<font face="Times New Roman, serif"><font style="box-sizing: border-box;"><font size="3"><font style="box-sizing: border-box;">(i) We have,</font></font></font></font>
<font color="#808080"><font style="box-sizing: border-box;">
</font></font>
<font face="Times New Roman, serif"><font style="box-sizing: border-box;"><font size="3"><font style="box-sizing: border-box;">Theorem states: </font></font></font></font>
<font face="Times New Roman, serif"><font style="box-sizing: border-box;"><font size="3"><font style="box-sizing: border-box;">Let </font></font></font></font>
<font face="Times New Roman, serif"><font style="box-sizing: border-box;"><font size="3"><font style="box-sizing: border-box;">be a rational number, such that the prime factorization of q is not of the form
</font></font>, where <font size="3"><font style="box-sizing: border-box;">m and n are non-negative integers.</font></font></font></font>
<font face="Times New Roman, serif"><font style="box-sizing: border-box;"><font size="3"><font style="box-sizing: border-box;">Then, x has a decimal expression which does not have terminating decimal.</font></font></font></font>
<font face="Times New Roman, serif"><font style="box-sizing: border-box;"><font size="3"><font style="box-sizing: border-box;">(ii) We have,</font></font></font></font>
<font color="#808080"><font style="box-sizing: border-box;">
</font></font>
<font face="Times New Roman, serif"><font style="box-sizing: border-box;"><font size="3"><font style="box-sizing: border-box;">Theorem states: </font></font></font></font>
<font face="Times New Roman, serif"><font style="box-sizing: border-box;"><font size="3"><font style="box-sizing: border-box;">Let </font></font></font></font><font face="Times New Roman, serif"><font style="box-sizing: border-box;"><font size="3"><font style="box-sizing: border-box;">be a rational number, such that the prime factorization of q is not of the form</font></font>, where <font size="3"><font style="box-sizing: border-box;">m and n are non-negative integers.</font></font></font></font>
<font face="Times New Roman, serif"><font style="box-sizing: border-box;"><font size="3"><font style="box-sizing: border-box;">Then, x has a decimal expression which does not have terminating decimal.</font></font></font></font>
<font face="Times New Roman, serif"><font style="box-sizing: border-box;"><font size="3"><font style="box-sizing: border-box;">(iii) We have,</font></font></font></font>
<font color="#808080"><font style="box-sizing: border-box;">
</font></font>
<font face="Times New Roman, serif"><font style="box-sizing: border-box;"><font size="3"><font style="box-sizing: border-box;">Theorem states: </font></font></font></font>
<font face="Times New Roman, serif"><font style="box-sizing: border-box;"><font size="3"><font style="box-sizing: border-box;">Let </font></font></font></font><font face="Times New Roman, serif"><font style="box-sizing: border-box;"><font size="3"><font style="box-sizing: border-box;">be a rational number, such that the prime factorization of q is not of the form</font></font>, where <font size="3"><font style="box-sizing: border-box;">m and n are non-negative integers.</font></font></font></font>
<font face="Times New Roman, serif"><font style="box-sizing: border-box;"><font size="3"><font style="box-sizing: border-box;">Then, x has a decimal expression which does not have terminating decimal.</font></font></font></font>
<font face="Times New Roman, serif"><font style="box-sizing: border-box;"><font size="3"><font style="box-sizing: border-box;">(iv) We have,</font></font></font></font>
<font color="#808080"><font style="box-sizing: border-box;">
</font></font>
<font face="Times New Roman, serif"><font style="box-sizing: border-box;"><font size="3"><font style="box-sizing: border-box;">Theorem states: </font></font></font></font>
<font face="Times New Roman, serif"><font style="box-sizing: border-box;"><font size="3"><font style="box-sizing: border-box;">Let </font></font></font></font><font face="Times New Roman, serif"><font style="box-sizing: border-box;"><font size="3"><font style="box-sizing: border-box;">be a rational number, such that the prime factorization of q is of the form</font></font>, where <font size="3"><font style="box-sizing: border-box;">m and n are non-negative integers.</font></font></font></font>
<font face="Times New Roman, serif"><font style="box-sizing: border-box;"><font size="3"><font style="box-sizing: border-box;">Then, x has a decimal expression which terminates after k places of decimals, where k is the larger of m and n.</font></font></font></font>
<font face="Times New Roman, serif"><font style="box-sizing: border-box;"><font size="3"><font style="box-sizing: border-box;">Then, x has a decimal expression which will have terminating decimal after 3 places of decimal.</font></font></font></font>
Test
Gaurav Seth 5 years, 1 month ago
