Standard and Scientific Notations for Numbers
| Standard Notation The standard notation is the general way of writing numbers. Examples: 2, 2.5, 3.14, 0.0047 Scientific Notation Very large or very small numbers are represented by scientific notation. In the scientific notation, there is always one digit to the left of the decimal point. The number to be represented is divided into two factors. The first factor is called the coefficient and the second factor consists of a power of 10. Here, the number 10 is known as the base. Example: 2.99792458 × 108 m/s is the speed of light. The first factor 2.99792458 is known as the coefficient, and the second factor consists of the number 10 (base) raised to the power of 8. Conversion from Standard to Scientific Notation The decimal point dictates the power the base 10 should represent. When converting to scientific notation, the base 10 gets a negative power if the decimal point is shifted to the right and a positive power if the decimal point is shifted to the left. |
| Standard Notation | Scientific Notation | Explanation for Converting from Standard to Scientific Notation |
| 0.0047 | 4.7 × 10−3 | Shift the decimal by three places to the right, so the power is −3. |
| 0.47 | 4.7 × 10−1 | Shift the decimal by one place to the right, so the power is −1. |
| 47 | 4.7 × 101 | Shift the decimal by one place to the left, so the power is 1. |
| 4700 | 4.7 × 103 | Shift the decimal by three places to the left, so the power is 3. |