Units of measure and scale
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Notes de leçon
Metric Units and Prefixes
- The metric system uses base units such as the metre (m) for length, kilogram (kg) for mass, and second (s) for time.
- Prefixes show multiples or fractions of a unit: kilo means ×1000, centi means ×0.01, milli means ×0.001.
- For example, 1 kilometre = 1000 metres, 1 centimetre = 0.01 metres, and 1 milligram = 0.001 grams.
- The International System of Units (SI) is the modern metric system, with seven base units including metre, kilogram, second, ampere (A), kelvin (K), mole (mol), and candela (cd).
- Derived units are combinations of base units, such as the newton (kg·m/s²) for force and the hertz (cycles per second) for frequency.
- The litre (L) is a widely used non-SI unit for capacity; 1 litre = 1000 cm³ and 1 m³ = 1000 litres.
Converting Between Metric Units
- To convert between metric units, multiply or divide by powers of 10 according to the prefix.
- Length: 1 km = 1000 m, 1 m = 100 cm, 1 cm = 10 mm.
- Mass: 1 tonne = 1000 kg, 1 kg = 1000 g, 1 g = 1000 mg.
- Capacity: 1 litre = 1000 ml, 1 cl = 10 ml, 1 litre = 100 cl.
- Time: 1 hour = 60 minutes, 1 minute = 60 seconds; these are not decimal conversions.
- When converting, check the direction: from a larger unit to a smaller unit, multiply; from smaller to larger, divide.
Area and Volume Unit Conversions
- Area units are squared, so conversions involve squaring the length conversion factor.
- 1 m² = 10 000 cm² because 1 m = 100 cm, so 100 × 100 = 10 000.
- 1 cm² = 100 mm² because 1 cm = 10 mm, so 10 × 10 = 100.
- Volume units are cubed, so conversions involve cubing the length conversion factor.
- 1 m³ = 1 000 000 cm³ because 1 m = 100 cm, so 100³ = 1 000 000.
- 1 cm³ = 1000 mm³ because 1 cm = 10 mm, so 10³ = 1000.
- 1 cm³ is the same as 1 millilitre (ml), and 1 m³ = 1000 litres.
Metric–Imperial Equivalents
- Approximate conversions between metric and imperial units are useful for everyday estimates.
- 1 inch ≈ 2.5 cm; 1 foot ≈ 30 cm; 1 mile ≈ 1.6 km.
- 1 kilogram ≈ 2.2 pounds (lb); 1 pound ≈ 0.45 kg.
- 1 litre ≈ 1.75 pints; 1 gallon ≈ 4.5 litres.
- These are approximations; exact values differ slightly.
Reading Scales
- To read a scale, first work out the value of each small division by counting the intervals between labelled marks.
- For example, if a scale from 0 to 10 has 10 intervals, each small division is 1 unit.
- If a scale from 0 to 5 has 10 intervals, each small division is 0.5 units.
- Always estimate the reading to the nearest small division or half-division if the pointer lies between marks.
- Check the unit label on the scale to ensure you record the correct unit.
Scale Drawings and Map Scales
- A scale drawing represents a real object or distance using a ratio, such as 1 : 100.
- A scale of 1 : 100 means 1 unit on the drawing represents 100 units in real life.
- Map scales are often written as ratios, e.g. 1 : 25 000, meaning 1 cm on the map represents 25 000 cm (250 m) in reality.
- To find a real distance, measure the drawing and multiply by the scale factor.
- To make a scale drawing, divide the real length by the scale factor.
- Ensure units are consistent when calculating with scales; convert if necessary.
Similar Shapes and Scale Factors
- Similar shapes have the same shape but different sizes; corresponding angles are equal and corresponding sides are in the same ratio.
- The scale factor is the multiplier that enlarges or reduces one shape to another.
- If the scale factor is k, then lengths are multiplied by k, areas by k², and volumes by k³.
- For example, if a shape is enlarged by scale factor 2, its area becomes 4 times larger and its volume 8 times larger.
- To find a missing length in similar shapes, set up a proportion using corresponding sides.
Choosing Units and Estimating
- Choose sensible units for the context: use millimetres for small lengths, metres for room sizes, kilometres for distances between towns.
- Use grams for small masses, kilograms for body mass, tonnes for large loads.
- Use millilitres for small volumes, litres for bottles, cubic metres for large volumes.
- Estimating with approximate conversions helps check that answers are reasonable.
- Always include units in your answer and round appropriately for the context.
Diapos
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Questions d'entraînement
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1.Which of these is a base unit in the International System of Units (SI)?
Easy- Athe litre
- Bthe kilogram
- Cthe newton
- Dthe hertz
2.The prefix milli means a factor of:
Easy- A1000
- B100
- C1/100
- D1/1000
3.A length is given as 3.5 km. What is this length in metres?
Medium- A35 m
- B350 m
- C3500 m
- D35000 m
4.The area of a rectangle is 0.04 m². What is this area in cm²?
Medium- A4 cm²
- B40 cm²
- C400 cm²
- D4000 cm²
5.The volume of a container is 2500 cm³. What is this volume in litres?
Medium- A0.25 L
- B2.5 L
- C25 L
- D250 L
6.Which of the following are SI base units? (select all that apply)
Medium- Asecond
- Bampere
- Cnewton
- Dkelvin
- Elitre
7.The litre is an SI base unit.
EasyTrue or false?
8.Match each prefix to its meaning.
Medium- kilo
- centi
- milli
- mega
- one thousandth
- one million
- one hundredth
- one thousand
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