Measurement of Length and Motion · Lesson 1 of 5
From Handspans to Standard Units
“Discover why reliable measurement needs shared units and learn how metres, centimetres, millimetres and kilometres fit together.”
• Explain why a measurement must contain both a number and a unit. • Compare informal body-based units with standard units. • Explain why standard units are necessary for reliable communication. • Use metre, centimetre, millimetre and kilometre appropriately. • Convert between common metric units of length.
Why Measurement Needs Units
Imagine buying cloth, measuring a table, or deciding how far apart two places are. Saying only a number such as “13” is not enough. We must also say what that number counts. A useful measurement therefore has two parts: a numerical value and a unit.
A chosen standard or reference length used to express how long, tall, wide or far something is.
Problem
Five students measure the same table using their own handspans and obtain slightly different answers. Why?
- 1.Each student is using a handspan as the unit.
- 2.Their handspans are not exactly the same size.
- 3.A smaller handspan must be repeated more times to cover the same table, while a larger handspan is repeated fewer times.
- 4.The table has not changed; the unit has changed from person to person.
- 5.This shows why body-based units are convenient for rough estimates but unreliable for precise shared measurements.
| Student | Approximate handspan count |
|---|---|
| Anish | Slightly more than 13 |
| Padma | 13 |
| Tasneem | Slightly less than 13 |
| Deepa | Between 13 and 14 |
| Hardeep | 14 |
People have long used body-based measures such as handspan, finger width, arm length, foot length and stride. They are easy to use because they need no instrument, but they vary from person to person. That variation becomes a problem when people need to trade, build, travel or compare measurements.
India has a long history of measurement. Traditional units such as angula, dhanusa and yojana are mentioned in old literature, and ruled objects that may have been used for measurement have been found at Harappan sites. Some craftspeople still use traditional body-based measures in practical work.
Why Standard Units Were Needed
As travel and trade increased, different local systems of measurement caused confusion. A shared system solves this problem because a metre measured in one place means the same length elsewhere. The internationally accepted system is called the International System of Units, often shortened to SI.
The SI unit of length is the metre, written with the symbol m.
Metres, Centimetres, Millimetres and Kilometres
A metre is useful for many everyday lengths, but not for everything. The distance between cities is more conveniently written in kilometres, while the thickness of a small object may be better expressed in millimetres. Choosing a suitable unit keeps the number easy to read and interpret.
A typical 15 cm ruler has ten small divisions within each centimetre. Each small division represents 1 mm. On such a ruler, 1 mm is the smallest marked length that can be read directly.
Problem
A school is 1.5 km from a student's home. Express the distance in metres.
- 1.We know that 1 km = 1000 m.
- 2.Multiply the kilometre value by 1000.
- 3.1.5 × 1000 = 1500.
- 4.Therefore, 1.5 km = 1500 m.
Problem
Which unit is more suitable for each: the distance between two cities, the length of an eraser, and the thickness of a coin?
- 1.A distance between cities is large, so kilometre is convenient.
- 2.An eraser is a few centimetres long, so centimetre is convenient.
- 3.A coin is only a few millimetres thick, so millimetre is convenient.
- 4.The best unit depends on the size of the length being described.
Some rulers also show inches. One inch is equal to 2.54 cm. Units such as inch and foot are still used in some contexts even though metre is the SI unit of length.
Do not write a measurement as a number alone. “15” does not tell the reader whether the length is 15 mm, 15 cm or 15 m. Always include the unit.
Quiz
Why can two students obtain different handspan counts for the same table?
What is the SI unit of length?
Which statement is correct?
Which unit is most suitable for the thickness of a coin?
A length is written as 24 cm. What does 24 represent?
Practice Problems
- Explain why handspan is not suitable as a standard unit of length.
- Write each measurement as a number and a unit: 7 metres, 35 centimetres and 4 millimetres.
- Convert 3 km to metres.
- Convert 2 m to centimetres.
- Convert 6 cm to millimetres.
- Choose a suitable unit for the length of a classroom, the thickness of a notebook page and the distance between two towns.
- A ruler has ten equal small divisions between 4 cm and 5 cm. What length does one small division represent?
Key Takeaways
• Every measurement needs both a number and a unit. • Body-based units vary from person to person, so they are not reliable standards. • The SI unit of length is the metre (m). • 1 km = 1000 m, 1 m = 100 cm and 1 cm = 10 mm. • Choose a unit that suits the size of the length being measured.
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Measuring Length Accurately