Advertisements
Advertisements
Question
Express each of the following as a rational number in its simplest form:
(i`) 0.bar (8)`
Solution
Let x = `bar(0.8)`
∴ x = 0.888 …(1)
10x = 8.888 …(2)
On subtracting equation (1) from (2), we get
9x = 8 ⇒ x =` 8/9`
∴0.8 =`bar(8)/9`
APPEARS IN
RELATED QUESTIONS
Show that any positive odd integer is of the form 4q + 1 or 4q + 3, where q is some integer.
Prove that the square of any positive integer is of the form 5q, 5q + 1, 5q + 4 for some integer q.
Define HOE of two positive integers and find the HCF of the following pair of numbers:
75 and 243
Using prime factorization, find the HCF and LCM of 96, 404 In case verify that HCF × LCM = product of given numbers.
Without actual division show that each of the following rational numbers is a non-terminating repeating decimal.
(i) `9/35`
Which of the following rational numbers have terminating decimal?
If the sum of LCM and HCF of two numbers is 1260 and their LCM is 900 more than their HCF, then the product of two numbers is
If HCF of 65 and 117 is expressible in the form 65n − 117, then find the value of n.
Prove that one and only one out of n, n + 2 and n + 4 is divisible by 3, where n is any positive integer.
Show that the square of any positive integer cannot be of the form 6m + 2 or 6m + 5 for any integer m.
