We shall look at some examples of rational numbers in the form of where decimal representations are terminating. [tex]\frac{2}{5} = 0.4[/tex] [tex]\frac{3}{100} = 0.003[/tex]
We observed that the denominators of above rational numbers are in the form of [tex]2^{a}[/tex] × [tex]5^{b}[/tex] Where [tex]\alpha[/tex] and [tex]b[/tex] are whole numbers. Hence if [tex]q[/tex] is in the form [tex]2^{a}[/tex] × [tex]5^{b}[/tex] then [tex]\frac{p}{q}[/tex] is a terminating decimal.
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Answer:
We shall look at some examples of rational numbers in the form of
where decimal representations are terminating.
[tex]\frac{2}{5} = 0.4[/tex] [tex]\frac{3}{100} = 0.003[/tex]
[tex]\frac{27}{16} = 1.6875[/tex] [tex]\frac{33}{50} = 0.66[/tex]
We observed that the denominators of above rational numbers are in the form of [tex]2^{a}[/tex] × [tex]5^{b}[/tex]
Where [tex]\alpha[/tex] and [tex]b[/tex] are whole numbers.
Hence if [tex]q[/tex] is in the form [tex]2^{a}[/tex] × [tex]5^{b}[/tex] then [tex]\frac{p}{q}[/tex] is a terminating decimal.