Page 76 - Start Up Mathematics_7

By taking adequate examples, find which of the following properties hold for the rest of
the fundamental operations and complete the table given below:

Operation Closure Commutative Associative Identity
Addition Yes Yes Yes Yes
Subtraction ________ ________ ________ ________
Multiplication ________ ________ ________ ________
Division ________ ________ ________ ________

Decimal Representation of Rational Numbers

Every rational number can be converted into an equivalent decimal form either by using long
division method or writing an equivalent rational number whose denominator is some power of
10 only.
Decimal numbers are of two types—terminating and non-terminating decimal numbers.
Terminating decimals are those which have a finite number of digits in the decimal part
(i.e., right of the decimal point).
7
Let’s convert into decimals.
8
8 7.0 0.875
–0
7
70 or 7 = = 7 × 5 3 = 875 = 0.875
3
–64 8 2 3 2 × 5 3 10 3
60
–56
40
–40
0

A rational number can be represented by a terminating decimal iff the prime factorization of its denominator
(in the simplest form) contains no primes other than 2 or 5.

Non-terminating decimals are those whose decimal representation has infinite number of digits
in the decimal part. In fact, non-terminating decimals are also of two types, i.e., non-terminating
recurring (or repeating) and non-terminating non-recurring decimals.
2
For example, can be written as
11 11 2.0 0.18

–0
20
–11
90
–88
2

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