Scientific notation: what is it, examples, solved exercise

THE cientific notation is to write number using power of 10. It is used to reduce the writing of numbers with many digits.

THE cientific notation makes it easy to annotate very large numbers, which can get in the way of more complex calculations.

The format of the cientific notation would be as follows:

N.10(n) squared

N = a real number equal to or greater than 1 and less than 10

N = an integer

Examples

a) 6 590,000,000,000,000 = 6.59. 10(15)

b) 0.000000000016 = 1.6. 10 (11)

Turning a number into scientific notation

• Write the number in decimal format using only a digit other than 0 in front of the comma.
• Put in the exponent of the power of 10 the exact number of decimal places that we had to walk. If on this floor the value has decreased, the exponent will be positive. If it increased, it will be negative.
• Write the product that resulted in the number by the power of 10.

Examples

Transforming the number 32 000

1. It is necessary to walk with the comma, placing it between the 3 and the 2, so we will have the number 3 before the comma.
2. To put the comma in this position, we had to go 4 decimal places, in whole numbers, the comma is at the end of the number. Here the 4 will be the exponent of the power of 10.
3. In cientific notation would be: 3.2. 10(4)

transforming electron mass

The electron's mass is approximately 0.00000000000000000000000000911 g. See how to turn this digit into scientific notation:

1. We must walk with the comma and place it between the 9 and the 1, so we will have only the 9 which is the first digit different from 0 before the comma.
2.  And to put the comma in this position, we must go 28 decimal places. By placing the comma, the number is given a larger value. In order not to change its value, the exponent becomes negative.
3. In scientific notation it would look like this: 9.11. 10(28)g

To perform operations between numbers described in scientific notation, it is necessary to review operations with potentiation.

Multiplication

The multiplication operation in cientific notation is done by multiplying the numbers, repeating the base 10 and adding the exponents:

1. 1,4. 10(3) x 3.1. 10(2) = (1.4 x 3.1). 10(3+2) = 4,34. 10(5)
2. 2.5 .10(8) x 2.3. 10(6) = (2.5 x 2.3). 10(8+8) = 5,75. 10(2)

Division

Here the numbers must be divided, repeated the base 10 and subtracted the exponents:

1. 9,42. 10(5): 1,2 10(2) = (9,42: 1,2). 10 (5+2) = 7,85. 10(3)
2. 8,64. 10(3): 3,2. 10(6) = (8,64: 3,2). 10 (3+6) = 2,7. 10(9)

addition and subtraction

To add or subtract with the numbers of the cientific notation, we have to add or subtract the numbers and repeat the power of 10. It is necessary that the powers of 10 show the same exponent.

1. 3,3. 10 (8) + 4,8. 10(a) = (3.3 + 4.8). 10(8) = 8,1. 10(a)
2. 6,4. 10(3) – 8,3. 10(3) = (6,4 – 8,3). 10(3) = – 1,9. 10(3)

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Basic Scientific Notation exercise solved

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