<font face="Times New Roman, serif"><font style="box-sizing: border-box;"><font size="3"><font style="box-sizing: border-box;">(i) We have,</font></font></font></font>
<font color="#808080"><font style="box-sizing: border-box;">
</font></font>
<font face="Times New Roman, serif"><font style="box-sizing: border-box;"><font size="3"><font style="box-sizing: border-box;">Theorem states: </font></font></font></font>
<font face="Times New Roman, serif"><font style="box-sizing: border-box;"><font size="3"><font style="box-sizing: border-box;">Let </font></font></font></font>
<font face="Times New Roman, serif"><font style="box-sizing: border-box;"><font size="3"><font style="box-sizing: border-box;">be a rational number, such that the prime factorization of q is not of the form
</font></font>, where <font size="3"><font style="box-sizing: border-box;">m and n are non-negative integers.</font></font></font></font>
<font face="Times New Roman, serif"><font style="box-sizing: border-box;"><font size="3"><font style="box-sizing: border-box;">Then, x has a decimal expression which does not have terminating decimal.</font></font></font></font>
<font face="Times New Roman, serif"><font style="box-sizing: border-box;"><font size="3"><font style="box-sizing: border-box;">(ii) We have,</font></font></font></font>
<font color="#808080"><font style="box-sizing: border-box;">
</font></font>
<font face="Times New Roman, serif"><font style="box-sizing: border-box;"><font size="3"><font style="box-sizing: border-box;">Theorem states: </font></font></font></font>
<font face="Times New Roman, serif"><font style="box-sizing: border-box;"><font size="3"><font style="box-sizing: border-box;">Let </font></font></font></font>
<font face="Times New Roman, serif"><font style="box-sizing: border-box;"><font size="3"><font style="box-sizing: border-box;">be a rational number, such that the prime factorization of q is not of the form
</font></font>, where <font size="3"><font style="box-sizing: border-box;">m and n are non-negative integers.</font></font></font></font>
<font face="Times New Roman, serif"><font style="box-sizing: border-box;"><font size="3"><font style="box-sizing: border-box;">Then, x has a decimal expression which does not have terminating decimal.</font></font></font></font>
<font face="Times New Roman, serif"><font style="box-sizing: border-box;"><font size="3"><font style="box-sizing: border-box;">(iii) We have,</font></font></font></font>
<font color="#808080"><font style="box-sizing: border-box;">
</font></font>
<font face="Times New Roman, serif"><font style="box-sizing: border-box;"><font size="3"><font style="box-sizing: border-box;">Theorem states: </font></font></font></font>
<font face="Times New Roman, serif"><font style="box-sizing: border-box;"><font size="3"><font style="box-sizing: border-box;">Let </font></font></font></font>
<font face="Times New Roman, serif"><font style="box-sizing: border-box;"><font size="3"><font style="box-sizing: border-box;">be a rational number, such that the prime factorization of q is not of the form
</font></font>, where <font size="3"><font style="box-sizing: border-box;">m and n are non-negative integers.</font></font></font></font>
<font face="Times New Roman, serif"><font style="box-sizing: border-box;"><font size="3"><font style="box-sizing: border-box;">Then, x has a decimal expression which does not have terminating decimal.</font></font></font></font>
<font face="Times New Roman, serif"><font style="box-sizing: border-box;"><font size="3"><font style="box-sizing: border-box;">(iv) We have,</font></font></font></font>
<font color="#808080"><font style="box-sizing: border-box;">
</font></font>
<font face="Times New Roman, serif"><font style="box-sizing: border-box;"><font size="3"><font style="box-sizing: border-box;">Theorem states: </font></font></font></font>
<font face="Times New Roman, serif"><font style="box-sizing: border-box;"><font size="3"><font style="box-sizing: border-box;">Let </font></font></font></font>
<font face="Times New Roman, serif"><font style="box-sizing: border-box;"><font size="3"><font style="box-sizing: border-box;">be a rational number, such that the prime factorization of q is of the form
</font></font>, where <font size="3"><font style="box-sizing: border-box;">m and n are non-negative integers.</font></font></font></font>
<font face="Times New Roman, serif"><font style="box-sizing: border-box;"><font size="3"><font style="box-sizing: border-box;">Then, x has a decimal expression which terminates after k places of decimals, where k is the larger of m and n.</font></font></font></font>
<font face="Times New Roman, serif"><font style="box-sizing: border-box;"><font size="3"><font style="box-sizing: border-box;">Then, x has a decimal expression which will have terminating decimal after 3 places of decimal.</font></font></font></font>
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