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Numbers

by kop » Wed Nov 20, 2013 3:05 am
What are the first six digits of 1/9+1/99+1/999, if expressed as a decimal?

a .122123
b .122213
c .123123
d .123212
e .123321
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by ganeshrkamath » Wed Nov 20, 2013 3:08 am
kop wrote:What are the first six digits of 1/9+1/99+1/999, if expressed as a decimal?

a .122123
b .122213
c .123123
d .123212
e .123321
a/9 = 0.aaaaa...
ab/99 = 0.abababab...
abc/999 = 0.abcabcabc...
(a,b,c are digits)

1/9 = 0.111111...
01/99 = 0.010101...
001/999 = 0.001001...
Sum = 0.122213...

Choose B

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by Mathsbuddy » Fri Nov 22, 2013 2:33 am
In the answer list the 1st 2 digits are all the same, so we only need to consider the 3rd and 4th digits to identify which is correct.

Knowing:

1/9 -> decimal positions of 1 are multiples of 1
1/99 -> decimal positions of 1 are multiples of 2
1/999 -> decimal positions of 1 are multiples of 3

gives us (3rd, 4th) digits of (1+1, 1+1) = (2,2)

Therefore answer B.
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by sanju09 » Fri Nov 22, 2013 3:34 am
kop wrote:What are the first six digits of 1/9+1/99+1/999, if expressed as a decimal?

a .122123
b .122213
c .123123
d .123212
e .123321
1/9 =0 .111111

1/99 = 0.010101

1/999 = 0.001001

ADD

3 in the last place, eliminate D and E, 1 in fifth place, eliminate A and C. We can stop and take the leftover.
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by sanju09 » Sat Nov 23, 2013 12:48 am
There must be something wrong with this website, a little edit work in post creates two posts when submitted.


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by buoyant » Sat Nov 23, 2013 8:44 pm
Mathsbuddy wrote:In the answer list the 1st 2 digits are all the same, so we only need to consider the 3rd and 4th digits to identify which is correct.

Knowing:

1/9 -> decimal positions of 1 are multiples of 1
1/99 -> decimal positions of 1 are multiples of 2
1/999 -> decimal positions of 1 are multiples of 3

gives us (3rd, 4th) digits of (1+1, 1+1) = (2,2)

Therefore answer B.
Hi,
Can you elaborate more on your steps please ?

More on "decimal positions of 1 are multiples of 1"etc.
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by [email protected] » Sat Nov 23, 2013 9:03 pm
Hi buoyant,

Mathsbuddy is referring to the patterns that exist in those 3 fractions:

1/9 = .111111
2/9 = .222222
3/9 = .333333
etc.

1/99 = .010101
2/99 = .020202
3/99 = .030303
11/99 = .111111
etc.

1/999 = .001001
2/999 = .002002
45/999 = .045045
217/999 = .217217
etc.

By adding up 1/9 + 1/99 + 1/999 =
.111111 + .010101 + .001001

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