What measurement is, units, and the qualities of a good unit
Measuring is counting how many times a chosen unit fits into a quantity. A result needs a number and a unit; a good unit is relevant, convenient and well defined.
Why we measure
We measure all day long. A cook measures rice and water. A tailor measures your waist. A doctor measures your temperature and the dose of a medicine. In the market, the buyer and the seller both want the right weight of mangoes for the money paid. Without a fair measurement, they would quarrel. In science, measurement matters even more. A spacecraft reaches the Moon only because its speed, time and distance were measured very accurately.
What a unit is
A friend says two trees are '100 apart'. 100 what? Steps, feet or metres? The number alone tells you nothing. Every measurement has two parts: a number (how many times) and a unit (the standard used). So the value of a physical quantity = number × unit, and 3 kg means 3 × 1 kilogram. Think of currency notes. Counting 20 notes tells you little until you know whether each is ₹10 or ₹500. The unit is like the value printed on the note.
Three qualities of a good unit
| Quality | Meaning | Example |
|---|---|---|
| Relevant | It suits the quantity being measured | Distance in metres, never in kilograms |
| Convenient | Its size suits the job, so the number is easy to use | Delhi to Agra in kilometres, not in centimetres |
| Well defined | Everyone understands it in the same way | '200 steps' is not well defined: whose steps, walking or running? |
Common measuring tools, their range and least count
| Tool | Measures | Typical range | Typical least count |
|---|---|---|---|
| Metre scale | Length | 0 to 1 m (100 cm) | 1 mm (0.1 cm) |
| Measuring tape | Length of cloth, rooms, land | A few metres to 30 m or more | Often 1 mm |
| Measuring cylinder | Volume of a liquid | 10 mL to 1000 mL, by size | Often 1 mL on a 100 mL cylinder |
| Pan balance | Mass, by comparing with standard weights | Up to a few kilograms in a shop | The smallest standard weight in the set |
| Stop watch | Time taken by an event | Many minutes | 0.01 s (digital); about 0.1 s (mechanical) |
| Quartz clock or watch | Time of day | 12 or 24 hours | 1 s (seconds hand) |
Range, least count and careful reading
- Range is the smallest to the largest value a tool can measure.
- Least count is the smallest value a tool can measure correctly. It equals the value of one smallest division.
- To find it: least count = (difference between two numbered marks) ÷ (number of divisions between them).
- A smaller least count gives a more precise measurement.
- Choose a tool whose range covers the quantity and whose least count is small enough for the job.
- Keep your eye level with the mark you read. For water in a cylinder, read the bottom of the curved surface.
Worked example: least count of a measuring cylinder
A measuring cylinder has 5 equal divisions between its 20 mL and 30 mL marks. Find its least count. Water stands at the second small mark above 20 mL. What is the volume of the water?
- Difference between the numbered marks = 30 mL − 20 mL = 10 mL.
- Number of divisions between them = 5.
- Least count = 10 mL ÷ 5 = 2 mL.
- Volume = 20 mL + 2 × 2 mL = 24 mL.
Least count 2 mL; volume of water 24 mL
In India, the government's Legal Metrology department checks and stamps shop scales and petrol pump meters. So the kilogram or litre you pay for is a true one.
1 marks: “What two parts must the result of every measurement have?” A number and a unit (value = number × unit).
2 marks: “What is a unit? Why is 'the shop is 200 steps away' not a good measurement?” A unit is the fixed standard in terms of which a quantity is measured. Steps differ from person to person and with speed, so the step is not well defined and the result means different things to different people.
2 marks: “Define least count. A metre scale has 10 divisions in each centimetre. What is its least count?” Least count is the smallest value a tool can measure correctly, the value of its smallest division. Here it is 1 cm ÷ 10 = 0.1 cm, which is 1 mm.
A good unit is R C W: Relevant, Convenient, Well defined.