Significant figures
All the reliable and one doubtful figures included in a measurement are called significant figures.
Some rules for calculating significant figures
1. All non-zero numbers are significant.
Example-
1,2,3,5,9 have 5 significant digits.
2. Zero between two non-zero numbers is significant.
Example-
12567.09 has 7 significant figures.
3. A zero to the right of the decimal point and a non-zero digit to the left is not significant.
Example-
0.0013 has 2 significant figures.
4. A number in which there is no decimal, the last and trailing zeros are not significant figures.
Example-
12040000 has 4 significant figures.
5. A number that has a decimal point is followed by zero significant digits.
Example-
2.500 has 4 significant figures.
6. The multipliers or divisors of an equation are real and have infinite significant figures.
Example-
diameter D=24
In this, 2 is a real number. it as required,
2.0, 2.00, 2.000, 2.0000_____
Numerical questions
1. The mass of a proton is 1.672649×10⁻²⁷kg and the mass of a neutron is 1.674956×10⁻²⁷kg. Find the difference in the masses of both and also the significant figures.
Solution-
Difference in mass,
=Mass of neutron-Mass of proton
=1.674956×10⁻²⁷-1.672649×10⁻²⁷
=0.002305
It has 4 significant figures.
2. The measurement of each side of a cube is 6.203 meters. Find the total area and volume of the cube to appropriate significant figures.
Solution-
a=6.203 meters
Area of cube=6a²
Area of cube=6(6.203)²
Area of cube=230.9 m²
Volume of cube=a³
Volume of cube=(6.203)³
Volume of cube=238.7 m³
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