Units of measure and scale

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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.

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Câu hỏi luyện tập

Xem trước miễn phí — 8 trên 65 câu hỏi. Đăng ký để xem tất cả.

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.
Easy
True or false?
8.Match each prefix to its meaning.
Medium
- kilo
- centi
- milli
- mega
- one thousandth
- one million
- one hundredth
- one thousand

Thêm câu hỏi

9.Which of the following are units of length? (select all that apply)
Medium
- Ametre
- Bkilometre
- Ckilogram
- Dcentimetre
- Elitre
10.Which of the following conversions are correct? (select all that apply)
Medium
- A1 km = 1000 m
- B1 m = 100 cm
- C1 cm = 10 mm
- D1 kg = 100 g
- E1 litre = 1000 cm³
11.Match each quantity to its SI base unit.
Medium
- length
- mass
- time
- electric current
- kilogram
- second
- metre
- ampere
12.Arrange these metric units of length in order from smallest to largest.
Medium
- millimetre
- centimetre
- metre
- kilometre
13.Arrange these areas in order from smallest to largest.
Medium
- 1 cm²
- 1 m²
- 1 hectare
- 1 km²
14.Which of the following is a derived unit?
Easy
- Ametre
- Bkilogram
- Cnewton
- Dsecond
15.A map has a scale of 1 : 50 000. Two towns are 4 cm apart on the map. What is the actual distance between them, in kilometres?
Medium
- A0.2 km
- B2 km
- C20 km
- D200 km
16.A model car is built to a scale of 1 : 24. The length of the model is 18 cm. What is the length of the real car, in metres?
Medium
- A0.432 m
- B4.32 m
- C43.2 m
- D432 m
17.Which of the following is approximately equal to 1 mile?
Medium
- A1 km
- B1.6 km
- C10 km
- D0.6 km
18.Which of the following is approximately equal to 1 kilogram?
Medium
- A2.2 pounds
- B0.45 pounds
- C10 pounds
- D1 pound
19.The prefix centi means a factor of 100.
Easy
True or false?
20.1 cm³ is equal to 1 millilitre.
Easy
True or false?
21.A container holds 2.5 litres of water. What is this volume in cubic centimetres?
Medium
- A250 cm³
- B2500 cm³
- C25 000 cm³
- D0.25 cm³
22.A pencil is 0.15 m long. What is its length in centimetres?
Easy
- A1.5 cm
- B15 cm
- C150 cm
- D1500 cm
23.A bottle contains 750 ml of water. What is this volume in litres?
Medium
- A0.075 litres
- B0.75 litres
- C7.5 litres
- D75 litres
24.A rectangle measures 3 m by 40 cm. What is its area in square metres?
Medium
- A1.2 m²
- B12 m²
- C120 m²
- D1200 m²
25.A map has a scale of 1 : 20 000. Two villages are 7 cm apart on the map. What is the actual distance between them, in kilometres?
Medium
- A0.14 km
- B1.4 km
- C14 km
- D140 km
26.A model boat is built to a scale of 1 : 50. The length of the model is 12 cm. What is the length of the real boat, in metres?
Medium
- A0.6 m
- B6 m
- C60 m
- D600 m
27.A rectangular field is 80 m long and 50 m wide. What is its area in square metres?
Medium
- A130 m²
- B400 m²
- C4000 m²
- D40000 m²
28.A cuboid has a volume of 0.002 m³. What is this volume in cubic centimetres?
Hard
- A2 cm³
- B20 cm³
- C200 cm³
- D2000 cm³
29.Match each metric unit to the quantity it measures.
Medium
- metre
- kilogram
- litre
- second
- length
- mass
- capacity
- time
30.Arrange these metric units of mass in order from smallest to largest.
Medium
- milligram
- gram
- kilogram
- tonne
31.A third town is 7 cm from the first town on the same map. How much farther is this, in kilometres, than the distance between the first two towns?
