Squares of 2

1 1 2 4 3 9 4 16 5 25 6 36 7 49 8 64 9 81 10 100 11 121 12 144 13 169 14 196 15 225 16 256 17 289 18 324 19 361 20 400 21 441 22 484 23 529 24 576 25 625                     Cubes of 2
1 1 2 8 3 27 4 64 5 125 6 216 7 143 8 512 9 729 10 1000 11 1331 12 1728
Powers of 2
2 ^1 2 2^2 4 2^3 8 2^4 16 2^5 32 2^6 64 2^7 128 2^8  256 2^9 512 2^10 1024 2^11 2048 2^12 4096

Powers of 3

Number	Value
3^1	3
3^2	9
3^3	27
3^4	81
3^5	243
3^6	729

Reciprocal of Fractions

1/1                     1

1/2                   0.5

1/3                   0.33

1/4                   0.25

1/5                   0.20

1/6                   0.1666....  

1/7                   0.142857..........

1/8                   0.125

1/9                   0.11111.........

1/10                 0.10 

1/11                 0.0909.....

1/12                 0.8333........

1/13                 0.076293 

1/14                 0.0714285.......

1/15                 0.066....... 

1/16                 0.0625 

1/17                 0.058823

1/18                 0.055...........

1/19                 0.052631 

1/20                 0.05

With a little practice, it's not hard to recall
the decimal equivalents of fractions up to 10/11!

First, there are 3 you should know already:

1/2 = .5
1/3 = .333...
1/4 = .25

Starting with the thirds, of which you already know one:

1/3 = .333...
2/3 = .666...

You also know 2 of the 4ths, as well, so there's only one new one to learn:

1/4 = .25
2/4 = 1/2 = .5
3/4 = .75

Fifths are very easy. Take the numerator (the number on top),
double it, and stick a decimal in front of it.

1/5 = .2
2/5 = .4
3/5 = .6
4/5 = .8

There are only two new decimal equivalents to learn with the 6ths:

1/6 = .1666...
2/6 = 1/3 = .333...
3/6 = 1/2 = .5
4/6 = 2/3 = .666...
5/6 = .8333...

What about 7ths? We'll come back to them
at the end. They're very unique.

8ths aren't that hard to learn, as they're just
smaller steps than 4ths. If you have trouble
with any of the 8ths, find the nearest 4th,
and add .125 if needed:

1/8 = .125
2/8 = 1/4 = .25
3/8 = .375
4/8 = 1/2 = .5
5/8 = .625
6/8 = 3/4 = .75
7/8 = .875

9ths are almost too easy:

1/9 = .111...
2/9 = .222...
3/9 = .333...
4/9 = .444...
5/9 = .555...
6/9 = .666...
7/9 = .777...
8/9 = .888...

10ths are very easy, as well.
Just put a decimal in front of the numerator:

1/10 = .1
2/10 = .2
3/10 = .3
4/10 = .4
5/10 = .5
6/10 = .6
7/10 = .7
8/10 = .8
9/10 = .9

Remember how easy 9ths were? 11th are easy in a similar way,
assuming you know your multiples of 9:

1/11 = .090909...
2/11 = .181818...
3/11 = .272727...
4/11 = .363636...
5/11 = .454545...
6/11 = .545454...
7/11 = .636363...
8/11 = .727272...
9/11 = .818181...
10/11 = .909090...

As long as you can remember the pattern for each fraction, it is
quite simple to work out the decimal place as far as you want
or need to go!

Oh, I almost forgot! We haven't done 7ths yet, have we?

One-seventh is an interesting number:

1/7 = .142857142857142857...

For now, just think of one-seventh as: .142857

See if you notice any pattern in the 7ths:

1/7 = .142857...
2/7 = .285714...
3/7 = .428571...
4/7 = .571428...
5/7 = .714285...
6/7 = .857142...

Notice that the 6 digits in the 7ths ALWAYS stay in the same
order and the starting digit is the only thing that changes!

If you know your multiples of 14 up to 6, it isn't difficult to,
work out where to begin the decimal number. Look at this:

For 1/7, think "1 * 14", giving us .14 as the starting point.
For 2/7, think "2 * 14", giving us .28 as the starting point.
For 3/7, think "3 * 14", giving us .42 as the starting point.

For 4/14, 5/14 and 6/14, you'll have to adjust upward by 1:

For 4/7, think "(4 * 14) + 1", giving us .57 as the starting point.
For 5/7, think "(5 * 14) + 1", giving us .71 as the starting point.
For 6/7, think "(6 * 14) + 1", giving us .85 as the starting point.

Practice these, and you'll have the decimal equivalents of
everything from 1/2 to 10/11 at your finger tips!

If you want to demonstrate this skill to other people, and you know
your multiplication tables up to the hundreds for each number 1-9, then give them a
calculator and ask for a 2-digit number (3-digit number, if you're up to it!) to be
divided by a 1-digit number.

If they give you 96 divided by 7, for example, you can think,
"Hmm... the closest multiple of 7 is 91, which is 13 * 7, with 5 left over.
So the answer is 13 and 5/7, or: 13.7142857

The reciprocal charts should be memorized by heart . For quick calculation of Percentages , Data Interpretation Questions and other questions requiring quick conversion.

Subsequent posts will show you the practical application of these forms.