Method to do this?

[swamprat]

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So I forgot how I used to do this quickly in my head but when you have a fraction like this: 1.5e1/16.4e-2

I know you subtract the exponents so you get 10^3 but how do you do the 1.5/16.4 quickly?

The only way I can think of is converting the denominator to .164 and then dividing it into 1.5. Any better ideas?

 

[ssiding]

What I would do is multiple the 1.5 by 10, so just move the decimal place to the right 1. That gives you 15 which is pretty close to 16.4. So by multiplying the 1.5 by 10 you get close to the denominator that mean the 1.5 must be close to 10% of 16.4. So just guestimate the the answer to be a little less than 10% or just 10%.
Hope that helps, let me know if I still didn't explain it?

 

[FutureScaresMe]

I think of it like:

1.5/16.4 = ~1/11 = ~0.091

It comes in handy to memorize what 1/5 , 1/6 , 1/7 etc. equate to.

 

[0Complications]

I know this might sound tacky, but I would say use long division. It's fast and easy. I think your first reply was hinting at it, because the method is similar. Just add 0's.

for example:


....._0.091_
16.4)1.50
........148
......------
...........20
...........16
..........----
............40etc, etc


Ok, so first I just write it out, then when you get good at it you can do it in your head.

_________
denominator) Numerator

Then place the decimal point directly above where it is listed under the "bracket."

ask yourself, does 16.4 go into 1 - no (add a 0 above the line at that point)
15 - no (add a 0)
150 - Yes
When it's a big number like this I use multiples of ten - so I would get 164 [too much, so drop one 16.4 so it goes into 150 9x = ~148]

write the 148 below the line. Then the 9 above it.

Now subtract 148 from 150 = 2

Then ask yourself does 16.4 go into 2? No so add a 0

does 16.4 go into 20? Yes 1 time (put the 1 above the line).


You can keep doing it to get as accurate as you want. For the mcat you can usually get away with 1 or sig figs.


It looks like a lot, but it is sooo easy and ensures that you don't mess up an easy calculation. Once you get it down you can knock out what would look like a pretty hairy piece of division in ~10 seconds or less.

 

[futuredoctor10]

1.5e1/16.4e-2

I know you subtract the exponents so you get 10^3 but how do you do the 1.5/16.4 quickly?

The only way I can think of is converting the denominator to .164 and then dividing it into 1.5. Any better ideas?

1.5 x 10^1 / 16.4 x 10^-2
1.5/16.4 x 10^3
15 x 10^-1 x 10^3 / 16.4
15 /16.4 x 10^2
<1 x 10^2
< 100

answer ~91

 

[G1SG2]

1.5 x 10^1 / 16.4 x 10^-2
1.5/16.4 x 10^3
15 x 10^-1 x 10^3 / 16.4
15 /16.4 x 10^2
<1 x 10^2
< 100

answer ~91

That's great!