# 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=a

³Volume of cube=(6.203)³

Volume of cube=238.7 m³