1. Chapter at a Glance
How long is your desk? You might say “about 5 handspans”. But your friend’s handspan is different from yours, so her answer may be 6 handspans. To avoid such confusion, the world uses standard units. This chapter teaches how to measure length correctly, how to describe where something is using a reference point, and how things move — in a straight line, in a circle or to and fro.
- Measurement = a number + a unit; why standard units are needed.
- The SI unit of length (metre) and conversions between km, m, cm and mm.
- Correct ways of measuring with a scale, and measuring curved lines.
- Reference point, rest and motion.
- Linear, circular, oscillatory and periodic motion.
2. How Do We Measure?
To measure means to compare an unknown quantity with a fixed, known quantity called a unit. Every measurement has two parts: a number and a unit. In “13 handspans”, 13 is the number and handspan is the unit.
In ancient India, people used body-based units like angula (finger width), dhanusa and yojana for long distances. Objects with ruled markings, possibly used as scales, have been found at Harappan sites. But body parts differ from person to person, so such units are not reliable.
3. Standard Units and the SI System
To make measurements the same everywhere, scientists agreed on the International System of Units (SI units). The SI unit of length is the metre (m).
| Conversion | Use |
|---|---|
| 1 kilometre (km) = 1000 metres (m) | Distance between towns |
| 1 metre (m) = 100 centimetres (cm) | Height of a door, a person |
| 1 centimetre (cm) = 10 millimetres (mm) | Length of an eraser, thickness of a coin |
| 1 inch = 2.54 cm | Screen sizes, some tools |
- Unit symbols are written in small letters: m, cm, km (not M or Cm).
- No “s” for plural: 5 cm, not 5 cms.
- No full stop after a symbol unless the sentence ends.
(a) 2.5 km = 2.5 × 1000 = 2500 m. (b) 1.35 m = 1.35 × 100 = 135 cm. (c) 45 mm = 45 ÷ 10 = 4.5 cm. (d) 7 cm 3 mm = 70 + 3 = 73 mm.
4. Correct Way of Measuring Length
- Place the scale correctly: keep it touching the object, along the length being measured.
- Start from zero: put one end of the object exactly at the zero mark.
- Keep your eye directly above the reading: looking from the side gives a wrong reading.
- If the zero mark is broken: start from any full mark (say 1.0 cm) and subtract it from the final reading.
A pencil begins at the 1.0 cm mark and ends at 13.5 cm. Length = 13.5 − 1.0 = 12.5 cm.
5. Measuring the Length of a Curved Line
A scale cannot bend along a curve. So we place a thread carefully along the curved line, mark where the line ends, straighten the thread and measure it on a scale. A flexible measuring tape (used by tailors) can also measure curved surfaces like the waist or the base of a bottle. Visually challenged students use scales with raised markings that can be felt.
6. Describing Position — Reference Point
“The library is 200 m from the school gate.” Here the school gate is the reference point — a fixed object with respect to which we state position and distance. Without a reference point, “200 m away” has no meaning.
7. Moving Things: Rest and Motion
- An object is in motion if its position changes with respect to a reference point with time — a moving bus compared with a tree by the road.
- An object is at rest if its position does not change with respect to the reference point with time — a building, a parked car.
Rest and motion depend on the reference point. A passenger sitting in a moving train is at rest with respect to the seat but in motion with respect to the platform.
8. Types of Motion
| Type | Meaning | Examples |
|---|---|---|
| Linear (rectilinear) | Along a straight line | Falling eraser, march-past, car on a straight road |
| Circular | Along a circular path | Stone whirled on a thread, merry-go-round, blades of a fan (each point) |
| Oscillatory | To and fro about a fixed position | Swing, pendulum, vibrating metal strip |
| Periodic | Repeats after a fixed time | Circular and oscillatory motions, hands of a clock |
An object can show more than one motion at the same time: the wheel of a moving bicycle rotates (circular) while the bicycle moves forward (linear).
9. Master Table: Units and Key Terms
| Quantity / Term | Value / Meaning |
|---|---|
| SI unit of length | metre (m) |
| 1 km | 1000 m |
| 1 m | 100 cm = 1000 mm |
| 1 cm | 10 mm |
| 1 inch | 2.54 cm |
| Length with broken scale | Final reading − starting reading |
| Reference point | Fixed point to describe position |
| Periodic motion | Motion repeating after fixed intervals |
10. Master Summary Table
| Topic | Key idea | Common question |
|---|---|---|
| Units | Number + unit; SI unit metre | Why handspan is not standard |
| Measuring | Zero mark, eye vertical, scale along object | Broken scale reading |
| Curved length | Thread or measuring tape | Measure base of a bottle |
| Rest/motion | Depends on reference point | Passenger in train |
| Motion types | Linear, circular, oscillatory, periodic | Rollercoaster, swing, fan |
Chart — sizes of everyday lengths:
Bars are not to scale; they show which unit suits each length.
