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

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​”

  1. [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.

  2. [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.

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