Medium
- A1.5 km
- B2.5 km
- C3.5 km
- D5 km
32.A rectangular garden measures 12 m by 750 cm. What is its area in square metres?
Medium
- A9 m²
- B90 m²
- C900 m²
- D9000 m²
33.A map has a scale of 1 : 40 000. Two villages are 9 cm apart on the map. What is the actual distance between them, in kilometres?
Medium
- A0.36 km
- B3.6 km
- C36 km
- D360 km
34.A model car is built to a scale of 1 : 20. The length of the model is 15 cm. What is the length of the real car, in metres?
Medium
- A0.3 m
- B3 m
- C30 m
- D300 m
35.A bottle contains 2.5 litres of water. What is this volume in cubic centimetres?
Medium
- A250 cm³
- B2500 cm³
- C25 000 cm³
- D250 000 cm³
36.A rectangular room is 4.5 m long and 3.2 m wide. What is its area in square metres?
Medium
- A7.7 m²
- B14.4 m²
- C15.4 m²
- D144 m²
37.Which of the following are units of volume? (select all that apply)
Medium
- Acm³
- Bm²
- Clitre
- Dkg
- Eml
38.Which prefix means a factor of one thousandth, 10^-3?
Easy
- Amilli
- Bcenti
- Ckilo
- Dmicro
39.Which of these is the SI base unit of time?
Easy
- Asecond
- Bminute
- Chour
- Dday
40.The degree Celsius (°C) is a shifted scale derived from the kelvin, where 0 °C equals 273.15 K.
Easy
True or false?
41.What is the SI base unit of mass?
Easy
42.Convert 2.5 kilograms to grams.
Medium
43.Complete the metric conversion statement.
Easy
1 kilometre = ____ metres
44.Convert 3.2 m² to cm².
Medium
45.Convert 4500 cm³ to litres.
Medium
46.A rectangle has length 4 m and width 50 cm. Calculate its area in square metres.
Medium
47.A piece of ribbon is 2.4 m long. What is its length in centimetres?
Easy
48.A map has a scale of 1 : 25 000. Two points are 6 cm apart on the map. What is the actual distance between them, in kilometres?
Medium
49.What is the SI base unit of length?
Easy
50.What is the actual distance between the two towns, in kilometres?
Medium
51.Convert 2.5 metres into centimetres. Give your answer in centimetres.
Easy
52.A bag of flour has a mass of 1.5 kilograms. What is this mass in grams?
Easy
53.Explain why the metric system is described as a decimal system.
Medium
54.A map has a scale of 1 : 25 000. Explain how you would find the actual distance in kilometres between two points that are 6 cm apart on the map.
Hard
55.Explain the difference between a base unit and a derived unit, giving one example of each.
Medium
56.Explain how to convert a volume given in cubic centimetres to litres.
Medium
57.Convert 2.5 kilograms to grams.
Medium
- A2750 g
- B3000 g
- C2250 g
- D2500 g
58.Convert 3.2 m² to cm².
Medium
- A32000 cm²
- B28800 cm²
- C35200 cm²
- D38400 cm²
59.Convert 4500 cm³ to litres.
Medium
- A5.5 litres
- B3.5 litres
- C4.5 litres
- D6.5 litres
60.A rectangle has length 4 m and width 50 cm. Calculate its area in square metres.
Medium
- A2 m²
- B3 m²
- C4 m²
- D1 m²
61.A piece of ribbon is 2.4 m long. What is its length in centimetres?
Easy
- A264 cm
- B288 cm
- C240 cm
- D216 cm
62.A map has a scale of 1 : 25 000. Two points are 6 cm apart on the map. What is the actual distance between them, in kilometres?
Medium
- A0.5 km
- B1.5 km
- C2.5 km
- D3.5 km
63.What is the actual distance between the two towns, in kilometres?
Medium
- A1 km
- B3 km
- C4 km
- D2 km
64.Convert 2.5 metres into centimetres. Give your answer in centimetres.
Easy
- A300 cm
- B250 cm
- C275 cm
- D225 cm
65.A bag of flour has a mass of 1.5 kilograms. What is this mass in grams?
Easy
- A1800 g
- B1350 g
- C1650 g
- D1500 g

