Significant figure: Significant figure are the number of digits upto which the accuracy is maintain.
Rules of significant figure:
(i) All non-zero digits are significant. For example, 1.235 has four significant figures.
(ii) The zeros appearing between two non-zero digits are significant. For example, 4.025 has four significant figures.
(iii) All the trailing zeros after decimal places are significant. For example, 6.200 has four significant figures.
(iv) If a measurement is less than 1 then all the zeros occurring to the left of the nonzero digit are not significant. For example, 0.0023 has two significant figures.
(v) For a number without a decimal point, the terminal zeors are not significant figures. For example, 6400 has 2 significant figures.
(vi) The powers of ten are not significant figures. For example, 2.1 106 has only two significant figures.
(vii) Change in unit for the measurement of a quantity does not change the number of significant figures. Suppose a measurement was done using mm scale and we get length I = 65 mm (two significant figures)
Then l = 0.065 m (two significant figures)
l = 0.000065 km (two significant figures)
l = 6.5 107 nm (two significant figures)
(viii) Exact measurements have infinite number of significant figures. For example, 5 balls in a basket, 40 students in a class, speed of light in vacuum, value of .
Rounding a digit:
(i) If the number lying to the right of cut off digit is less than 5, then the cut off digit is retained as such. If the cut off digit is more than 5, then it is increased by 1. For example, 6.243 = 6.24 (rounding up to three significant figures) 6.246 = 6.25 (rounding up to three significant figures).
(ii) If the digit be dropped is 5 and the preceding digit is raised by one if it is odd. For example, 6.235 = 6.24.
(iii) If the digit be dropped is 5 and the preceding digit is remained unchanged if it is even. For example, 6.225 = 6.22
Significant figure in algebraic operations:
Addition, subtraction: The final result of addition or subtraction of numbers should have the number of digits to the right of the decimal same as the digits to the right of decimal of least precise number.
For addition of 2.2 + 2.56 + 3.254 = 8.014 = 8.0 [least precise number is 2.2 with 1 digit after decimal, so the result should be rounding off upto 1 digit after decimal]
Multiplication, Division: The final result of multiplication or division of numbers should have the significant figure equal to the least number of significant figure in any of the numbers.
Multiplying 2.3 and 13.58 we get, 2.3 13.58 = 31.234 = 31 [least significant number is 2.3 with 2 significant figures so the result should be rounding off upto 2 significant figures.]
Order of magnitude: The power of ten method is used to express some physical quantity like mass of earth, radius of atom or Avogadro’s number etcetera. If any number is expressed by m 10n where 1 m 10 and n is a positive or negative integer.
If m is less than or equal to 5, then the order of number is 10n and if m is greater than 5, then the order of number is 10n+1.
For example, 2.55 106 order of number is 106 and for 6.55 106 order of number is 107.
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