Chapter : Unit, Dimension & Error

Order of Magnitudes

(a) Normally decimal is used after first digit using powers of ten,
Example : 3750 m will be written as 3.750 × 103m
(b) The order of a physical quantity is expressed in power of 10 and is taken to be 1 if ≤ (10) 1/2 = 3.16 and 10 if > 3.16
Example : speed of light = 3 × 108, order = 108
Mass of electron = 9.1 × 10––31, order = 10–30
(c) Significant digits : In a multiplication or division of two or more quantities, the number of significant digits in the answer is equal to the number of significant digits in the quantity which has the minimum number of significant digit.
Example : 12.0/7.0 will have two significant digits only.
(d) The insignificant digits are dropped from the result if they appear after the decimal point. They are replaced by zeroes if they appear to the left of two decimal point. The least significant digit is rounded according to the rules given below.
Rounding off : If the digit next to one rounded as more then 5, the digit to be rounded is increased by 1 ; if two digit next to the one rounded is less than 5, the digit to be rounded is left unchanged, if the digit next to one rounded is 5, then the digit to be rounded is increased by 1 if it is odd and is left unchanged if it is even.
(e) For addition and subtraction write the numbers one below the other with all the decimal points in one line now locate the first column from left that has doubtful digits. All digits right to this column are dropped from all the numbers and rounding is done to this column. The addition and subtraction is now performed to get the answer.
(f) Number of 'Significant figure' in the magnitude of a physical quantity can neither be increased nor decreased.
Example : If we have 3.10 kg than it can not be written as 3.1 kg or 3.100 kg.

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