A certain street has 1000 buildings. A sign-maker is contracted to number the houses from 1 to 1000. How many zeroes will be need?

Options

A. 190
B. 180
C. 182
D. 192

Answer

D

Explanation

For two digit numbers :
`{:("____",ul0),(" "uarr,),("number",),("1 to 9",):}`
So, total no. of zeroes = 9
For three digit numbers: `{:("____",ul0),(" "uarr,),("number",),("1 to 9",):}" "{:("____"),(" "uarr),("number"),("1 to 9"):}`
So, total no. of zeroes = `9 xx 9 = 81`.
Again for three digit numbers :
`{:("____"),(" "uarr),("number"),("1 to 9"):}{:("____"),(" "uarr),("number"),("1 to 9"):}{:(ul0),(),():}`
So, total no. of zeroes = `9 xx 9 = 81`
Again for three digit numbers :
`{:("____"),(" "uarr),("number"),("1 to 9"):}{:(ul0),(),():}{:(ul0),(),():}`
So, total no. of zeroes = `2 xx 9 = 18`.
Also, No. of zeroes in 1000 = 3
So, required number of zeroes = `9+81 +81 + 18 + 3 = 192`.