Standard and non-standard measurement
Two friends measure the same bench: one gets 5 hand spans, the other gets 7. Both are right for their own hands, but nobody can order a bench from "5 spans". A fixed unit solves this.
Measurement (मापन) is comparing a quantity with a unit using a suitable tool. Measuring with a hand span, finger-width or footstep gives non-standard results because bodies differ. A fixed unit gives standard measurement.
In the figure : Child A measures the table as 6 hand spans and child B as 4 hand spans. The answers differ because the hand spans are not equal, so hand spans give non-standard measurement.
Rule 1: Non-standard measurement — Hand span, fist, footstep and cubit differ from person to person.
- Easy : A tall father's footstep is longer than a child's footstep.
- Medium : The Egyptian cubit (elbow to the tip of the middle finger) varied, so a fixed Royal Cubit was made.
- Exam-type : The Romans used foot, inch and mille passus (1,000 paces), which led to the mile.
Rule 2: Standard measurement — A standard unit is the same for everyone, anywhere.
- Easy : A metre scale shows the same length for everyone.
- Medium : A shopkeeper's weight of 1 kilogram is the same in every city.
- Exam-type : Two tailors with a tape get the same answer for the same cloth.
A measurement needs a number and a unit. "5" alone means nothing; "5 metres" does.
Using the hand span for exact measurement. It is only good for a rough idea.
Memory clue: Same for all = Standard.
Spot the difference
| Point | Non-standard | Standard |
|---|---|---|
| Unit | Hand span, foot | Metre, kilogram |
| Same for everyone? | No | Yes |
| Use | Rough idea | Exact work |
Practice questions
- 1What is measurement?
- 2Give two non-standard units.
- 3Why is a hand span a non-standard unit?
- 4What was the Egyptian cubit?
- 5What did the Romans' mille passus lead to?
- 6Two children measure a desk as 6 and 4 hand spans. Why do they differ?
- 7A carpenter says "my table is 8 footsteps". Why is it not useful to a buyer?
- 8Is "5" a complete measurement? Why?
Show answers (try them yourself first)
- 1Comparing a quantity with a unit using a suitable tool.
- 2Hand span and footstep.
- 3Hand spans differ from person to person.
- 4The distance from the elbow to the tip of the middle finger.
- 5The mile.
- 6Their hand spans are of different sizes.
- 7Footsteps differ; a fixed unit like metre is needed.
- 8No. A unit is also needed, like 5 m.
Units of length
A tailor measures cloth in metres, a student draws a line in centimetres and a road sign shows the distance to the next city in kilometres. We choose a unit that suits the size of the thing.
The SI units are: length – metre, mass – kilogram, time – second. 1 km = 1000 m, 1 m = 100 cm, 1 cm = 10 mm.
Rule 1: Bigger to smaller: multiply — Multiply by 1000, 100 or 10.
- Easy : 3 km = 3 × 1000 = 3000 m.
- Medium : 7 m = 7 × 100 = 700 cm.
- Exam-type : 3 m 20 cm = 300 + 20 = 320 cm.
Rule 2: Smaller to bigger: divide — Divide by 1000, 100 or 10.
- Easy : 250 cm = 2.5 m.
- Medium : 45 mm = 4.5 cm.
- Exam-type : 1500 m = 1.5 km.
Units of length
In the app you can move this figure with your finger.
Open in the appUse cm for a line, metre for cloth or a ground, km for the distance between cities.
Dividing by 10 to change m to cm. It is × 100.
Memory clue: km–m–cm–mm : ×1000, ×100, ×10 going down.
Spot the difference
| Unit | Equal to | Used for |
|---|---|---|
| 1 km | 1000 m | Distance between cities |
| 1 m | 100 cm | Cloth, ground |
| 1 cm | 10 mm | Line, pencil |
Practice questions
- 1Name the SI unit of length.
- 2Name the SI unit of mass.
- 3Name the SI unit of time.
- 4Convert 3 km to metres.
- 5Convert 250 cm to metres.
- 6Convert 3 m 20 cm to centimetres.
- 7Which unit is best for the distance between two cities?
- 8Ravi writes 2 m = 20 cm. Correct him.
