The decimal expansion of a number p-q was found to be 2-444- - Find the value of p - 2q-

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Operations on Irrational Numbers

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Question

The decimal expansion of a number $\frac{p}{q}$ was found to be 2.444... . Find the value of p + 2q.

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Solution

The correct option is A 11
Let x = 2.444… (1)
Multiplying both sides by 10, we get
10x = 24.444… (2)
Subtracting (1) from (2), we get
10x - x = 24.444.. - 2.444…
x = $\frac{22}{9}$ = $\frac{p}{q}$

Now, to find p + 2q, we take p = 22 and q = 9
22 + 2(9) = 22 + 18 = 40

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The decimal expansion of a number pq was found to be 2.444... . Find the value of p + 2q.

The correct option is A 11Let x = 2.444… (1) Multiplying both sides by 10, we get 10x = 24.444… (2) Subtracting (1) from (2), we get 10x - x = 24.444.. - 2.444… x = 229 = pq Now, to find p + 2q, we take p = 22 and q = 9 22 + 2(9) = 22 + 18 = 40

The decimal expansion of a number $\frac{p}{q}$ was found to be 2.444... . Find the value of p + 2q.

The correct option is A 11
Let x = 2.444… (1)
Multiplying both sides by 10, we get
10x = 24.444… (2)
Subtracting (1) from (2), we get
10x - x = 24.444.. - 2.444…
x = $\frac{22}{9}$ = $\frac{p}{q}$

Now, to find p + 2q, we take p = 22 and q = 9
22 + 2(9) = 22 + 18 = 40