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Answer:
Significant figures of a number are the digits that are meaningful during the calculations.
i.e. They are the digits that helps in the uncertainty of how many digits are there in the final answer during the calculations.
We know that all the non-zero numbers are significant and the first non-zero digit on the left is known as the most significant figure and the last digit is known as the least significant figure.
Now, we see,
1. Use of significant figures in addition and subtraction.
The rule for the uncertainty is that 'the number of digits after the decimal in the result is equal to the least number of digits after the decimal in each term'.
for e.g.
A. 3.126 + 8.64 = 11.766.
But, according to the rule, we round of the digits after the decimal places to hundredth place as the least number of digits after decimal is 2.
So, 3.126 + 8.64 = 11.77
B. 29.4165 - 234.65 = -205.2335
But, according to the rule, we round of the digits after the decimal places to hundredth place as the least number of digits after decimal is 2.
So, 29.4165 - 234.65 = -205.23
2. Use of significant figures in multiplication and division.
The rule for the uncertainty is that 'the number of significant digits in the result is equal to the least number of significant figures in each term'.
for e.g.
A. 13.1 × 2.25 = 29.475
But, according to the rule, we round of the digits so we have the same number of significant figures as the least significant figures in both i.e. 3
So, 13.1 × 2.25 = 29.5
B. 3.68 ÷ 0.07925 = 46.43533123
But, according to the rule, we round of the digits so we have the same number of significant figures as the least significant figures in both i.e. 3
So, 3.68 ÷ 0.07925 = 46.4
Hence, in this way significant figures helps in the uncertainty during calculations or measurements.
The uncertainty allied with a measurement is carried through the suitable use of significant figures.
Further explanation:
Significant figures are those figures of a number that bring meaning to the value of the number.
The rules to identify the significant figures.
All non-zero digits are significant figures.
The digits starting from 0 or zeroes to the left is never significant. Example 001.887.
Zeroes looking anywhere between two non-zeroes are significant. Example 101, 1203
The last digit is least significant figure.
The uncertainty in a measurement is an approximation of the quantity by which the measurement conclusion may vary from this value.
The uncertainty rule is 'the number of digits after the decimal in the conclusion is the same to the least number of digits after the decimal in all term'.
The significant figures can be used in the addition and subtraction
[tex]5.126+9.64=14.766[/tex]
It can be seen that the least number of digits after decimal is 2.
Therefore, by the uncertainty rule, round the digits to the hundredths place.
Thus, the number is [tex]14.77[/tex] .
The significant figures can be used in the multiplication and division.
[tex]13.2\times3.28=43.296[/tex]
It can be seen that the least number of digits after decimal is 3.
Therefore, by the uncertainty rule, round the digits to the tenths place.
Thus, the number is [tex]43.3[/tex]
Thus, the uncertainty allied with a measurement is carried through the suitable use of significant figures.
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Answer details:
Grade: High school
Subject: Mathematics
Chapter: Significant figures
Keywords: uncertainty, associated, proper use, figures, vary, approximation, quantity, measurement, hundredth place, tenth place, non-zero digits, significant figures, addition, subtraction, multiplication, division.
