DECIMAL FRACTIONS 



1732 



DECIMAL FRACTIONS 



with the decimal fractions he begins to won- 

 der what to do when he has halves, fifths 

 and so forth. If one can work only with 

 tenths, hundredths and so on, he thinks the 

 scheme of not much general value. Here is 

 the time for introducing reduction of common 

 fractions to decimals. He readily knows 



i-.5;i-.2;*-.8; 1-.75 

 and so on (see Fig. 2), but how can he re- 



.4 



and finds still a common fraction; he tries 

 thousandths and finds the form rid of a com- 

 mon fraction, so he has % = i.ooo _ ^5, reading 

 % = % of one-thousand-thousandths, or 125- 

 thousandths. Therefore, 



= .375 



(Fig. 4). Now he is ready to change any 

 common fraction to a decimal fraction. He 

 changes the numerator to tenths, hundredths, 



01 



.01 







X 



^ 



\|* 



f \ t- 



w 



FIG. 2 



duce a fraction when he does not know what 

 decimal is its equivalent? Let us investigate. 



11.0. (Read, 1 equals ten-tenths, and write it as 

 shown). 1-1.0. 



5 r- .5. Read, - equals 5 of ten-tenths, or .5. 



B A m M 



; "- .2. Read, - equals - of ten-tenths, or .2. 

 8 o o o 



21020 2 1 



-= 2 X-4- =-=- .4. Read, ^ equals 2 X^ of ten-tenths, 



o o o o o 



or - of 20-tenths, or .4. 



-. Read, = f 30-tenths. 

 o o 55 



He sees that to reduce a common fraction to 

 tenths he changes the numerator to 'tenths 

 and divides by the denominator: 



etc., and divides by the denominator. He sees 

 that his answer must be the same decimal 

 name as his numerator (or dividend). 



1 -L2_ i 1 

 (Fig. 3) 



I-T 9 -' 15 



1 1.000 

 8~ 8 ' ] 



FIG. 3 



Read % equals % of ten-tenths, or .1^4. This 

 is not a desirable form, because there is still a 

 common fraction; he changes it to hundredths 



FIG. 4 



Put into rule form, it becomes: To change 

 a common fraction to a decimal fraction, 

 change the numerator to tenths, hundredths, 

 etc.; divide by the denominator, and point 

 off as many places in the answer as there are in 

 the numerator; for example: 



7 7.000 



= .875 



^ 



16 



3.0000 

 16 



= .1875 



