while the exponent communicates its scale. When a measurement has a required level of precision, significant figures should also be considered. Converting a number into scientific notation does not, by itself, determine the measurement's accuracy.
Frequently asked questions
1. What is scientific notation?
Scientific notation is a compact way to write a number as a coefficient multiplied by a power of ten. For a non-zero number, the coefficient has an absolute value of at least 1 and less than 10.
2. How do I convert a number to scientific notation?
Move the decimal point until one non-zero digit remains to its left. Count the places moved: use a positive exponent when moving left and a negative exponent when moving right.
3. What does the exponent mean in scientific notation?
The exponent tells you the power of 10 used to scale the coefficient. A positive exponent generally represents a large magnitude, while a negative exponent represents a non-zero magnitude smaller than 1.
4. Can scientific notation be used for negative numbers?
Yes. Keep the negative sign with the coefficient. For example, −4,500 is written as −4.5 × 10³.
5. How do I write a small decimal in scientific notation?
Move the decimal point to the right until the coefficient is between 1 and 10 in absolute value. The number of places moved becomes a negative exponent.
6. How do I write a large number in scientific notation?
Move the decimal point to the left until the coefficient is between 1 and 10 in absolute value. The number of places moved becomes a positive exponent.
7. Is scientific notation the same as standard form?
In many mathematics and science contexts, scientific notation and standard form refer to the same format: a coefficient multiplied by a power of ten. Terminology can vary by region or subject.
8. What is the scientific notation of zero?
Zero is written simply as 0. It does not have a unique normalized coefficient and integer exponent in the usual scientific notation format.
9. Why is scientific notation useful?
It makes very large and very small numbers easier to read, compare and use in calculations. It also reduces long strings of zeros and clearly shows the order of magnitude.
10. Does scientific notation show significant figures?
The coefficient can show the digits being reported, including significant figures, but the notation alone does not tell you the measurement uncertainty. Follow the precision required by your question or measurement.
Related calculators
Explore these related SRIKAMI calculators for working with powers, roots, number formats and numerical precision.