Question

Two fractions are given. For each one, write its decimal equivalent and determine if the decimal is terminating or non-terminating.
A. 9/20
B. 4/15

Answer 1

A=0.45 ;Terminating

B=0.26666.....;Non-Terminating

Step-by-step explanation:

In both the fractions the numerator is less than the denominator thereby indicating that the decimal equivalent is definitely less than one.

Now for A-

We are making the denominator to a multiple of 10.

$\dfrac{9}{20}\times\dfrac{5}{5}=\dfrac{45}{100}=0.45$

Now for B-

Using normal long division, divide 4 by 15.

              ;reminder at each step;calculation of the decimal equivalent

15×2=30;10                                   ;0.2

15×6=90;10                                   ;0.26

15×6=90;10                                   ;0.266

15×6=90;10                                   ;0.2666

15×6=90;10                                   ;0.26666

and so on....

Therefore we can see that the reminder is remained constant throughout so there the decimal equivalent is non-terminating.