Question

Express the following decimal numbers in the form of

p

q

and write the prime factors of


q. What do you observe?

(i) 43.123 (ii) 0.120112001120001... (iii) 43.12 (iv) 0.63
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only 4 solution ​

Answer 1

Answer:

hey mate

1) Ans- The prime factors of q are 2 and 5.

Denominator q is in the form of 2 n .5 m

Hence 43.123 is terminating decimal form.

2) Ans- 0.1201201 in form of p/q is and the prime factor of q are in terms of 2 and 5.

3) Ans- The prime factors of q are 2 and 5.

Denominator q is in the form of 2 n .5 m

Hence 43.12 is terminating decimal form.

4) The denominator is not in the form of 2 n .5 m

∴0.636363.. is a non terminating, repeating decimal form.

Step-by-step explanation:

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Answer 2

Answer:

The numbers in fraction form along with the prime factors are shown

$\frac{43123}{1000} - - > 2 \: and \: 5 \\ \frac{1201}{10000} - - - > 2 \: and \: 5 \\\frac{1078}{25} - - - > 5 \\ \frac{63}{100} - - - > 2 \: and \: 5$

Step-by-step explanation:

Given numbers are decimals and we have to express them in form of a fraction and also fimd the prime factors of denominators of fractions.

(i)43.123

As it has 3 digits after decimal,we shall multiply and divide it with 1000.It is done as shown,

$= 43.123 \times \frac{1000}{1000} = \frac{43123}{1000}$

The prime factors of 1000 are found as follows

$1000 = 2 \times 2 \times 2 \times 5 \times 5 \times 5$

Hence,the prime factors are 2 and 5.

(ii)0.120112001120001...

We shall multiply with 10000 and divide it with 10000

$\approx0.1201 \times \frac{10000}{10000} = \frac{1201}{10000}$

The prime factors of 10000 are also 2 and 5 as

$10000 = 2 {}^{4} \times {5}^{4}$

iii)43.12

We shall multiply and divide it with 100.Therefore,

$= 43.12 \times \frac{100}{100} = \frac{4312}{100} = \frac{1078}{25}$

The prime factor of 25 is only 5 as,

$25 = 5 \times 5$

(iv)0.63

We shall multiply and divide it with 100.Therefore,

$= 0.63 \times \frac{100}{100} = \frac{63}{100}$

The prime factors of 100 are 2 and 5 as,

$100 = {2}^{2} \times {5}^{2}$

Hence all the numbers are expressed in fractions and the prime factors of their denominators are deduced.

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