Number Properties – pls help a poor “non-math” soul...

[GMATCHPOINT]

(pls help me with my two questions below, I am not good with math, actually I am terrible)

QUESTION 1) On page 323 exercise 107 OG11 defines terminating decimal as follow:

“…Any decimal that has only a finite number of nonzero digits is a terminating decimal. For example, 24, 0.82 and 5.096 are three terminating decimals…”

Then on the explanation for this exercise OG11 says: “Division by the number 4 must terminate: the remainder when dividing by 4 must be 0, 1, 2 or 3, so the quotient must end with .0, .25, .5 or .75, respectively…”

My question is: I have noticed that it also happens (i.e. be a terminating decimal) with other numbers such as 2, 5, 8 …??..). What GMAT is testing here? What concept must I draw from this?


QUESTION 2) Page 337 ex 148, OG11 says the following:

“…having a remainder of 30 when x is divided by 100 can only happen if x has a tens digit of 3 and a ones digit of 0, as in 130, 230, 630, and so forth..”

My question is: can I assume it is true for any reminder (i.e. 30, 15, 60, 12 and etc…) when x is divided by 100


Once again, pls apologize if above seems obvious. (definitely not for me)

Cheers!

[cramya]

Hi GMATCHPOINT,


QUESTION 1)

The takeaway for terminating decimal is this:

If a denominator of a fraction can be expresed as powers of 2 and powers of 5 then that fraction would result in a terminating decimal

Eg:
1) 3/8 = 3 / 2^3 (8 = 2 ^3)

U could also write 3/8 as 3/2^3 * 5 ^0 (since 5 ^ 0 =1 )

2) 356/625 = 356 / 5 ^4 (625 = 5 ^ 4)

U could also write 356/625 as 325/5 ^ 4 * 2 ^ 0 (since 2 ^ 0 is again 1)

Try it for some numbers u will see.

Let me know if u still have questions


Regards,
Cramya

[GMATCHPOINT]

this is great cramya!
thank you for your habitual assistance.