Show answers (try them yourself first)
- 1Metre
- 2Kilogram
- 3Second
- 43000 m
- 52.5 m
- 6320 cm
- 7Kilometre
- 81 m = 100 cm, so 2 m = 200 cm.
Measuring length accurately
When you measure a notebook, you put the ruler flat against its edge and read the mark straight in front of your eye. A careless measurement of the same notebook can be wrong by a centimetre.
For accurate length: keep the object in direct contact with the ruler, start at the 0 mark, and read straight above the mark. If 0 is not clear, subtract the starting reading from the final one. Use a thread for curves.
In the figure : The pencil starts at the 0 mark and its tip is at 7 cm and 4 mm, so its length is 7.4 cm (74 mm).
Rule 1: Correct way — Ruler in contact with the object, 0 mark at the edge, eye straight above the mark.
- Easy : A pencil from 0 to 5 cm 6 mm is 5.6 cm = 56 mm.
- Medium : If the ruler starts at 2.0 cm and the object ends at 9.5 cm, length = 9.5 − 2.0 = 7.5 cm.
- Exam-type : Reading from the side makes the answer wrong; look straight above the mark.
In the figure : A is the correct way: the strip touches the ruler and its end is at the 0 mark. In B the strip is slanting and in C it is held away from the ruler.
Rule 2: Curves — Lay a thread along the curve, then straighten it beside the ruler.
- Easy : The length of a road on a map can be measured with a thread.
- Medium : A tailor's tape measures a round waist.
- Exam-type : An industry uses screw gauge and vernier caliper for very small lengths.
In the figure : The length of a curve is measured with a thread: lay the thread along the curve and then straighten it beside the ruler. Here it is 13.5 cm long.
Rule 3: Reference point — The fixed point from which a distance is measured.
- Easy : On a road, milestones show distance from a town.
- Medium : If A is 10 km and B is 25 km from O on the same side, the distance AB = 25 − 10 = 15 km.
- Exam-type : If they are on opposite sides of O, the distance is 10 + 25 = 35 km.
In the figure : O is the reference point, the fixed point from which distances are measured. Here A is 6 km, B is 15 km and C is 31 km from O.
Always check where the ruler's 0 mark is. A broken ruler may start at 1 cm.
Reading the number at the end without subtracting the starting reading.
Memory clue: Touch – Zero – Straight: object touches the ruler, start at zero, look straight.
Spot the difference
| Situation | Tool or method |
|---|---|
| Straight edge | Ruler |
| Curved line | Thread + ruler |
| Round waist | Tailor's tape |
Practice questions
- 1What should you do if the 0 mark of the ruler is unclear?
- 2How do you measure a curved line?
- 3What is a reference point?
- 4A pencil starts at 0 and ends at 5 cm 6 mm. Find its length in mm.
- 5An object starts at 2.0 cm and ends at 9.5 cm. Find its length.
- 6Name a tool for very small lengths in industry.
- 7Towns A and B are 10 km and 25 km from O on the same side. Find AB. And find AB if they are on opposite sides.
- 8Meena reads a measurement by looking from the side. Why is her answer wrong?
Show answers (try them yourself first)
- 1Subtract the starting reading from the final reading.
- 2Lay a thread along it, straighten the thread and measure it.
- 3The fixed point from which distance is measured.
- 456 mm
- 57.5 cm
- 6Screw gauge or vernier caliper.
- 715 km; 35 km
- 8The reading shifts; she must look straight above the mark.
Temperature and thermometers
When you have fever, your forehead feels hot. But touch cannot tell if it is 38 °C or 40 °C. A thermometer shows the exact temperature as a number.
Temperature (तापमान) tells how hot or cold a thing is. It is measured with a thermometer in °C (Celsius), °F (Fahrenheit) or K (Kelvin, SI unit). Normal body temperature is about 37 °C.
In the figure : A clinical thermometer reads from 35 °C to 42 °C. The figure shows 38.6 °C, which is higher than the normal body temperature of about 37 °C.
Rule 1: Clinical thermometer — Range 35 °C to 42 °C; used for body temperature. Shake it so the liquid goes down before use.
- Easy : A reading of 36.9 °C is normal.
- Medium : A reading of 39.2 °C is higher than 37 °C, so the person has fever.
- Exam-type : Difference from normal: 39.2 − 37 = 2.2 °C higher.
