Question

convert the following rational numbers into decimal form (1)1/2 (2) 1/3 (3)25/16 (4)20/17 (5)1/7 (6)3/25 (7)1/10 (8)17/6 (9)11/9 (10)5/3​

Answer 1

Explanation:

• If you can express the denominator of a simplified rational number in form $2^{p} 5^{q}$ or $2^{p}$  , $5^{q}$ where p, q ∈ N, then the number has a terminating decimal expansion.
• If you can not express the denominator of a simplified rational number in form $2^{p} 5^{q}$ or $2^{p}$ , $5^{q}$ where p, q ∈ N, then the number has a non-terminating decimal expansion.

1. $\frac{1}{2} = \frac{1}{2}$×$\frac{5}{5}=$ $\frac{5}{10} = 0.5$                                           terminating decimal
2. $\frac{1}{3} = 0.3334$                                                        non-terminating decimal
3. $\frac{25}{16} = \frac{5^{2} }{2^{4} } = \frac{5^{6} }{2^{4} 5^{4} } = \frac{5^{6} }{10^{4} } = \frac{15625}{10000} = 1.5625$            terminating decimal
4. $\frac{20}{17} = 1.1765$                                                      non-terminating decimal
5. $\frac{1}{7} = 0.1429$                                                        non-terminating decimal
6. $\frac{3}{25} = \frac{3}{25} \frac{4}{4} = \frac{12}{100} = 0.12$                                      terminating decimal
7. $\frac{1}{10} = 0.1$                                                             terminating decimal
8. $\frac{17}{6} = 2.83334$                                                      non-terminating decimal
9. $\frac{11}{9} = 1.2223$                                                        non-terminating decimal
10. $\frac{5}{3} = 1.6667$                                                         non-terminating decimal

Hence

rational numbers into decimal form $\frac{1}{2}= 0.5 , \frac{1}{3} = 0.3334, \frac{25}{16} = 1.5625 , \frac{20}{17} = 1.1765, \frac{1}{7} = 0.1429, \frac{3}{25} = 0.12 , \frac{1}{10} = 0.1 , \frac{17}{6} = 2.83334, \frac{11}{9} = 1.2223, \frac{5}{3} = 1.6667$

#SPJ3

Answer 2

Answer:

(1) 0.5

(2) 0.333....

(3) 1.5625

(4) 1.1764

(5) 0.1428

(6) 0.12

(7) 0.1

(8) 2.833333

(9) 1.2222......

(10) 1.6666..........7

Step-by-step explanation:

Rational number:-

A rational number is a number that is in the form of p/q, where p and q are integers, and q is not equal to 0. Some of the examples of rational numbers include 1/3, 2/4, 1/5, 9/3, and so on.

½  = 0.5

1/3 = 0.3333…

25/16 = 1.5625

20/17 = 1.1764

1/7 = 0.14228

3/25 = 0.12

1/10 = 0.1

17/6 = 2.83333….

11/9 = 1.2222….

5/3 = 1.66666……7

#SPJ3