Express 5-324in the form - where - and - are integers- and -

Take 𝑥 = 5.324324… nbsp; nbsp;(I) Multiplying both sides with 1000, we get 1000x = 5324.324324… nbsp; nbsp; (II) Subtracting (I) from (II), we get ...

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Standard IX

Mathematics

Decimal Expansion of Rational and Irrational Numbers

Express 5.324...

Question

Express $5.324$ in the form $\frac{p}{q}$ where $p$ and $q$ are integers, and $q \neq 0$ .

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Solution

Take 𝑥 = 5.324324… (I)
Multiplying both sides with 1000, we get

1000x = 5324.324324… (II)

Subtracting (I) from (II), we get

999x = 5319

x = $5.324$ = $\frac{5319}{999}$

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Express 5.324in the form pq where p and q are integers, and q≠0.

Take 𝑥 = 5.324324… (I) Multiplying both sides with 1000, we get 1000x = 5324.324324… (II) Subtracting (I) from (II), we get 999x = 5319 x = 5.324= 5319999

Express $5.324$ in the form $\frac{p}{q}$ where $p$ and $q$ are integers, and $q \neq 0$ .

Take 𝑥 = 5.324324… (I)
Multiplying both sides with 1000, we get

1000x = 5324.324324… (II)

Subtracting (I) from (II), we get

999x = 5319

x = $5.324$ = $\frac{5319}{999}$