RATIONAL NUMBERS TO DECIMALS WORKSHEET

Problem 1 :

Express 7/16  in decimal form. Explain whether 7/16 terminates. 

Solution :

7/16  =  0.4375

In this problem, we observe that the remainder becomes zero after a few steps.

So, the decimal expansion of 7/16 terminates.

Problem 2 :

Express 5/11 and 7/6 in decimal form. Explain, whether every rational number has a terminating decimal expansion. 

Thus, the decimal expansion of a rational number need not terminate.

In the above workings, we can observe that the remainders never become zero. Also we note that the remainders repeat after some steps. So, we have a repeating (recurring) block of digits in the quotient.

Problem 3 : 

Express the following rational numbers as decimal numbers.

3/4

5/8

9/16

7/25

47/99

1/999

26/45

27/110

2/3

14/9

Solution : 

3/4  =  0.75

5/8  =  0.625

9/16  =  0.5625

7/25  =  0.0.28

47/99  =  0.474747.........

1/999  =  0.001001001........

26/45  =  0.577777........

27/110  =  0.2454545.........

2/3  =  0.6666........

14/9  =  1.5555..........

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