How far a city from another city is measured in miles or kilometers. How heavy a box of apples is measured as grams or kilograms. How much time the train takes to travel from one city to another city is measured in minutes or hours. So, the mile, kilometer, gram, kilogram, minutes and hours are the units which are used to measure quantities.
There are many more units available in science and mathematics to measure quantities, few of the examples are temperature measured in celsius or fahrenheit, volume in liter, angles in degrees, area in square meter and volume in cubic meter.
This chapter primarily introduces the following concepts:
- Which are the basic units that are used in day to day measurements?
- How units are used to measure large and small quantities?
- Can units be made smaller and larger?
- How to convert units into one another using the conversion tables?
Units
Unit is a standard that is used to measure quantities. For example, the quantity length is measured in metres, so metre is called a unit of length. Mass of an object is measured in kilograms, so kilogram is the unit of mass. Time is measured in seconds, so seconds is a unit of time.
These units are placed next to the number value of the quantity measured, for example the distance between two cities is 10 kilometers, where 10 is the number value and kilometer is the unit.
There are symbols available for all units. The short form of centimeter is cm, for kilogram it is kg and short form of second is only "s".
| Quantity | Name of unit | Symbol of unit |
|---|---|---|
| Length | Meter | m |
| Mass | Kilogram | kg |
| Time | Seconds | s |
The above table shows only one unit of length, mass and time, but more units are available to measure these quantities. The following tables list the units of length, mass and time.
Units of length
| Name of unit | Symbol of unit |
|---|---|
| Meter | m |
| Centimeter | cm |
| Millimeter | mm |
| Kilometer | km |
| Miles | mi |
| Yards | yd |
| Foot | ft |
| Inch | in |
Units of mass
| Name of Unit | Symbol of Unit |
|---|---|
| Kilogram | kg |
| Gram | g |
| Milligram | mg |
| Pounds | lbs |
| Ounce | oz |
Units of time
| Name of Unit | Symbol of Unit |
|---|---|
| Hour | hr |
| Minute | m |
| Second | s |
List of more units
Area
In geometry we come across many measurements that need area calculations like area of circle, surface area of sphere or area of lawn and there are many such examples. So, area is quantity that is measured in units of metre square m2 or centimeter square cm2.
Volume
In geometry volume measurements like volume of sphere or volume of cylinder or volume of a cup is measured in units of metre cube m3 or cm3.
| Name of Unit | Symbol of Unit |
|---|---|
| Litre | l |
| Millilitre | ml |
| Cup | C or c |
| Pint | pt |
| Gallon | gal |
Temperature
| Name of Unit | Symbol of Unit |
|---|---|
| Celsius | °C |
| Fahrenheit | F |
| Kelvin | K |
Angle
Angles are also a quantity that can be measured and have units of degree ° or radian.
Measure large and small quantities
Can the distance between two cities be measured in centimeter units of length? All units of length are not meant to measure the same distances. Different units are used to measure quantities depending upon if the quantity is big or small.
Length
To measure lengths like the distance between two cities, which is very long, the unit kilometer is used for this purpose. It can be noted too while travelling, the kilometer and miles milestones can be seen on sides of the road telling how far is the destination city. So the such distances are larger and hence kilometer and miles are used for them.
The following table shows the best suitable units to measure different types of lengths.
| Quantity | Best suitable units |
|---|---|
| Distance between two cities | kilometer |
| Length of a car | meter |
| Height of a person | centimeter, meter |
Mass
Kilogram is the bigger unit than grams so is their use. Kilogram is used to measure larger weights and grams to measure small weights.
| Quantity | Best suitable units |
|---|---|
| Mass of person | kilogram |
| Mass of toothpaste | gram |
| Mass of big box of bananas | kilogram |
Time
Long durations of time are counted in days not in hours. Hours or minutes or seconds are small units and are used to measure shorter durations.
| Quantity | Best suitable units |
|---|---|
| Time to travel one country to another | hour |
| Time to start a car's engine | second |
| Time to walk to next door market | minute |
| Number of vacations | day |
| Cooking time to bake a cake | minute |
Scaling of units
The term scaling refers to changing the size in a fixed proportion. Units can be scaled up or down. Scaling up means making the unit bigger and scaling down is making the unit smaller.
