Introduction to significant relationship:
In mathematics, the word significant indicates significant figures or significant digits. There are some rules to identify the significant digits. In this section, we shall discuss the significant relationship. The following rules and solved example problems will help the students to prepare for significant relationship.
Significant Relationship :
The following points represent relationship between the uncertainty estimates and the significant digits.
Fining a number to 3 significant digits shows that the relative improbability or uncertainty in that number is less than 1%.
If we know a number to 6 significant digits, the relative improbability or uncertainty is less than 0.001 %.
Some definitions for significant relationship can be shown as follows:
Relative uncertainty = `max (|described Value - True Value|/|True Value|)`
Absolute uncertainty = `max (|described Value| - |True Value|)`
Rules for identifying significant figures:
Rule 1:
All non zero figures in any number are significant.
That is, 353.76 has five significant figures.
In addition, 76 has two significant figures.
Rule 2:
Zeroes between the other figures are also significant.
That is, 23009 has five significant figures.
In addition, 9.02 has two significant figures.
Rule 3:
Zeroes located at the last part of decimal values are also significant.
That is, 2.450 has four significant figures.
In addition, 7.0 has two significant figures.
Rule 4:
Zeroes located at the start of decimal values are not significant.
That is, 0.00093 has two significant figures.
In addition, 0067 has two significant figures.
Then 0.000008 has one significant figure.
Rule 5:
Zeroes located at the last part of the whole number are indefinite.
For example, 7800 has at least two significant figures.
However, it may also has more than two significant figures as shown as follows.
7.8 x 103 has two significant figures
7.8 x 103 has three significant figures
7.800 x 103 has four significant figures.
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Example Problem for Significant Relationship :
Identify the number of significant digits from the following.
56, 0.023, 7.2530, 7003, 2300
Solution:
56 – The number 56 is a non-zero number that has two significant digits.
0.023 – Zeroes placed before the other numbers are not significant digits and the number of significant digits in 0.023 is two.
7.2530– Zeroes placed after the other numbers but after a decimal point are significant digits and the number of significant digits in 7.2530 is five.
7003 – The number 7003 has four significant digits because the Zeroes placed between the digits are always significant.
2300:
The number 2300 may have at least two significant digits. It also has three and four significant digits.
That is:
2300 – 2.3 x 103 has two significant digits.
2300 – 2.30 x 103 has three significant digits.
2300 – 2.300 x 103 has four significant digits.
In mathematics, the word significant indicates significant figures or significant digits. There are some rules to identify the significant digits. In this section, we shall discuss the significant relationship. The following rules and solved example problems will help the students to prepare for significant relationship.
Significant Relationship :
The following points represent relationship between the uncertainty estimates and the significant digits.
Fining a number to 3 significant digits shows that the relative improbability or uncertainty in that number is less than 1%.
If we know a number to 6 significant digits, the relative improbability or uncertainty is less than 0.001 %.
Some definitions for significant relationship can be shown as follows:
Relative uncertainty = `max (|described Value - True Value|/|True Value|)`
Absolute uncertainty = `max (|described Value| - |True Value|)`
Rules for identifying significant figures:
Rule 1:
All non zero figures in any number are significant.
That is, 353.76 has five significant figures.
In addition, 76 has two significant figures.
Rule 2:
Zeroes between the other figures are also significant.
That is, 23009 has five significant figures.
In addition, 9.02 has two significant figures.
Rule 3:
Zeroes located at the last part of decimal values are also significant.
That is, 2.450 has four significant figures.
In addition, 7.0 has two significant figures.
Rule 4:
Zeroes located at the start of decimal values are not significant.
That is, 0.00093 has two significant figures.
In addition, 0067 has two significant figures.
Then 0.000008 has one significant figure.
Rule 5:
Zeroes located at the last part of the whole number are indefinite.
For example, 7800 has at least two significant figures.
However, it may also has more than two significant figures as shown as follows.
7.8 x 103 has two significant figures
7.8 x 103 has three significant figures
7.800 x 103 has four significant figures.
Algebra is widely used in day to day activities watch out for my forthcoming posts on algebra equation solver free and define an algebraic expression. I am sure they will be helpful.
Example Problem for Significant Relationship :
Identify the number of significant digits from the following.
56, 0.023, 7.2530, 7003, 2300
Solution:
56 – The number 56 is a non-zero number that has two significant digits.
0.023 – Zeroes placed before the other numbers are not significant digits and the number of significant digits in 0.023 is two.
7.2530– Zeroes placed after the other numbers but after a decimal point are significant digits and the number of significant digits in 7.2530 is five.
7003 – The number 7003 has four significant digits because the Zeroes placed between the digits are always significant.
2300:
The number 2300 may have at least two significant digits. It also has three and four significant digits.
That is:
2300 – 2.3 x 103 has two significant digits.
2300 – 2.30 x 103 has three significant digits.
2300 – 2.300 x 103 has four significant digits.
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