How you change a mixed number to a decimal?

Answer 1

A "mixed number" has a whole number followed by a fraction part, which is the ratio between a "numerator" (on top) and a "denominator (on the bottom).

If the fraction is "improper" (i.e. with a numerator that is larger than the denominator, such as 27/20), then first convert it to a proper fraction and increase the whole number accordingly. For example, "3 and 27/20" becomes "4 and 7/20" by subtracting the denominator from the numerator (bottom from top) as many times as possible, and adding one to the whole number each time. This gives a whole number of 4.0 with a fraction part of 7/20.

Next, we must convert the fraction part to decimal digits following a decimal point, by changing the denominator to some power of ten, such as 10 or 100 or 1000, etc. This is done by multiplying both the numerator and the denominator by the same number.

Using the fraction 7/20 as an example, we need to multiply both the numerator and the denominator by a number that changes the denominator to a power of ten. If we multiply 20 by 5, the denominator becomes 100. Multiplying both numerator and deminator by 5 will change the fraction part, 7/20, to 35/100, gives 0.35 for the decimal digits following the whole number (4). Thus, "4.35" is the final result for 4 and 7/20 (or 3 and 27/20). This decimal number, 4.35, may also be written as 4.350 or 4.3500 or 4.35000..., etc. but we usually drop the repeating zeroes that follow the last non-zero digit.

If, however, the denominator cannot be multiplied by something to get a power of ten (i.e. if it has prime factors other than 2 and 5), then the decimal part will not end with repeating zeroes, but it will have a repeating decimal part, such as "33333..." or "27272727..." that goes on forever. (All "rational" numbers are repeating decimals.) To get this repeating decimal, you will need to do long division (or use a calculator).

For example, if the "mixed number is "4 and 7/22" then then the fraction part is obtained by dividing 22 by 7, and the result is "4.318181818..."

.318181818181818181818...

________________

22 ) 7.0000000000....

- 6.6

____

.40

- .22

_______

180

- 176

_______

40

- 22

_________

180

- 176

_________

40

and so on!