Scientific Notation Calculator
Calculator
How it works
To convert to scientific notation, move the decimal point until you have a number between 1 and 10, then multiply by 10 raised to the power of the number of places moved.
What is Scientific Notation?
Scientific Notation (also known as Standard Form) is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10.
For example, the number 650,000,000 can be written in scientific notation as 6.5 × 108.
Why Use Scientific Notation?
Scientists, engineers, and mathematicians use scientific notation because it makes it easier to work with very large or very small numbers. For instance, the distance from Earth to the Sun is about 150,000,000 kilometers, or 1.5 × 108 km. The mass of a dust particle might be 0.000000000753 kg, or 7.53 × 10-10 kg.
- It simplifies calculations with large/small numbers.
- It makes it easier to read and compare magnitudes.
- It clearly indicates the number of significant figures.
Rules of Scientific Notation
Format
a × 10n
Where 1 ≤ |a| < 10 and n is an integer.
Exponent Rules
• If decimal moves Left, exponent is Positive.
• If decimal moves Right, exponent is Negative.
Examples
| Decimal Number | Scientific Notation | Explanation |
|---|---|---|
| 4,500 | 4.5 × 103 | Moved decimal 3 places left. |
| 0.00052 | 5.2 × 10-4 | Moved decimal 4 places right. |
| 6.7 | 6.7 × 100 | No movement needed. |
Frequently Asked Questions
What is E notation?
E notation (e.g., 2.5E6) is a way to write scientific notation where "E" stands for "times 10 to the power of". It is commonly used in calculators and computer programming. 2.5E6 is the same as 2.5 × 106.
Are sig figs important?
Yes, in science, the number of significant figures (sig figs) indicates the precision of a measurement. Scientific notation is very useful for explicitly showing the correct number of significant figures.
Can the base number be negative?
Yes, scientific notation handles negative numbers just fine. For example, -0.005 is written as -5 × 10-3. The sign of the number is separate from the sign of the exponent.