Length
Measurement · Length
Syllabus tag: KCSE | Mathematics | Form 1 | Topic 12 Length
Lesson objectives
By the end of this topic, you should be able to:
- State the units of length and convert from one to another.
- Express numbers to a required number of significant figures.
- Find the perimeter of plane figures and the circumference of circles.
- Solve problems involving length in real situations.
Length
Length measures distance. This topic converts units, expresses answers to a stated accuracy, and finds distances round the edges of shapes.
a) Units
| Unit | In metres |
|---|---|
| Kilometre (km) | 1 000 |
| Hectometre (Hm) | 100 |
| Decametre (Dm) | 10 |
| Metre (m) | 1 |
| Decimetre (dm) | 0.1 |
| Centimetre (cm) | 0.01 |
| Millimetre (mm) | 0.001 |
Each step down multiplies by 10; each step up divides by 10.
A check: the smaller the unit, the larger the number.
b) Significant figures
Significant figures are counted from the first non-zero digit.
Zeros before the first non-zero digit are not significant; they only hold the place.
Zeros between non-zero digits are significant. In 3 004 there are four.
Trailing zeros after a decimal point are significant. In 2.50 there are three.
Round from the original value, never from an already rounded one.
c) Decimal places against significant figures
Decimal places are counted after the point. Significant figures are counted from the first non-zero digit.
For 0.004567: to 3 decimal places it is 0.005, but to 3 significant figures it is 0.00457.
They are very different answers. Read which one the question asks for.
d) Perimeter
The perimeter is the distance round a plane figure.
For any straight-sided shape, add all the sides.
Rectangle: P = 2(l + w). Square: P = 4s.
Work inside the bracket before doubling.
e) Circumference
The circumference is the perimeter of a circle.
C = 2πr, or equally C = πd.
Use 22/7 for π when the radius is a multiple of 7; otherwise 3.142 is usual.
If given the diameter, halve it first. Using the diameter as the radius doubles every answer.
f) Composite figures
For a shape combining straight and curved parts, work out each part separately.
Include only the edges on the outside of the figure.
Where two shapes join, that internal edge is not part of the perimeter.
For a semicircle, the curved part is half the circumference. Add the straight diameter if it forms an outside edge.
g) Where this is used
Fencing land. Edging a garden bed. Measuring cloth for a hem. Calculating how far a wheel travels in one revolution.
Words to know
- Perimeter -- the total distance around a closed plane figure.
- Circumference -- the perimeter of a circle.
- Diameter -- a straight line through the centre joining two points on a circle.
- Radius -- the distance from the centre of a circle to its edge, half the diameter.
- Significant figures -- digits counted from the first non-zero digit.
:::checkpoint Check yourself
- Convert 3.5 km into centimetres.
- Express 0.0080654 to 3 significant figures.
- Find the circumference of a circle of diameter 28 cm, taking π as 22/7.
- How many significant figures are there in 3 004? :::
Bridge to practice
The exercises begin with units and conversion, move through significant figures, perimeter and circumference, and finish with composite figures and costing problems. Before adding any lengths, confirm that every measurement is in the same unit.