Home
Class 9
MATHS
Express 2.4overline178 in the form (p)/(...

Express `2.4overline178` in the form `(p)/(q)` where p and q are integers and `q ne 0` .

Text Solution

Verified by Experts

Let `x = 2.overline4178`
Then , `x = 2.4178178…." "…(i)`
Since the reqeating block 178 has 3 digits , we multiply x by 1000 to get
`1000x = 2417.8178178178……" "…(i)`
Subtractibg (i) form (ii), we get
`999x = 2415.4 rArr x = (2415.4)/(999) = (24154)/(9990) = (12077)/(4995)`
Promotional Banner

Topper's Solved these Questions

  • NUMBER SYSTEMS

    RS AGGARWAL|Exercise Exericse 1A|9 Videos

  • NUMBER SYSTEMS

    RS AGGARWAL|Exercise Exericse 1B|5 Videos

  • MEAN , MEDIAN AND MODE OF UNGROUPED DATA

    RS AGGARWAL|Exercise Multiple Choice Questions (Mcq)|18 Videos

  • POLYNOMIALS

    RS AGGARWAL|Exercise Multiple Choice Questions (Mcq)|32 Videos

Similar Questions

Explore conceptually related problems

Express 0.overline57 in the form (p)/(q) , where p and q are integers and q ne 0 .

Express 0.overline3 in the form (p)/(q) , where p and q are integer and q ne0

Express 0.357 in the form (p)/(q), where p and q are integers and q!=0

Express 0.6 + 0.overline(7) + 0. overline(47) in the form (p)/(q) where p and q are integers and q =! 0

Express 0.6 in the form p/q where p and q are integers and q!=0

The number 0.7 in the form (p)/(q) , where p and q are integers and q =! 0 is

Express 0.2bar(35) in the form p/q where p and q are integers and q ne 0 .

Express 0.3178 is the form of p/q where p and q are integers

Express 3.bar(2) in the form (p)/(q) where p and q are integers and q!=0