Units of Measurement
MAT1501 - Fundamental Mathematics · Number Skills
Units of Measurement
Understanding units of measurement is essential in mathematics and science. Units provide a standard way to quantify and compare different quantities. In this topic, you will learn about the metric system, how to convert between units, and the importance of checking units in calculations.
Key idea: After studying this unit, you should be able to:
- Convert units and derived units in the metric system.
- Convert non-metric units to metric units or vice versa.
- Check that you obtain the correct units for an answer.
1. The Metric System
1.1 Basic Units
South Africa uses the metric system, which is based on the decimal number system. The basic units include:
- Metre (m) for length
- Gram (g) for mass
- Second (s) for time
These units can be combined to create derived units. For example, speed is measured in metres per second (m/s).
1.2 Metric Prefixes
Metric prefixes are used to denote multiples or fractions of the basic units. Common prefixes include:
| Prefix | Symbol | Conversion Factor (to basic unit) | Conversion Factor (from basic unit) |
|---|---|---|---|
| Tera | T | 1012 | 10-12 |
| Giga | G | 109 | 10-9 |
| Mega | M | 106 | 10-6 |
| Kilo | k | 103 | 10-3 |
| Hecto | h | 102 | 10-2 |
| Deci | d | 10-1 | 10 |
| Centi | c | 10-2 | 102 |
| Milli | m | 10-3 | 103 |
| Micro | µ | 10-6 | 106 |
| Nano | n | 10-9 | 109 |
| Pico | p | 10-12 | 1012 |
For example, 1 kilometre (km) is equal to 1,000 metres (m) or 103 m.
1.3 Converting Units
To convert between units, you can use the conversion factors provided by the prefixes. For example, to convert 5 km to metres:
5 km × 10^3 m/km = 5,000 mSimilarly, to convert 2,500 m to kilometres:
2,500 m × 1 km/10^3 m = 2.5 km1.4 Derived Units
Derived units are formed by combining different units. For example, the unit for speed is derived from distance and time:
Speed = Distance / Time
If you travel 100 km in 2 hours, your speed is:
Speed = 100 km / 2 h = 50 km/h2. Converting Between Metric and Non-Metric Units
2.1 Non-Metric Units
Non-metric units, such as miles and pounds, are used in some countries. To convert these units to metric, you need the appropriate conversion factors. For example:
- 1 mile = 1.609 km
- 1 pound = 0.453592 kg
2.2 Example of Conversion
To convert 10 miles to kilometres:
10 miles × 1.609 km/mile = 16.09 kmTo convert 5 pounds to kilograms:
5 pounds × 0.453592 kg/pound = 2.26796 kg3. Checking Units
It is important to check that your calculations yield the correct units. For example, if you calculate speed:
Speed = Distance / Time
If distance is in kilometres and time is in hours, the resulting unit should be km/h.
Watch out: If you mix units, such as using minutes with hours without converting, your calculations will be incorrect. Always ensure your units are consistent.
Summary
- The metric system is based on the decimal number system.
- Common metric prefixes include kilo, centi, and milli.
- Derived units are formed by combining basic units.
- Check units in calculations to ensure accuracy.
Check your understanding
- Convert 1500 m to kilometres.
- How many grams are there in 2.5 kg?
- Convert 60 km/h to m/s.
- What is the speed in km/h if a car travels 200 m in 5 seconds?