Measurements

Measurement:

Measurement is a process of comprising an object with a standard ‘unit of measurement’. Standard unit of measuring length is called meter.

Need of standard units of measurement – we can use a variety of objects as units of measurement of length.

We can measure the length of an object by using ‘hand-span’, ‘forearm length’ or ‘foot step’ as the units of measuring length. But hand span, forearm length and foot step cannot be used as standard unit’s measurements because their length is not the same for all the persons. The length of hand-span, forearm-length and foot step of different persons is different. It varies from person to person. So, hand span, forearm length and foot step are not standard units of measuring length.

A unit of measurement which has a fixed value which does not change from person to person or place to place, is called a standard unit of measurement length. Whether a meter is used by one person or another person, whether the meter is used in one country or another country, it always represents exactly the ‘same length’. The length of meter does not change from one person to person or place to place. It is necessary to have standard units of measurements for the sake of uniformity in measurements.

Every Measurement consists of a number and a unit 

The result of every measurement consists of two parts:-

1) The first part of the measurement consists of a number (1, 2,3,4,5 …… etc.) which tells us the ‘magnitude of measurement’

2) Second part tells us the ‘name of the unit of measurement’. Every measurement consists of a number and a unit.

Every measurement consists of a number and a unit.

For example:

If the length of table is 2 meters, then 2 is the number and meter is the unit. The number ‘2’ tells us the magnitude of the length of the table and ‘meter’ tells us the unit in which the length has been measured. A measurement is not complete unless both, the number and the unit are mentioned.

SI unit of Length

The SI unit of measuring length is meter. The symbol of meter is m. The SI unit of measuring mass is Kilogram “kg” and the SI unit of measuring time is ‘second’ (s).

Prefixes used with SI units

Prefix is a kind of word used before the name of an SI unit to get a bigger value or a smaller value of the unit.

Three common prefixes are: kilo, centi, and mili

1. Kilo is a prefix which denotes one thousand, i.e.  kilo means “one thousand or 1000

1 kilometer = 1000 meters 

2. Centi is prefix which denotes hundredth i.e.  Centi means “one hundredth” or 1/100

1 meter = 100 centimeters

3. Milli is a prefix which denotes “one thousandth” i.e. milli means “one thousandth” or 1/1000

So, if we write ‘milli’ before the unit of length ‘meter’, it becomes ‘millimeter’ which means one thousandth of a meter or 1/1000 meters. In other words 1 meter = 1000 millimeters.

Kilometer is written as ‘km’, centimeter as ‘cm’ and millimeter as mm.

1. The comparison of an unknown quantity with a known quantity is known as measurement.

Eg: To measure the length of your pencil (unknown quantity), you can compare it with a scale (known quantity)

b. Measurement of a quantity has two parts: a number and its unit.

2 a. For the sake of uniformity, scientists all over the world have adopted a common set of units to express measurements. This system is called as the International System of Units or SI Units.

The following are the SI units of the basic 7 quantities. All other quantities are derived from these seven.

Length – meter

Mass – kilogram

Time – second

Temperature – kelvin

Current – ampere

Substance – mole

Intensity of light - candela

3 a. Length - The distance between one end and the other desired end is called as length.

Eg: Length of a table, distance between home to school, or distance between the sun and the earth.

b. The standard unit of length is 'Meter'. It is represented by letter ‘m’.

3. Other units for measurement

a. smaller units have a prefix milli (‘m’), centi (‘c’), deci (‘d’)

b. Larger units have a prefix deca (‘da’), hecta (‘h’), kilo (‘m’)

c. For meter we add the suffix ‘m’, for gram we add the suffix ‘g’ and for liter we add suffix ‘l’.

4. Conversion of units for metre

1m = 1000 mm

1m = 100 cm

1m = 10 cm

1 dam = 10 m

1hm = 100 m

1km = 1000 km

· Similar conversion is done for gram and liter.

