Using long division, write the rational number -9/24 as a terminating decimal?

Question

Mila Anderson · Accepted Answer

#-9/24=-0.375#

Let us divide #9# by #24# using long division.

#color(white)(xxxxx)0 .color(white)(1)3 color(white)(x)7color(white)(x)5# #color(white)(xx) 24| bar(9color(white)(x).0color(white)(x) 0)color(white)(x) 0# #color(white)(xxxxx)ul(7color(white)("x)2)color(red)(darr# #color(white)(xxxxx)1color(white)(x)8 color(white)(x) "0"# #color(white)(xxxxx)ul(1color(white)(x)6color(white)(x)8) # #color(white)(xxxxxxx)1color(white)(x)2color(white)(x) "0"# #color(white)(xxxxxxx)ul(1color(white)(x)2color(white)(x)0 # #color(white)(xxxxxxxxx) color(white)(x)-#

and hence

#-9/24=-0.375#

Noah Archer · Answer

undefined To write the rational number $-\frac{9}{24}$ as a terminating decimal, you can use long division as follows:

```
       -0.375
_________________
24 | -9.00000000000
       -8.00
_______________
           1000
           -960
_______________
              400
             -384
_______________
               160
             -144
_______________
                160
              -144
_______________
                   16
```

Thus, $-\frac{9}{24} = -0.375$ when expressed as a terminating decimal.