Practice the questions given in the worksheet on rational number as decimal numbers.
A fraction \(\frac{a}{b}\) (in its lowest terms) is a terminating decimal only when its denominator that is b can be expressed as n = 2^m5^n where m, n = 0, 1, 2, ....
A fraction \(\frac{a}{b}\) (in its lowest terms) is a recurring decimal only when its denominator that is b has a prime factor other than 2 or 5.
1. Which of the following will changes into a terminating decimal? Justify.
\(\frac{13}{125}\), \(\frac{2}{9}\), \(\frac{23}{60}\), \(\frac{7}{250}\)
2. Write the following fractions as decimal number:
(i) \(\frac{1}{4}\)
(ii) \(\frac{17}{40}\)
(iii) \(\frac{11}{9}\)
(iv) \(\frac{13}{44}\)
(v) \(\frac{4}{7}\)
3. Which of the following will be converted into a nonterminating decimal? Justify.
\(\frac{3}{5}\), \(\frac{9}{75}\), \(\frac{7}{20}\), \(\frac{4}{30}\)
4. Express \(\frac{5}{48}\) as a decimal fraction correct to four decimal places.
5. Which of the following will change into a recurring decimal? Justify.
\(\frac{3}{4}\), \(\frac{7}{150}\), \(\frac{11}{200}\), \(\frac{5}{44}\)
6. Without actual division, find which of the following fractions are terminating decimals:
(i) \(\frac{7}{16}\)
(ii) \(\frac{21}{80}\)
(iii) \(\frac{136}{250}\)
(iv) \(\frac{5}{6}\)
(v) \(\frac{54}{60}\)
(vi) \(\frac{48}{55}\)
(iii) \(\frac{44}{63}\)
(iv) \(\frac{115}{640}\)
7. If \(\frac{3}{14}\) is changed into a decimal number, what type of a decimal number will it be?
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Answers for the worksheet on rational number as decimal numbers are given below.
Answers:
1. \(\frac{13}{125}\), \(\frac{7}{250}\)
2. (i) 0.25
(ii) 0.425
(iii) 2.\(\dot{2}\)
(iv) 0.29\(\dot{5}\)\(\dot{4}\)
(v) 0.\(\bar{538461}\)
3. \(\frac{9}{75}\), \(\frac{4}{30}\)
4. 0.1042
5. \(\frac{7}{150}\), \(\frac{5}{44}\)
6. (i) \(\frac{7}{16}\)
(ii) \(\frac{21}{80}\)
(iii) \(\frac{136}{250}\)
(v) \(\frac{54}{60}\)
(iv) \(\frac{115}{640}\)
7. Nonterminating, recurring
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