Without actual division show that 24/125 has a terminating decimal expansion

### 2 thoughts on “Without actual division show that 24/125 has a terminating decimal expansion”

### Leave a Comment

You must be logged in to post a comment.

Without actual division show that 24/125 has a terminating decimal expansion

You must be logged in to post a comment.

## [tex]\tt\colorbox{plum}{αɴѕωєя}[/tex]

[tex]=> 24/125[/tex]

[tex]=> 24/5³ [/tex]

[tex]=> 24 × 2³/ 53 x 2³[/tex]

[tex]=> 192/1000[/tex]

[tex]=> 0.1[/tex]

We know 5 is not a factor of 23, so it is in its simplest form.

[tex]\huge\mathbb\fcolorbox{purple}{lavenderblush}{✰Answer}[/tex]

24/125 =

24/5³ = 24 × 2³/ 53 x 2³

= 192/1000

= 0.1

We know 5 is not a factor of 23, so it is in

its simplest form.

Moreover, it is in the form of (2m x 5n). Hence, the given rational is terminating.