How do you change the decimal to a mixed number?

Answer 1

There are three different situations, corresponding to the three types of decimal numbers: terminating, repeating and those which are neither terminating nor repeating. Terminating: If the decimal number has d digits after the decimal point, then rename it as a fraction whose numerator is the decimal number without the decimal point, and the denominator is 10^d or 1 followed by d zeros. For example, 34.56 d = 2 so the denominator is 100. and the fraction is 3456/100. Repeating: Until you become expert at this I suggest you do this in two stages (using c and d separately). Suppose there are c digits after the decimal place where the digits are non-repeating, and then you get a string of d digits which repeat. Then the numerator is part of the original string including one lot of the repeated digits minus the original string with none of the repeating digits. The denominator is 10^c*(10^d - 1), which is a string of d 9s followed by c 0s. For example 123.26159159… There are 2 digits, "26", after the decimal point before the repeats kick in so c = 2, and the repeating string "159" is 3 digits long so d = 3. So the numerator is 12326159 – 123216 = 12313833 and the denominator is 99900 Therefore the fraction is 12313833/99900. Non-terminating and non-repeating: There is no way to get a proper fraction since, by definition, this is an irrational number. The best that you can do is to round it to a suitable number of digits and then treat that answer as a terminating decimal. In all cases, you should check to see if the fraction can be simplified.

Answer 2

Say it out loud.

7.47 = "seven and forty-seven hundredths" = 7 and 47/100