Scientific Notation Calculator
Convert numbers to and from scientific notation, with full arithmetic. Handle very large and very small numbers with ease.
Scientific notation
1.23 × 10⁻⁴
Coefficient
1.23
Exponent
-4
Expanded
0.000123
Scientific notation is used for very large or very small numbers — e.g. 6.022 × 10²³.
How it works
value = coefficient × 10^exponent, with 1 ≤ |coefficient| < 10.
Example: 0.000123 → 1.23 × 10⁻⁴.
Last updated: February 2026
How this calculator is verified
Checked by True Calculator automated test suite on
- Formula verified against a published worked example in the automated test suite
- Edge cases (zero, negative, boundary and unit-mismatch inputs) covered by unit tests
The full verification method is on our how we verify page. Found an error? Tell us and we will re-check it.
When to Use This Calculator
A student in Bhopal studying physics notes that the Moon is about 384,400 kilometres from Earth. Entering this number and choosing convert gives 3.844 times 10 to the fifth. For small numbers, a wavelength of 0.000000125 metres converts to 1.25 times 10 to the minus seventh. Multiplying 2 times 10 to the third by 4 times 10 to the fourth gives 8 times 10 to the seventh, because exponents add when powers multiply and the coefficient 8 stays below 10.
How to Use This Calculator
- Step 1: Enter a number in standard form, such as 450000000, or directly in scientific notation.
- Step 2: Choose convert to see the equivalent form of your number.
- Step 3: For arithmetic, enter two numbers and pick add, subtract, multiply or divide.
- Step 4: Read the result in scientific notation, and check the exponent to judge the scale.
Worked Example
A student in Bhopal studying physics notes that the Moon is about 384,400 kilometres from Earth. Entering this number and choosing convert gives 3.844 times 10 to the fifth. For small numbers, a wavelength of 0.000000125 metres converts to 1.25 times 10 to the minus seventh. Multiplying 2 times 10 to the third by 4 times 10 to the fourth gives 8 times 10 to the seventh, because exponents add when powers multiply and the coefficient 8 stays below 10.
Tips and Common Mistakes
- •Tip 1: When multiplying in scientific notation, add the exponents; when dividing, subtract them.
- •Tip 2: A coefficient must lie between 1 and 10; if your result has a larger coefficient, the exponent needs adjusting.
- •Tip 3: Use scientific notation for very large or very small answers so that no digits are lost to rounding.
- ✗Mistake 1: Treating 45.6 times 10 to the 4 as final scientific notation, when the coefficient must be below 10 and the correct form is 4.56 times 10 to the 5.
- ✗Mistake 2: Adding numbers in scientific notation by adding their exponents; convert them to the same power first.
Frequently Asked Questions
What is scientific notation?
Scientific notation writes a number as a coefficient between 1 and 10 multiplied by a power of 10. For example 1,230,000 = 1.23 × 10⁶.
Why is scientific notation used?
It makes very large and very small numbers readable — like the speed of light (3 × 10⁸ m/s) or the charge of an electron (1.6 × 10⁻¹⁹ C).
How do I convert scientific notation back to a normal number?
Move the decimal point by the exponent — right for positive, left for negative. 1.23 × 10⁻⁴ = 0.000123.
How do I multiply numbers in scientific notation?
Multiply the coefficients and add the exponents. (2 × 10³) × (3 × 10⁴) = 6 × 10⁷, adjusting the coefficient only if it exceeds 10.
Compare these tools
- Percentage Calculator — Calculate percentages, percentage difference and percentage change instantly
- Rounding Calculator — Round any number to the nearest value, or up and down, to any decimal places
- Standard Form Calculator — Convert numbers to and from standard form (scientific notation) with one click
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