In the figure : The bulb of a laboratory thermometer is filled with mercury or coloured alcohol. In the figure the liquid has risen to 64 °C.
Rule 2: Laboratory thermometer — Range 0 °C to 110 °C; used for water, liquids and experiments.
- Easy : Ice melts at 0 °C and water boils at 100 °C.
- Medium : A laboratory thermometer can read 100 °C, but a clinical one cannot (it stops at 42 °C).
- Exam-type : Never use a clinical thermometer in hot water.
Touch only gives a rough feeling; a thermometer gives an exact number.
Using a clinical thermometer to measure boiling water. Its range is only 35 °C to 42 °C.
Memory clue: Clinical = Closer to body (35–42); Lab = Lots of range (0–110).
Spot the difference
| Thermometer | Range | Use |
|---|---|---|
| Clinical | 35 to 42 °C | Body temperature |
| Laboratory | 0 to 110 °C | Water, liquids |
| Normal body | About 37 °C | Healthy person |
Practice questions
- 1What does a thermometer measure?
- 2What is the normal body temperature?
- 3Name the SI unit of temperature.
- 4What is the range of a clinical thermometer?
- 5What is the range of a laboratory thermometer?
- 6A clinical thermometer shows 39.2 °C. By how much is it above normal?
- 7Why can't we measure boiling water (100 °C) with a clinical thermometer?
- 8Why is a thermometer better than the touch of the hand?
Show answers (try them yourself first)
- 1Temperature
- 2About 37 °C
- 3Kelvin
- 435 °C to 42 °C
- 50 °C to 110 °C
- 639.2 − 37 = 2.2 °C
- 7Its scale stops at 42 °C.
- 8Touch gives only a rough feeling; a thermometer gives an exact number.
Types of thermometers and correct use
At airports, a staff member points a small gun-like device at your forehead and it shows your temperature without touching. That is an infrared thermometer. There are different thermometers for different jobs.
Types: digital (button cell, beeps), infrared (no touch; used during COVID-19) and laboratory (bulb filled with mercury or coloured alcohol). The meteorological department (IMD) records temperatures for weather forecasts.
In the figure : In B the bulb is inside the liquid without touching the bottom or the sides and the thermometer is vertical, which is the correct way. In A the bulb touches the bottom, and in C it is above the liquid.
Rule 1: Correct use of a laboratory thermometer — Bulb in contact with the liquid, thermometer vertical, not touching the container, read at eye level.
- Easy : Keep the bulb in the middle of the water in a beaker.
- Medium : If the bulb touches the hot bottom, the reading is too high.
- Exam-type : If the bulb is above the liquid, it reads the air temperature, not the liquid.
Rule 2: Which thermometer? — Choose the thermometer to suit the job and safety.
- Easy : Digital: quick body temperature at home.
- Medium : Infrared: no touch, so it is safe in a crowd.
- Exam-type : Anna Mani, the "Weather Woman of India", designed weather instruments.
A thermometer must be vertical and not touch the container.
Reading the thermometer after taking it out of the liquid. Read it while the bulb is in the liquid.
Memory clue: Bulb In, Upright, Eye level – BUE.
Spot the difference
| Type | Feature |
|---|---|
| Digital | Button cell, beeps |
| Infrared | No touch needed |
| Laboratory | Mercury or coloured alcohol |
Practice questions
- 1Name three types of thermometers.
- 2Which thermometer does not touch the body?
- 3What fills the bulb of a laboratory thermometer?
- 4Who is called the "Weather Woman of India"?
- 5Why should the thermometer be kept vertical?
- 6Why should the bulb not touch the bottom of the beaker?
- 7Why was an infrared thermometer used during COVID-19?
- 8In a test the bulb was above the water. What does the thermometer show?
Show answers (try them yourself first)
- 1Digital, infrared and laboratory.
- 2Infrared
- 3Mercury or coloured alcohol
- 4Anna Mani
- 5For a correct reading in the liquid.
- 6The bottom can be hotter than the liquid.
- 7It measures temperature without touching, which avoids spreading infection.
- 8The air temperature, not the water's.
Quick revision
- Standard units: metre, kilogram, second, kelvin. 1 km = 1000 m, 1 m = 100 cm, 1 cm = 10 mm.
- Reference point; use thread for curves; thermometer for temperature.