How To Add Fractions Virtual Nerd

hello. i'm professor von schmohawkand welcome to why u. in the last lecture we saw that any fractioncan be converted to a decimal number by simply dividing the numerator by the denominator. the result of this division will be a decimalnumber which is equivalent to the fraction. this decimal number will either terminate,

How To Add Fractions Virtual Nerd, meaning that it can be represented witha finite number of digits, or it will have one or more digitswhich repeat forever. in this lecture, we will see how to convertany terminating decimal number back into a fraction.

remember that each digit in a decimal number represents a value ten times thatof the digit to its right. now if we take any decimal numberand multiply it by ten, each digit is shifted one column to the left. we have increased the value of each digitby a factor of ten. this is also true when there are digitsto the right of the decimal point. for example, the decimal equivalent tothe fraction one-eighth is zero point one-two-five. if we multiply this number by ten, each digitis shifted one column to the left.

if we multiply by ten again, each digit isshifted one more column to the left. and if we multiply by ten a third time, there will be no more digitsto the right of the decimal point. we will have an integer. so by multiplying our decimal number by tenthree times, which is the same as multiplying by one-thousand, we have produced an integer which isone-thousand times the original number. if we then divide this integer by one-thousand,the result will be equal to the original number. so zero point one-two-five

is equivalent to the fractionone-hundred-twenty-five one-thousandths. now, using the techniques we learned in ourlecture on reducing fractions, we can simplify this fraction to one-eighth. so we have converted the decimal numberzero point one-two-five, to the fraction one-eighth. we can use this same technique to convert any decimal number witha finite number of digits to a fraction, by multiplying it by ten enough timesto produce an integer, and then dividing the integer bythe same amount we multiplied by.

if the number we are converting also has digitsto the left of the decimal point, we just separate it into an integer, plusthe digits to the right of the decimal point, and then convert the digits on the rightinto a fraction. we can then combine the integer and the fraction,to create a mixed number. so far we have seen how to convert anydecimal number with a finite number of digits to a fraction. in the next lecture we will see how to convert any decimal numberwith infinitely repeating digits to a fraction.