Significant figures of a number. Significant figures represent the use of one or more uncertainty scales in certain approximations.
Summary
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- 1 Numbering system
- 2 Definition 1
- 3 Example 1
- 1 Solution
- 4 Definition 2
- 5 Example 2
- 1 Solution:
- 6 Sources
Numbering system
In working with approximate numbers, it is very common to use the language of figures . The numbering system that is used today throughout the world. Except for very specific questions, it is the one created by the ancient Hindu civilization and later defended by the Arabs in Europe during the Middle Ages . It is a base 10 positional system , due to the simplicity of the algorithms it uses for arithmetic operations . it quickly displaced other systems used at that time, such as the Roman or the Greek. In this system any real number can be expressed using only 10 symbols (or digits): 0. 1. 2. 3. 1. 5. 6. 7.8, 9. When a digit appears as part of a number, it represents a value that depends of his figure and his position. To simplify the following exposition, the concept of place value of a number is introduced.
Definition 1
If the digit d occupies in a real number the k-sima position according to the following table:
| Decimal place | k |
| Thousandths | -3 |
| Hundredths | -2 |
| Tenths | -one |
| Units | 0 |
| Tens | one |
| Hundreds | 2 |
Place value of d as denoted p (d) and is defined as p (d) = 10 k Note that the positional value of a digit in a number not more than the value that would have placed unit in the same position . The value of a digit d within a number that will be abbreviated as v (d) . It is obtained by multiplying the digit by its place value and the value of the number is the sum of the values of each of its digits. These ideas are clarified in the example that follows.
Example 1
Determine the place value and value of each digit in the real number 65,403
Solution
| p (6) = 10 1 = 10 | v (6) = 6p (6) = 60 |
| P (5) = 10 0 = 1 | v (5) = 5p (5) = 0 |
| P (4) = 10 -1 = 0.1 | v (4) = 4p (4) = 0.4 |
| p (0) = 10 -2 = 0.01 | v (0) = 0p (0) = 0 |
| p (3) = 10 -3 = 0.001 | v (3) = 3p (3) = 0.003 |
Note that the sum v (6) + v (5) + v (4) + v (0) + v (3} matches the value of the real number, this is 65,403, although the value of any digit 0 is zero. regardless of their position, in the expression of the number the zeros cannot be omitted because this would affect the position of the remaining digits, for example, the numbers 65.403 and 65.43 do not mean the same thing since when omitting the digit 0 the position of the 3 is -2 and not -3 as in the first case.
Definition 2
When a digit 0 is included in a number for the sole purpose of occupying a position within the number. that digit is called non-significant zero. In all other cases, e1 0 is said to be significant. All digits other than 0 are significant
Example 2
In the number 0.0002030, which digits are significant?
Solution:
The first four zeros of the number are not significant. they only serve to inform that digit 2 occupies position -4. The fifth and sixth zeros are both significant, in both cases you want to note that the value of that decimal position must be zero. In conclusion- the significant digits of the number are shown below: 0.0002030 In general. all zeros that appear between significant digits are significant. In some cases. only the context where the number is found allows to determine if a 0 is significant or not. according to the intention of the person who wrote you.
