The Scientific notation, also called exponential notation or standard form, allows you to express very large or very small numbers in a shorter and easier way, which simplifies writing and helps when you have to perform mathematical operations with these numbers or incorporate them into formulas or equationstions.
It is believed that it was Archimedes who introduced the first approaches that led to the concept of scientific notation.
Numbers in scientific notation are written as the product of an integer or decimal number between 1 and 10 and a power of base 10.
In this way, the scientific notation responds to the following formula: nx 10x onx 10-x. As a practical procedure, it can be said that to convert figures greater than 1 to scientific notation, you have to place a comma after the first digit and calculate the exponent based on how many places to the left were left.
To convert figures less than 1 to scientific notation, you must place a comma after the third to last digit and calculate the exponent based on how many places to the right were left, expressed as negative. In the examples given above, Avogadro’s number would be 6.022 × 1023 and the weight of hydrogen is 1.66 × 10-23.
Numbers in scientific notation can also be written as exponential notation. For example, 4 × 108 It could be written as 4e + 8.
To multiply figures in scientific notation, you have to multiply the numbers that are on the left side, that product is then multiplied by 10 raised to the sum of the individual exponents. To divide figures in scientific notation, you have to divide the numbers that are on the left side, that result is multiplied by 10 raised to the subtraction of the exponents.
Examples of scientific notation
Here are examples of figures in scientific notation:
- 7.6 x 1012 kilometers (distance between the sun and Pluto at the farthest point in its orbit)
- 1.41 x 1028 cubic meters (volume of the sun).
- 7.4 x 1019 tons (mass of the moon)
- 2.99 x 108 meters / second (speed of light in vacuum)
- 3 x 1012 number of bacteria that can be in a gram of soil
- 5.0 × 10-8 Planck’s constant
- 6.6 × 10-12 Rydberg’s constant
- 2.2 × 10-9 proton radius
- 1.5 x 10-5 mm size of a virus
- 1.0 x 10-8 cm size of an atom
- 1.3 x 10fifteen liters (volume of water in a pool)
- 0.6 x 10-9
- 3.25 x 107
- 2 x 10-4
- 3.7 x 10eleven
- 2.2 x 107
- 1.0 x 10-9
- 6.8 x 105
- 7.0 x 10-4
- 8.1 x 10eleven