- Scientific notation is used to express very large or very small numbers.
- A number in scientific notation is written as the product of a number (integer or decimal) and a power of 10.
Co-efficient x BaseExponent
- The coefficient must be greater than or equal to 1 and less than 10.
That is 1 <= 1 < 10
- The base must be 10.
- The exponent must show the number of decimal places that the decimal needs to be moved to change the number to standard notation.
A negative exponent means that the decimal is moved to the left when changing to standard notation.
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Example:
3.14 x 1015 is correct scientific notation
31.4 x 1014 is not correct scientific notation
To change Natural Number to Scientific Notation:
- Place decimal point such that there is one non-zero digit to the left of the decimal point.
- Count number of decimal places the decimal has "moved" from the original number. This will be the exponent of the 10.
- The original number here is greater than 1, the exponent is positive (If the original number was less than 1, the exponent is negative)
Examples:
The number 4,000,000,000 can be written in scientific notation as 4x109.
The number 1 can be written in many ways 0.1x101, 1.0x100 etc.
But the scientific notation is expressed as 1x100. Since the number is always 1 or more and less than 10.
| Standard Number | Scientific Notation |
| 1 | 1.0 x 100 |
| 5 | 5 x 100 |
| 8 | 8.0 x 100 |
| 10 | 1.0 x 101 |
| 15 | 1.5 x 101 |
| 25 | 2.5 x 101 |
| 35 | 3.5 x 101 |
| 100 | 1.0 x 102 |
| 200 | 2.0 x 102 |
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| Standard Number | Scientific Notation |
| 210 | 2.1 x 102 |
| 1000 | 1.0 x 103 |
| 1020 | 1.02 x 103 |
| 123,000,000 | 1.23 x 108 |
| 456,000 | 4.56 x 105 |
| 1,000,000 | 1.0 x 106 |
| 1,000,000,000 | 1.0 x 109 |
| 1,000,000,000,000 | 1.0 x 1012 |
| 123,000,000,000 | 1.23 x 1011 |
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Directions: Choose the scientific notation for the numbers given below. Also write atleast 5 examples of your own.
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