The name of the scaled unit is written by just adding a prefix word to the base unit. For example, kilo in kilogram is the prefix and gram is the base unit.
Scale units up
The units can be scaled up by multiplying the base units by 10, 100, and 1000. The name of the unit is also prefixed with deca, hecto and kilo after they are scaled up or made bigger.
| Prefix | Base unit multiplied by | Example |
|---|---|---|
| Deca | 10 | 1 decameter = 1 × 10 = 10 m |
| Hecto | 100 | 1 hectometer = 1 × 100 = 100 m |
| Kilo | 1000 | 1 kilometer = 1 × 1000 = 1000 m |
Decameter, hectometer, and kilometer are the bigger units of meter.
Scale units down
The base units can also be scaled down or made smaller by dividing them by 10, 100, and 1000 and prefixing them with deci, centi, and milli respectively.
| Prefix | Base unit divided by | Example |
|---|---|---|
| Deci | 10 | 1 decimeter = = 0.1 m |
| Centi | 100 | 1 centimeter = = 0.01 m |
| Milli | 1000 | 1 millimeter = = 0.001 m |
Decimeter, centimeter, and millimeter are the smaller units of meter.
Questions on unit conversions
The above tables have examples which convert single value of a unit into other units. For example, 1 decameter = 10 m. Here, 1 decameter is a single unit and the conversion of 1 decameter into meter is called unit conversion. Here, unit means a value of 1.
This unit conversion can be used to solve unit values which are more than one. For example, in converting 5 decameter into meter.
Convert 5 decameter into meter.
5 decameter can be written as 5 × 1 decameter
∴ 5 decameter = 5 × 1 decameter
We know that 1 decameter = 10 meter
∴ 5 decameter = 5 × 10 m
= 50 m
Convert 2 m into cm.
2 m = 2 × 1 m
We know that 1 m = 100 cm
∴ 2 m = 2 × 100 cm
= 200 cm
Conversion table
Conversion table depicts a way to memorize the unit conversions. It helps to convert the base units to its larger or smaller units or even can change into each other.
Conversion of units can only be carried out on the same type of quantities. Conversions never change the magnitude of measurement. The magnitude of a quantity remains the same, only the unit changes.
A unit of length can be converted to another unit of length, but the magnitude of length will remain same.
Below are the three conversion tables with base units of meter, gram, and litre. The larger units kilo, hecto and deca are written on the left hand side and the smaller units deci, centi and milli on the right hand side of the base units.
Convert bigger to smaller units
To convert a bigger unit into a smaller unit, the direction of movement in conversion table is chosen from right to left and the following steps are taken.
- Step 1: Move from left to right in the conversion table.
- Step 2: Count the positions moved starting from the given units until the reached upto the new units.
- Step 3: Make the conversion number by adding zeros next to 1. The number of zeros being added will be equal to the number of positions moved in step 2.
- Step 4: Multiply the value of unit with the conversion number to get the new units.
Convert 20 kilometers into centimeters.
Kilometer is bigger unit than centimeter.
Step 1: Move from left to right.
Step 2: The starting point is kilo and the end point is centi. So, start counting from hecto as Ist position, then deca as 2nd, meter as 3rd, deci as 4th and centi as 5th position. The total number of positions moved are 5.
Step 3: Make the conversion number by adding 5 zeros next to 1 i.e. conversion number = 100000
Step 4: Multiply 20 in 20 kilometer by the conversion number.
New value in centimeter units = 20 × 100000 = 2000000 centimeter
Convert smaller to bigger units
- Step 1: Move from right to left.
- Step 2: Count the number of positions moved from the given units to the new units.
- Step 3: Make the conversion number by adding zeros next to 1. The number of zeros being added will be equal to the number of positions moved in step 2.
- Step 4: Divide the value of unit with the conversion number to get the new units.
Convert 6 meters into hectometers.
Step 1: Move from right to left because it is conversion from the smaller unit meter to bigger unit hectometer.
Step 2: Find the number of positions to be moved. The starting point is the meter and the end point is hecto. So, start counting after meter. Deca as Ist and hecto as 2nd position. The total number of positions moved are 2.
Step 3: Conversion number = 100
Step 4: Divide the 6 in 6 meter by the conversion number.
New value in hectometer units = hectometer
