To convert a fraction to a decimal, divide it out. For example
1/2 = 1.0/2 = .5 (note this is the same as 10/2, but a decimal point is stuck in 1 place from the right in the dividend and quotient)
1/4 = 1.00/4 = .25 (note this is the same as 100/4, but a decimal point is stuck in 2 places from the right in the dividend and quotient)
You can see that 1/4 = (1/2)/2 = .50/2 = .25
Similarly, 1/8 = (1/4)/2 = .250/2 = .125
And 1/16 = (1/8)/2 = .1250/2 = .0625
These are the basic fractions associated with the usual inch-ruler divisions.
To get 3/8, you compute 3(.125) = .375;
similarly 5/8 = 5(.125) = .625,
and 7/8 = 7(.125) = .875.
Any fraction consisting only of powers of 2 or 5 in the denominator (1/5, 1/20, 1/25, 1/32, 1/40, and so on) will have a nice decimal representation in a finite number of digits. Any other fraction will not. 1/3, 1/7, 1/9, 1/11 are good examples. Often, the repeating portion of a repeating decimal is shown with an overbar. I will show it with an underline, as that is something I can do on blurtit.
1/3 = .33
1/7 = .142857142857
1/9 = .11
1/11 = .0909
These are good ones to learn, because they pop up often enough to be interesting. You will note that every multiple of 1/9 is easy to form:
2/9 = .22, 3/9 = 1/3 = .33, 4/9 = .44, 5/9 = .55, 6/9 = 2/3 = .66, and so on.
You will also note that 9/9 = .99. (It's really true--an infinite sequence of .9s is equal to 1.)
It is good to remember the sequence of digits in 1/7, because that sequence is the same for all multiples of 1/7. It is just shifted.
2/7 = .285714285714. 3/7 = .428571428571.
(I remember the sequence as 14, 2*14=28, 2*28(+1)=57.)
You may recall that an approximation of Pi that is sometimes used is 22/7. That would be 3 1/7 = 3.142857..., whereas the real value of Pi is 3.141592...
Multiples of 1/11 are interesting because each repeat is 9 times the numerator.
2/11 = .(2*9) = .1818. 9/11 = .(9*9) = .8181.
I find it relatively amusing that 1/9 ≈ .11 and 1/11 ≈ .09.
That about covers fractions and decimals and the "table" you wanted
____
Percent (%) means "per hundred." And "per" is often shown in math with a division symbol--per hundred = /100.
For example, 6% = 6/100. 23.2% = 23.2/100.
You know from your place value of decimal numbers that anything in hundredths shows up 2 places to the right of the decimal point.
6/100 = .06
23/100 = .23 (and 23.2/100 = .232)
Thus, 1/2 = .5 = .50 = 50%
1/4 = .25 = 25%
1/3 ≈ .333 = 33.3%
1/8 = .125 = 12.5%
1/2 = 1.0/2 = .5 (note this is the same as 10/2, but a decimal point is stuck in 1 place from the right in the dividend and quotient)
1/4 = 1.00/4 = .25 (note this is the same as 100/4, but a decimal point is stuck in 2 places from the right in the dividend and quotient)
You can see that 1/4 = (1/2)/2 = .50/2 = .25
Similarly, 1/8 = (1/4)/2 = .250/2 = .125
And 1/16 = (1/8)/2 = .1250/2 = .0625
These are the basic fractions associated with the usual inch-ruler divisions.
To get 3/8, you compute 3(.125) = .375;
similarly 5/8 = 5(.125) = .625,
and 7/8 = 7(.125) = .875.
Any fraction consisting only of powers of 2 or 5 in the denominator (1/5, 1/20, 1/25, 1/32, 1/40, and so on) will have a nice decimal representation in a finite number of digits. Any other fraction will not. 1/3, 1/7, 1/9, 1/11 are good examples. Often, the repeating portion of a repeating decimal is shown with an overbar. I will show it with an underline, as that is something I can do on blurtit.
1/3 = .33
1/7 = .142857142857
1/9 = .11
1/11 = .0909
These are good ones to learn, because they pop up often enough to be interesting. You will note that every multiple of 1/9 is easy to form:
2/9 = .22, 3/9 = 1/3 = .33, 4/9 = .44, 5/9 = .55, 6/9 = 2/3 = .66, and so on.
You will also note that 9/9 = .99. (It's really true--an infinite sequence of .9s is equal to 1.)
It is good to remember the sequence of digits in 1/7, because that sequence is the same for all multiples of 1/7. It is just shifted.
2/7 = .285714285714. 3/7 = .428571428571.
(I remember the sequence as 14, 2*14=28, 2*28(+1)=57.)
You may recall that an approximation of Pi that is sometimes used is 22/7. That would be 3 1/7 = 3.142857..., whereas the real value of Pi is 3.141592...
Multiples of 1/11 are interesting because each repeat is 9 times the numerator.
2/11 = .(2*9) = .1818. 9/11 = .(9*9) = .8181.
I find it relatively amusing that 1/9 ≈ .11 and 1/11 ≈ .09.
That about covers fractions and decimals and the "table" you wanted
____
Percent (%) means "per hundred." And "per" is often shown in math with a division symbol--per hundred = /100.
For example, 6% = 6/100. 23.2% = 23.2/100.
You know from your place value of decimal numbers that anything in hundredths shows up 2 places to the right of the decimal point.
6/100 = .06
23/100 = .23 (and 23.2/100 = .232)
Thus, 1/2 = .5 = .50 = 50%
1/4 = .25 = 25%
1/3 ≈ .333 = 33.3%
1/8 = .125 = 12.5%