11. Mind Map
- Number + unit
- SI: metre
- Zero mark, eye above
- Thread for curves
- Reference point
- Rest vs motion
- Linear, circular
- Oscillatory, periodic
12. Tips and Tricks
- Big unit to small unit → multiply; small to big → divide (km → m ×1000; mm → cm ÷10).
- “King Many Centipedes Move”: km → m → cm → mm (×1000, ×100, ×10).
- In motion questions, always name the reference point.
- Writing “cms” or “Kms” — symbols never take “s” and are lowercase.
- Reading a broken scale without subtracting the starting mark.
- Calling a swing’s motion circular — it is oscillatory (to and fro).
13. Important One-liners
- A measurement has a number and a unit.
- Handspan and cubit are not standard units.
- The SI unit of length is the metre.
- 1 km = 1000 m; 1 m = 100 cm; 1 cm = 10 mm.
- The eye should be vertically above the mark while reading a scale.
- A thread helps measure a curved line.
- Position is described with respect to a reference point.
- Motion of a swing is oscillatory and periodic.
- A fan blade’s tip shows circular motion.
14. Exam-pattern Questions with Detailed Answers
Which of these is a standard unit of length?
- Handspan
- Cubit
- Metre
- Footstep
Show answer
Metre is the SI unit; the others depend on body size and vary between people.
Answer: (C) Metre
Convert 3.2 km into metres.
Show answer
3.2 × 1000 = 3200 m.
Answer: 3200 m
Give one example each of circular and oscillatory motion.
Show answer
Circular: a merry-go-round. Oscillatory: a swing or pendulum.
Answer: Merry-go-round; swing
A pencil is placed from the 2.0 cm mark to the 16.8 cm mark of a broken scale. Find its length.
Show answer
Length = 16.8 − 2.0 = 14.8 cm.
Answer: 14.8 cm
Why do different students get different results when they measure a desk with handspans?
Show answer
Each student’s handspan is of a different length, so the unit itself changes. A standard unit such as the metre gives the same result for everyone.
Answer: Handspan is not a standard (fixed) unit
Explain how you would measure the length of a curved line on a map.
Show answer
Place a thread carefully along the curved line, tying a knot at the start and marking the end. Straighten the thread and measure the marked length on a scale. Convert using the map scale if needed.
Answer: Use a thread along the curve, then measure it on a scale
A passenger sits in a moving bus. Is she at rest or in motion? Explain.
Show answer
Both, depending on the reference point. With respect to her seat or the bus, her position does not change — she is at rest. With respect to trees outside, her position changes — she is in motion.
Answer: At rest w.r.t. bus; in motion w.r.t. road
Arrange in increasing order: 1.5 m, 120 cm, 1600 mm, 0.001 km.
Show answer
Convert to cm: 150 cm, 120 cm, 160 cm, 100 cm. Increasing order: 0.001 km < 120 cm < 1.5 m < 1600 mm.
Answer: 0.001 km, 120 cm, 1.5 m, 1600 mm
Identify the types of motion in a rollercoaster ride that has a straight track, a loop and a car swinging at the end.
Show answer
Straight track — linear motion. Loop — circular motion. Swinging car — oscillatory motion. The loop and the swinging are also periodic if repeated regularly.
Answer: Linear, circular, oscillatory
You need a makeshift metre scale. Would you choose a rope, a wooden stick or a rubber band? Why?
Show answer
A wooden stick: it does not stretch or bend, so its length stays fixed. A rubber band stretches and a rope sags or bends, giving unreliable measurements.
Answer: Wooden stick — fixed, non-stretching length
A bicycle moves along a straight road. Describe the motions of the bicycle and of its wheel.
Show answer
The bicycle as a whole shows linear motion. Its wheel rotates about the axle (circular motion) while also moving forward with the bicycle (linear). So the wheel shows both motions together.
Answer: Bicycle — linear; wheel — circular + linear
15. Quick Revision Summary
- Measurement = number + unit; body units vary, so SI units are used; SI unit of length = metre.
- 1 km = 1000 m, 1 m = 100 cm, 1 cm = 10 mm; symbols lowercase, no “s”.
- Measure from zero, keep eye vertically above, subtract start mark for broken scales; use thread for curves.
- Rest and motion depend on the reference point.
- Motion types: linear, circular, oscillatory; circular and oscillatory are periodic.