Our free Scientific Notation Calculator makes it simple to convert numbers into scientific notation, engineering notation, or standard decimal form. You can also choose the number of significant figures and even see SI unit prefixes like k, M, µ, and n. The tool also works in reverse, converting notation back to decimal values. Step-by-step solutions are included so you understand exactly how each conversion is performed.
Convert Number to Notation
Convert Notation to Decimal
Compare Two Numbers
What is Scientific Notation?
Scientific notation is a way of expressing very large or very small numbers in the form:
\( N \times 10^e \)
Where:
- \( N \) is the coefficient (a number between 1 and 10)
- \( e \) is the exponent (how many times 10 is multiplied)
For example, \( 45,600 = 4.56 \times 10^4 \).
Why Do We Need Scientific Notation?
- To simplify writing extremely large numbers (like the distance to stars).
- To handle very small numbers (like atomic sizes).
- To make calculations easier in science and engineering.
When Do We Use Scientific Notation?
- When working with data in physics, chemistry, or astronomy.
- When numbers are too large or too small for convenient decimal writing.
- In exams, assignments, and scientific research papers.
Who Can Use This Calculator?
- Students in high school and college for science and math problems.
- Teachers for demonstrations in class.
- Researchers and engineers who deal with scientific data.
All Formulas Used
Scientific Notation: \( N \times 10^e \)
Engineering Notation: \( N \times 10^{\text{multiple of 3}} \)
Standard Form: Decimal expansion of the number.
SI Prefix Conversion:
- \( 10^3 = k \) (kilo)
- \( 10^6 = M \) (mega)
- \( 10^9 = G \) (giga)
- \( 10^{-3} = m \) (milli)
- \( 10^{-6} = \mu \) (micro)
- \( 10^{-9} = n \) (nano)
Examples
Example 1: Decimal to Scientific Notation
Convert \( 45,600 \):
- Coefficient: \( 4.56 \)
- Exponent: \( 4 \)
- Answer: \( 4.56 \times 10^4 \)
Example 2: Scientific Notation to Decimal
Convert \( 3.2 \times 10^5 \):
- Decimal: \( 320,000 \)
Example 3: Engineering Notation
Convert \( 7,890,000 \):
- Answer: \( 7.89 \times 10^6 \)
How to Use the Scientific Notation Calculator
- Enter a number in the Decimal to Notation box.
- Click Convert to see results in Scientific, Engineering, Standard, and SI Prefix form.
- Enter a notation (like 5.6e7) in the Notation to Decimal box to convert back.
- Adjust Significant Figures for more or fewer decimal places.
- Check the Step-by-Step Solution for detailed working.
FAQ
Q1. What is the difference between scientific and engineering notation?
Scientific notation allows any exponent, while engineering notation restricts the exponent to multiples of 3 for easy use with SI prefixes.
Q2. Can I use this calculator for exams?
Yes, it’s ideal for practice, but always check if your exam allows online tools.
Q3. Does this calculator support negative exponents?
Yes, small numbers (like 0.00056) will be expressed with negative exponents.
Q4. What are SI prefixes?
They are shorthand symbols for powers of ten, such as k (10³), M (10⁶), µ (10⁻⁶).