# Chapter 1: Measurements and Units

• Physical Quantity is a quantity that can be measured. It consists of a numerical magnitude and a unit.

# Numbers and Units

## Scientific Notation

• Numbers written using powers of ten are in scientific notation or standard form.

• For example;

# System of Units

## SI Units

• Are set systematic international units, for measuring mass, time, and other base units and derived quantities.

### Mass

• Is the measure of the amount of substance in an object.

• Has the following effects:

• all objects are attracted to the Earth. The greater the mass of an object, the stronger is he Earth’s gravitational pull on it.

• all objects resist attempts to make them go faster, slower, or in a different direction. The greater the mass, the greater is the resistance to change in motion.

• SI base unit is kilogram (kg).

### Time

• SI base unit is second (s).

• Following are some of other units for second:

### Length

• SI base unit is metre (m).

# Measuring Length and Time

## Measuring Length

• Ruler can be used to measure small distances of a few centimetres (cm).

• They are able to measure to the nearest millimetre (mm).

• Can measure upto one metre.

• Example of usage:

• height of the table

• Micrometer is used to measure objects that are too small to be measured with vernier calipers

• Gives a precision of 0.01 mm

• Can measure measurements of less than 25 cm.

• Example of usage:

• diameter of a wire

• Vernier Calliper is a useful tool for measuring both internal and external diameters.

• They are able to measure to a precision of 0.01 cm.

## Measuring Time

• Time intervals of many seconds or minutes can be measured using a a stopwatch.

• Some instruments have analogue or a digital display.

# Volume and Density

## Volume

• It is the quantity of space an object takes up.

• It’s SI unit is cubic metre (m^3).

## Density

• It is the quantity of mass per unit volume of a substance.

• Formula:

• Density= Mass/Volume

• ρ=m/v

• ρ is a greek letter ‘rho’ .

• (both equations are same, written in different ways; i.e first one is the word equation and the other one is symbolic equation.

• SI unit of density is kilogram per cubic metre (kg m^-3).

• Objects that are less dense than water will float on water; and objects that are denser than water will sink.

# Measuring Volume and Density

## Measuring Volume

### Liquid

• Its volume can be measured using a measuring cylinder.

• Most cylinders have scale marked in millilitres (ml) or cubic centimetres (cm^3).

### Regular Solid

• If an object has a simple shape, its volume can be calculated through formula. For example:

• volume of a regular block = length x width x height

### Irregular Solid

• If the shape of the object is too awkward to calculate its volume, then immerse the object in a measuring cylinder filled with water and then calculate the increase in water level. This value will be the volume of the object.

## Measuring Density

• Once volume of the object is obtained through one of the above methods suitable, find the mass of the object using a balance.

• Following is one of the example:

## Checking the mass and density of a liquid

• An easy method of finding the density of a liquid is by using a small float called hydrometer.

• The relative density on a hydrometer indicates the relative density of the liquid.

• Checks like these are important in some production processes.