1. Choose a conversion direction
Convert an ordinary decimal into scientific notation or expand coefficient-and-exponent form into a decimal.
Powers-of-ten and precision calculator
Scientific Notation Calculator
Convert decimal numbers to normalized scientific notation, expand scientific notation into standard form, calculate with powers of ten, and compare scientific and engineering notation with significant-figure control.
Two-way conversion
Scientific operations
Significant figures
Scientific notation
6.022 × 10²³
Coefficient
6.022
Exponent
23
Convert and calculate scientific notation
Select a mode, enter the number or scientific components, and review normalized notation, standard form, engineering notation, significant figures, and decimal movement.
JavaScript number precision is limited for extremely large values
and very long exact integers. The calculator preserves the requested
significant figures, but values beyond normal floating-point
precision should be verified with specialist arbitrary-precision
software.
How the Scientific Notation Calculator works
A number in normalized scientific notation uses a coefficient whose absolute value is at least 1 and less than 10, multiplied by a power of ten. The exponent tells how far and in which direction to move the decimal point.
2. Set the significant figures
Control the displayed precision while keeping the coefficient normalized.
3. Perform arithmetic
Multiply, divide, add, or subtract scientific-notation values with operation-specific precision rules.
Scientific Notation
a × 10^n, where 1 ≤ |a| < 10
Multiplication
(a × 10^m)(b × 10^n) = (ab) × 10^(m+n)
Division
(a × 10^m) ÷ (b × 10^n) = (a ÷ b) × 10^(m−n)
Exponent type
Decimal movement
Example
Positive exponent
Move the decimal right
4.2 × 10^3 becomes 4,200 because the decimal moves three places to the right.
Negative exponent
Move the decimal left
4.2 × 10^-3 becomes 0.0042 because the decimal moves three places to the left.
Zero exponent
No movement
Any non-zero coefficient multiplied by 10^0 remains unchanged because 10^0 equals 1.
Engineering notation
Exponent is a multiple of three
The coefficient may range from 1 to less than 1,000, making it convenient for metric-prefix interpretation.
Frequently asked questions
Important details for converting and calculating scientific notation.
What is scientific notation?
Scientific notation writes a number as a coefficient multiplied by a power of ten, usually with the coefficient between 1 and 10 in absolute value.
How do I convert a decimal to scientific notation?
Move the decimal point until one non-zero digit remains to its left. The number of places moved becomes the exponent.
What does a negative exponent mean?
It means the decimal point moves left when expanding the number, producing a value smaller than one when the coefficient is between 1 and 10.
What is normalized scientific notation?
It is scientific notation with a coefficient whose absolute value is at least 1 but less than 10.
What is engineering notation?
Engineering notation uses an exponent divisible by three, so the coefficient may be between 1 and 1,000.
How do I multiply numbers in scientific notation?
Multiply the coefficients, add the exponents, normalize the coefficient, and round to the appropriate number of significant figures.
How do I add scientific-notation values?
First express both values with a common exponent, add the coefficients, normalize the result, and round to the least precise place value.
Why are significant figures important?
They communicate the precision of a measured or calculated value and prevent reporting more certainty than the inputs support.