Q1. Express the following rational numbers as decimals:
(i) \(\frac{42}{100}\)
(ii) \(\frac{327}{500}\)
(iii) \(\frac{15}{4}\)
Solution:
(i) By long division method
100) \(\overline{42}\)
400
\(\overline{200}\)
200
\(\overline{0}\)
Therefore, \(\frac{42}{100}\)
(ii) By long division method
500) \(\overline{327.000}\)
3000
\(\overline{2700}\)
2500
\(\overline{2000}\)
2000
\(\overline{0}\)
Therefore, \(\frac{327}{500}\)
(iii) By long division method
4) \(\overline{15.00}\)
12
\(\overline{30}\)
28
\(\overline{20}\)
20
\(\overline{0}\)
Therefore, \(\frac{15}{4}\)
Q2. Express the following rational numbers as decimals:
(i) \(\frac{2}{3}\)
(ii) –\(\frac{4}{9}\)
(iii) –\(\frac{2}{15}\)
(iv) –\(\frac{22}{13}\)
(v) \(\frac{437}{999}\)
Solution:
(i) By long division method
3) \(\overline{2.0000}\)
18
\(\overline{20}\)
18
\(\overline{2}\)
Therefore, \(\frac{2}{3}\)
(ii) By long division method
9) \(\overline{4.000}\)
3600
\(\overline{4000}\)
3600
\(\overline{4000}\)
3600
\(\overline{400}\)
Therefore, – \(\frac{4}{9}\)
(iii) By long division method
15) \(\overline{2.00}\)
15
\(\overline{50}\)
45
\(\overline{50}\)
45
\(\overline{50}\)
45
\(\overline{5}\)
Therefore, \(\frac{2}{15}\)
(iv) By long division method
13) \(\overline{22.000}\)
13
\(\overline{90}\)
78
\(\overline{120}\)
117
\(\overline{30}\)
26
\(\overline{40}\)
39
\(\overline{100}\)
91
\(\overline{90}\)
78
\(\overline{120}\)
117
\(\overline{3}\)
Therefore, – \(\frac{22}{13}\)
(v) By long division method
999) \(\overline{437.0000}\)
3996
\(\overline{3740}\)
2997
\(\overline{7430}\)
6993
\(\overline{4370}\)
3996
\(\overline{3740}\)
2997
\(\overline{743}\)
Therefore, \(\frac{437}{999}\)
Q3. Look at several examples of rational numbers in the form of
\(\frac{p}{q}\)
common factor other than 1 and having terminating decimal
representations. Can you guess what property q must satisfy?
Solution:
A rational number \(\frac{p}{q}\)
only, when prime factors of q are q and 5 only. Therefore,
\(\frac{p}{q}\)
factorization of q must have only powers of 2 or 5 or both.