Page 26 - Mathematics

7. John wants to divide a 1 metre-long ribbon so that he can share it equally
with his two friends. How much in metres will each get? Express your
answer in decimals.
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
8. If m = 0.2 and n = 0.04, show that m = ( nm + 1).
2
9. A car travels 2/3 of the total distance to its destination at a speed of 30
km/h, and then travels the remaining distance at a speed of 40 km/h. If
the car took 4 hours for the whole journey, what is the total distance of
the journey? Express your answer as a repeating decimal.
10. The base of a lid of bucket has an area of 25 π m . Find its diameter in
2
484
decimal.
Tanzania Institute of Education

Irrational numbers
Irrational numbers are special numbers in our life. A widely known and used irrational
number is Pi ( )π which appears in formulas for determining circumferences, areas,
and volumes of circular shapes. Activity 2.4 allows you to use your experience
in decimals to learn about irrational numbers.

Activity 2.4: Differentiating types of decimal numbers

1. Identify 10 different fractions which can be converted into terminating
or repeating decimals.
2. Use a calculator to find answers to the square roots of at most 10 numbers
that have no perfect squares and write your answers with at least 10
decimal places.
3. Compare the answers in tasks 1 and 2 and write down the differences
observed.

An irrational number is a number which can be written as a non-terminating and
a
non-repeating decimal. Also, these numbers cannot be expressed in the form of ,
b
Mathematics Form One they can always be approximated to rational numbers.
where a and b are integers and b ≠ . The set of irrational numbers is denoted by
0
. ′ Irrational numbers cannot be represented exactly on a number line. However,
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Example 2.10

Write any 6 irrational numbers.

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