updated: 2012. Images to better illustrate the point
Maybe it would surprise you (or maybe not), that one of the common ways people trip while doing basic math in numerical reasoning / quantitative aptitude or problem solving tests and case interviews is because of the confusion with zeros (0's). Yes, zeros. The moment someone has to deal with something like this:
24000*50000*1000000 or
60 thousand people earning 1.3 million $ each for 200 days = ?
all hell breaks loose. You miss zeros, add extra zeros, get all zero'd up - so how do you do it without getting confused like crazy? Here's a valuable tip - use '10 to the power notation'. If you don't know what it is, then spend a little time learning it - the notation is essentially
100 = 10-squared = 10^2 (10 to the power of 2)
1000 = 10^3
10000 = 10^4
a million = 10^6
a billion = 10^9
so
60 thousand people earning 1.3 million $ each for 200 days = ?
instead of killing yourself with 60000 * 1300000 * 200 and getting your zeros messed up, you would write it is
(6*10^4)*(1.3*10^6)*(2 * 10^2)
= 6*1.3*2* (10^4*10^6*10^2)
=7.8*2*(10^(4+6+2))
=7.8*2*(10^12)
=15.6*10^12
Don't get worried about this looking confusing - do it a couple of times and you'll find it a whole lot easier than writing lots of 0's. The basic steps are
1. Write all the '00, '000 etc in 10^ notation and isolate them to one side
2. Add up the powers (you have to learn basic math of multiplication and division of powers)
3. Multiply the other numbers
Kind of looks like this on paper
Compare this with the oops situation of tripping with zeros!
Let's take another example, how much is 75000 * 13 million divided by 9000?
=75*(10^3)*(13*10^6)/(9*10^3)
=(75*13)*(10^6*10^3)/(9*10^3)
=(75*13/9)*10^6
~108 million
Look at it the old fashioned zero's way
Let's do it cleaner with the powers way
Try this a few times and you'll no longer lose points because you messed up a few too many zeros!
Coming soon in the series - some little tricks in handling numbers
Maybe it would surprise you (or maybe not), that one of the common ways people trip while doing basic math in numerical reasoning / quantitative aptitude or problem solving tests and case interviews is because of the confusion with zeros (0's). Yes, zeros. The moment someone has to deal with something like this:
24000*50000*1000000 or
60 thousand people earning 1.3 million $ each for 200 days = ?
all hell breaks loose. You miss zeros, add extra zeros, get all zero'd up - so how do you do it without getting confused like crazy? Here's a valuable tip - use '10 to the power notation'. If you don't know what it is, then spend a little time learning it - the notation is essentially
100 = 10-squared = 10^2 (10 to the power of 2)
1000 = 10^3
10000 = 10^4
a million = 10^6
a billion = 10^9
so
60 thousand people earning 1.3 million $ each for 200 days = ?
instead of killing yourself with 60000 * 1300000 * 200 and getting your zeros messed up, you would write it is
(6*10^4)*(1.3*10^6)*(2 * 10^2)
= 6*1.3*2* (10^4*10^6*10^2)
=7.8*2*(10^(4+6+2))
=7.8*2*(10^12)
=15.6*10^12
Don't get worried about this looking confusing - do it a couple of times and you'll find it a whole lot easier than writing lots of 0's. The basic steps are
1. Write all the '00, '000 etc in 10^ notation and isolate them to one side
2. Add up the powers (you have to learn basic math of multiplication and division of powers)
3. Multiply the other numbers
Kind of looks like this on paper
Compare this with the oops situation of tripping with zeros!
Let's take another example, how much is 75000 * 13 million divided by 9000?
=75*(10^3)*(13*10^6)/(9*10^3)
=(75*13)*(10^6*10^3)/(9*10^3)
=(75*13/9)*10^6
~108 million
Look at it the old fashioned zero's way
Let's do it cleaner with the powers way
Try this a few times and you'll no longer lose points because you messed up a few too many zeros!
Coming soon in the series - some little tricks in handling numbers
wow, this was super helpful.
ReplyDeleteI agree.. made those HUGE numbers so easy to manipulate. Now when i look at them again they dont look frightening at all.. Thanks.......
ReplyDeleteAbsolute life-saver!
ReplyDelete