5 a. Steps to measure a pin using scale

• The head of the pin has to coincide with ‘0’ of the scale.

• Count the number of centimeter and from there count the number of finer divisions. The count of the division is ‘mm’

b. Error in measurement: Parallax error

Parallax is a displacement or difference in the apparent position of an object viewed along two different lines of sight.

Correction:

Your eye must be exactly in front of vertically above the point where the measurement has to be taken.

c. Steps to measure a curve using a thread

• Place a string along the curved line. Make sure that the string covers every bit of the curved line.

• Mark the points where the curved line begins and ends on the string.

• Now, stretch the string along the length of a meter scale and measure the distance between the two markings of the string. Note it.

• This will give you the length of a curved line.

d. Measure a curve using a divider

• Separate the legs of the divider by 0.5 cm or 1 cm using a ruler.

• Place it on the curved line starting from one end. Mark the position of the other end. Move it along the line again and again cutting the line into number of segments of equal lengths.

• The remaining parts of the line can be measured using a scale. Count the number of segments

• Therefore, the length of the line = (number of segments × length of each segment) + length of the left over part.

e. Other tools for measuring length: Ruler or scale, and a metre rod is used to measure length.

6. Derived units from length

a. Area:

Area is obtained by using two lengths. So, Area = Length × Breadth.

Thus, SI units of area = m × m = m² (square metre or metre square)

b. Volume:

Volume is obtained by using three lengths. So, Volume = Length × Breadth × Height

Thus, SI units of area = m × m × m = m³ (cubic metre or metre cube)

Eg: Assume the volume of cubical box is 1000 cubic cm.

It means 1000 cubes each with dimensions 1cm × 1cm × 1cm can be placed inside the box.

7. Measuring Volume of Liquid

Liquids take the shape of the container in which they are kept. A liquid whose volume is to be found can simply be poured into a graduated container. The volume of liquid is usually measured in liters.

8. Measuring Volume using the Water Displacement Method

a. This method is used to measure the volume of irregular shapes.

b. Property used:

Volume is the space occupied by an object. We can use this property to measure the volume of an object with irregular shape

c. Method

• Fill a graduated measuring cylinder with water to certain level, say 50 ml.

• Tie the object whose volume is to be calculated with a piece of fine thread.

• Immerse the object completely into water.

• As the object is immersed, we can observe that water level increases. The object displaces the water to occupy the space inside the measuring cylinder.

• The displacement is equal to the space taken up by the object. So the amount of water displaced will be the volume of the object.

9. Measuring Volume of Gas

a. Property of Gas: Gases expand to fill the container into which they are placed. When you compress, a gas you can make the same gas to occupy lesser space. Therefore it is not easy to talk about the volume of gas.

b. Requirements for measuring volume of gas: It is essential to take into account the pressure at which the gases are kept.

10 a. Mass is the measure of the amount of matter in an object.

b. Weight is the gravitational pull experienced by the mass.

c. Relation of mass and weight: The weight is directly proportional to the mass on earth’s surface.

d. The SI unit of mass is kilogram. It is represented by the ‘kg’.

11. Measuring mass of an object: We use balances to measure mass.

a. A beam balance works by comparing the mass of an object to that of known mass (called a standard mass)

b. An electronic balance is a device used to find accurate measurements of weight.

12 a. Time is always moving in a forward direction, i.e., time passes. Thus, measuring time is same as measuring how much time has passed.

b. Measuring device: A clock is the standard device used to measure time.

c. other measuring devices to measure time

• Sand Clock/ Water Clock

In earlier days people used sand clock to measure the passage of time during the day.

One can also use a vessel with a small hole for computing time. Take a vessel or bottle having a small hole in it and fill it with water. The time taken for water to drain can also be used as a measuring device.

• Sundial: Another way to measure time was by using a sundial. The shadow cast by a stick can be used to estimate time.

• Now-a-days, we use electronic clock, stopwatch and other instruments to count even smaller duration of time.