Page 18 - Mathematics

Activity 2.3: Expressing measurements of quantities in decimals

1. Take some fruits or similar objects and divide them into two, three, four,
five, six, and seven equal parts.
2. Convert each fraction in task 1 into decimals in many decimal places as
possible. You can work manually or use a calculator.
3. Study carefully the decimal part of the fractions and write down their
unique characteristics.

A repeating decimal, also known as recurring decimal is a decimal number with
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at least one digit in the decimal part that repeats consecutively in a regular order
without an end. For example, 1.6666666… and 0.639639639639… are repeating
decimals because 6 and 639 digits from the two decimal numbers, respectively,
in the decimal part repeat themselves without an end. The three dots indicate that
the repeating digits continue infinitely.
Repeating decimals can also be represented by using a dot or a bar that is placed

on top of a repeating digit.

Example 2.4

Write each of the following repeating decimals by using a dot and a bar.
(a) 0.3333... (b) 0.639639639... (c) 0.474747474...

Solution


(a) 0.3333... is a repeating decimal which can be written as 0.3 or 0.3

(b) 0.639639639... can be written as 0.639 or 0.639
 
(c) 0.474747474... can be written as 0.47 or 0.47
Mathematics Form One (c), it can be observed that if a group of digits is repeating, a dot should be put
In Example 2.4, the digits with a dot or a bar are repeating infinitely. In (b) and

over the first and the last repeating digits.
Decimals are either terminating or non-terminating. Terminating decimals have a
definite number of digits after the decimal point while non-terminating decimals
have an endless number of digits after the decimal point. Thus, repeating decimals
are non-terminating with one or more repeating digits in the decimal part.

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Mathematics form 1.indd 12
Mathematics form 1.indd 12 25/10/2024 09:51:03