Ghi chú ôn tập

## Units of Measure and Scale — KS3 Revision ### Metric units and prefixes A **system of measurement** quantifies physical qualities with numbers. The metric system uses **decimal (base-10) prefixes** on base units. - kilo → ×1000 (10^3): 1 km = 1000 m - centi → ×1/100 (10^{-2}): 1 cm = 0.01 m - milli → ×1/1000 (10^{-3}): 1 mg = 0.001 g **SI base units:** metre (m), kilogram (kg), second (s), ampere (A), kelvin (K), mole (mol), candela (cd). **Derived units** are combinations of base units, e.g. hertz (cycles per second), newton (kg⋅m/s^2). ### Converting units - Length: 1 km = 1000 m, 1 m = 100 cm, 1 cm = 10 mm - Mass: 1 kg = 1000 g, 1 g = 1000 mg - Capacity: 1 litre = 1000 ml, 1 ml = 1 cm^3 - Time: 1 min = 60 s, 1 h = 60 min **Area:** 1 m^2 = 10000 cm^2 (×100^2) **Volume:** 1 m^3 = 1000000 cm^3 (×100^3); 1 litre = 1000 cm^3 ### Metric–imperial approximations - 1 inch ≈ 2.5 cm - 1 mile ≈ 1.6 km - 1 kg ≈ 2.2 lb - 1 litre ≈ 1.75 pints ### Reading scales Count the intervals between labelled marks to find the value of one division, then read off the position. ### Scale drawings and map scales A **scale** is written as a ratio, e.g. 1 : 50000. This means 1 unit on the drawing represents 50000 of the same unit in real life. **Formula:** real length = drawing length × scale factor ### Similar shapes Similar shapes have equal angles and corresponding sides in the same ratio. The **scale factor** k relates lengths: - Lengths: multiply by k - Areas: multiply by k^2 - Volumes: multiply by k^3 Example: if k = 3, area factor = 9, volume factor = 27.

Metric system: A decimal system of measurement using base units and prefixes such as kilo and milli.
SI base units: The seven fundamental units: metre (m), kilogram (kg), second (s), ampere (A), kelvin (K), mole (mol), candela (cd).
Derived unit: A unit formed from base units, e.g. newton (kg⋅m/s^2) or hertz (cycles per second).
Scale: A ratio comparing a drawing or model to the real object, e.g. 1 : 50000.
Scale factor: The multiplier k relating corresponding lengths in similar shapes; areas scale by k^2 and volumes by k^3.
Similar shapes: Shapes with equal corresponding angles and sides in the same ratio.

Thẻ ghi nhớ

What is a system of measurement?

A frame in which physical qualities (such as length, weight, temperature, etc.) can be quantified with numbers.

What does the metric system standardise?

A set of base units and a nomenclature describing relatively large and small quantities using decimal-based multiplicative unit prefixes (such as kilo and milli).

What is the International System of Units (SI)?

A good example of the metric system, and there are other widely accepted systems (less popular than SI) mainly used in specific fields, such as the Gaussian units for electromagnetism.

List the seven SI base units and their symbols.

metre (m), kilogram (kg), second (s), ampere (A), kelvin (K), mole (mol), and candela (cd).

What is an SI derived unit? Give two examples.

A named combination of base units, such as the hertz (cycles per second) and the newton (kg⋅m/s²).

How is the degree Celsius defined in terms of the kelvin?

It is a shifted scale derived from the kelvin: 273.15 K is equal to 0 °C while 1 K interval is same to the 1 °C interval.

What does the prefix kilo imply?

A factor of 1000 (10³).

What does the prefix milli imply?

A factor of 1/1000 (10^-3).

Express the relationship between kilometres and metres using a prefix.

A kilometre is a thousand metres.

Express the relationship between milligrams and grams using a prefix.

A milligram is one thousandth of a gram.

Which country is a notable outlier in not fully adopting the SI system?

The United States (US). Although it uses the system in some contexts, the US has resisted full adoption, and continues to use different measurement systems.

What is metrication?

Adopting the metric system.

What is a base quantity?

A set of independent dimensions of nature selected in terms of which all natural quantities can be expressed.

What is a base unit of measure?

For each base quantity, a representative quantity is defined as a base unit of measure.

What is a derived unit? Give an example.

A unit derived from the base units used for expressing quantities of dimensions that can be derived from the base dimensions of the system—e.g., the square metre is the derived unit for area, which is derived from length.

What does it mean for derived units to be coherent?

They involve only products of powers of the base units, without any further factors.

What is the unit of time in the metric system?

The second.

What is the unit of length in the metric system?

The metre or a decimal multiple of it.

What is the unit of mass in the metric system?

The gram or a decimal multiple of it.

Name three other metric systems besides SI.

The MKS system, the centimetre–gram–second (CGS) system, and the metre–tonne–second (MTS) system.

What is the Gaussian system?

A still-popular blend of the CGS electrostatic (cgs-esu) system and the CGS electromagnetic (cgs-emu) system.

What is the katal?

A derived unit for catalytic activity equivalent to one mole per second (1 mol/s), added in 1999.

How are all base units defined today?

All base units are defined by physical constants – not by prototypes in the form of physical objects, as they were in the past.

What is the relationship between the metre and the kilogram in the MKS system?

The MKS system is based on the metre, kilogram, and second.

What is the relationship between the centimetre, gram, and second in the CGS system?

The CGS system is based on the centimetre, gram, and second.

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