Respuesta :
Answer :
(a) 3.14286
(b) 3.14159
(c) [tex]\frac{355}{113}[/tex]
Explanation :
Significant figures : The figures in a number which express the value -the magnitude of a quantity to a specific degree of accuracy is known as significant digits.
Rules for significant figures:
Digits from 1 to 9 are always significant and have infinite number of significant figures.
All non-zero numbers are always significant. For example: 654, 6.54 and 65.4 all have three significant figures.
All zero’s between integers are always significant. For example: 5005, 5.005 and 50.05 all have four significant figures.
All zero’s preceding the first integers are never significant. For example: 0.0078 has two significant figures.
All zero’s after the decimal point are always significant. For example: 4.500, 45.00 and 450.0 all have four significant figures.
All zeroes used solely for spacing the decimal point are not significant. For example : 8000 has one significant figure.
Accuracy : It is defined as the closeness of a measured value to a standard or known value.
Precision : It is defined as the closeness of two or more measurements to each other.
As per question, we have to convert each approximation of π to six significant figures.
(a) [tex]\frac{22}{7}[/tex]
[tex]\frac{22}{7}=3.14286[/tex]
(b) [tex]\frac{355}{113}[/tex]
[tex]\frac{355}{113}=3.14159[/tex]
(c) As we know that the true value of π is, 3.14159 that means [tex]\frac{355}{113}[/tex] is accurate because it gives exact value of π with six significant figures.
