You visited us 1 times! Enjoying our articles? Unlock Full Access!

Check If a Given Rational No. Is Terminating or Not

Without actua...

Question

Without actual division, show that each of the following rational numbers is a terminating decimal. Express each in decimal form.

$(i) \frac{23}{(2^{3} \times 5^{2})} (i i) \frac{24}{125} (i i i) \frac{171}{800} (i v) \frac{15}{1600} (v) \frac{17}{320} (v i) \frac{19}{3125}$

Open in App

Solution

i) $fraction numerator 23 over denominator 2 cubed cross times 5 squared end fraction equals fraction numerator 23 cross times 5 over denominator 2 cubed cross times 5 cubed end fraction equals 115 over 1000 equals$ 0.115

We know either 2 or 5 is not a factor of 23, so it is in its simplest form.

Moreover, it is in the form of ().

Hence, the given rational is terminating.

ii) $24 over 125 equals 24 over 5 cubed equals fraction numerator 24 cross times 2 cubed over denominator 2 cubed cross times 5 cubed end fraction equals 192 over 1000 equals 0.192$

We know 5 is not a factor of 24, so it is in its simplest form.

Moreover, it is in the form of ().

Hence, the given rational is terminating.

(iii) $171 over 800 equals fraction numerator 171 over denominator 5 squared cross times 2 to the power of 5 end fraction equals fraction numerator 171 cross times 5 cubed over denominator 5 to the power of 5 cross times 2 to the power of 5 end fraction equals 21375 over 100000 equals 0.21375$

We know either 2 or 5 is not a factor of 171, so it is in its simplest form.

Moreover, it is in the form of ().

Hence, the given rational is terminating.

iv) $15 over 1600 equals fraction numerator 15 over denominator 5 squared cross times 2 to the power of 6 end fraction equals fraction numerator 15 cross times 5 to the power of 4 over denominator 5 to the power of 6 cross times 2 to the power of 6 end fraction equals 375 over 1000000 equals 0.009375$

We know either 2 or 5 is not a factor of 15, so it is in its simplest form.

Moreover, it is in the form of ().

Hence, the given rational is terminating.

v) $17 over 320 equals fraction numerator 17 over denominator 5 cross times 2 to the power of 6 end fraction equals fraction numerator space 17 cross times 5 to the power of 5 over denominator 5 to the power of 6 cross times 2 to the power of 6 end fraction equals 53125 over 1000000$

We know either 2 or 5 is not a factor of 17, so it is in its simplest form.

Moreover, it is in the form of ().

Hence, the given rational is terminating.

vi) $19 over 3125 equals 19 over 5 to the power of 5 equals fraction numerator begin display style 19 cross times 2 to the power of 5 end style over denominator begin display style 5 to the power of 5 cross times 2 to the power of 5 end style end fraction equals fraction numerator begin display style 608 end style over denominator 100000 end fraction equals 0.00608$

We know either 2 or 5 is not a factor of 19, so it is in its simplest form.

Moreover, it is in the form of ().

Hence, the given rational is terminating

Suggest Corrections

Similar questions

\frac{23}{(2^{3} \times 5^{2})}

\frac{24}{125}

\frac{171}{800}

\frac{15}{1600}

\frac{17}{320}

\frac{19}{3125}

\frac{11}{(2^{3} \times 3)}

\frac{73}{(2^{2} \times 3^{3} \times 5)}

\frac{129}{(2^{2} \times 5^{7} \times 7^{5})}

\frac{9}{35}

\frac{77}{210}

\frac{32}{147}

\frac{29}{343}

\frac{64}{455}

(i) \frac{29}{343} (i i) \frac{64}{455}

Without actual division, show that each of the following rational numbers is a nonterminating repeating decimal.

$(i) \frac{11}{(2^{3} \times 3)} (i i) \frac{73}{(2^{2} \times 3^{3} \times 5)}$

\frac{13}{80}

\frac{7}{24}

\frac{5}{12}

Join BYJU'S Learning Program