Scientific notation

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• Examples of scientific notation

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 having to perform mathematical operations with these numbers or incorporate them into formulas or equations.

It is believed that it was Archimedes who introduced the first approaches that led to the concept of scientific notation.

Thenumbers in scientific notation they 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: n x 10^x o n x 10^-x. As a practical procedure, it can be said that to convert figures greater than 1 to scientific notation, we must 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 have to 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 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

Examples of figures in scientific notation are given below:

1. 7.6 x 10¹² kilometers (distance between the sun and Pluto at the farthest point in its orbit)
2. 1.41 x 10²⁸ cubic meters (volume of the sun).
3. 7.4 x 10¹⁹ tons (mass of the moon)
4. 2.99 x 10⁸ meters / second (speed of light in vacuum)
5. 3 x 10¹² the number of bacteria that can be in a gram of soil
6. 5,0×10^-8 Planck's constant
7. 6,6×10^-12 Rydberg's constant
8. 8,41 × 10^-16proton m radius
9. 1.5 x 10^-5 mm the size of a virus
10. 1.0 x 10^-8 cmà size of an atom
11. 1.3 x 10¹⁵ liters (volume of water in a pool)
12. 0.6 x 10^-9                  
13. 3.25 x 10⁷
14. 2 x 10^-4
15. 3.7 x 10¹¹
16. 2.2 x 10⁷
17. 1.0 x 10^-9
18. 6.8 x 10⁵
19. 7.0 x 10^-4
20. 8.1 x 10¹¹