Problem Solving

a bar over a sequence of digits in a decimal indicates that the sequence repeats indefinitely.

what is the the value of (10^4-10^2) (.0012)? "bar of 12"


I got (10000-100)(.0012)=11.7800 closest answer was E. HA HA but there has to be easier way..cheers

a. 0
b..12 Bar over 12
c.1.2
d.10
e.12


I think there is a way of heavy division and multiplication that can make this much easier than my approach. I got the answer right but is there an easier way for this.

QA is E

Enginpasa1 wrote:a bar over a sequence of digits in a decimal indicates that the sequence repeats indefinitely.

what is the the value of (10^4-10^2) (.0012)? "bar of 12"

I got (10000-100)(.0012)=11.7800 closest answer was E. HA HA but there has to be easier way..cheers

QA is E

In your approach, you've neglected the bar which is incorrect.

Instead
(10^4-10^2) (.0012)? "bar of 12"
Take 10^2 common you get
10^2(10^2-1) (.0012)? "bar of 12"
Which gives you
(10^2-1) (.12)? "bar of 12"
which is
[100-1] (.12)? "bar of 12"
which equals
12.12"bar of 12" - (.12)"bar of 12"
which is Exactly = 12

When the answer choices are spread out, estimation is a great way to answer questions

(10000 - 100) is pretty close to 10000.

10000 * (.00121212121212...) = 12.12121212...

pick (e) 12

Guys, my approach was similar to the OG's but I think there is a typo there or I need to take a break.

(10^4 - 10^2)(0.0012 bar)
10^4 (0.0012 bar) - 10^2 (0.0012 bar)
10000 (0.0012 bar) - 100 (0.0012 bar)
12 - 0.12= 11.88 ..

10^4 times 0.0012 should moves the decimal 4 places to the right, so what is my mistake?

Abdulla wrote:Guys, my approach was similar to the OG's but I think there is a typo there or I need to take a break.

(10^4 - 10^2)(0.0012 bar)
10^4 (0.0012 bar) - 10^2 (0.0012 bar)
10000 (0.0012 bar) - 100 (0.0012 bar)
12 - 0.12= 11.88 ..

10^4 times 0.0012 should moves the decimal 4 places to the right, so what is my mistake?

Your mistake is that you're ignoring the repeating decimal.

10000(.0012 bar) = 12.12(bar), not 12.

Similarly, 100(.0012bar) = .12(bar), not .12

So, we end up with:

12.1212121212121212... - .1212121212121212... = 12

Thanks Stuart..

It's clear now.

Here is a little trick ya can pull off.

0.111.. = 1/9
0.121212.. = 12/99
0.123123123... = 123/999

0.030303.. = 03/99
0.0121212.. = 012/990
0.00121212.. = 0012/9900

10^4 - 10^2 = 9900

Look at the last fraction, the denominator is 9900, look at the 0's on numerator as well as on denominators side as well.