बिना लंबी विभाजन प्रक्रिया किए बताइए कि निम्नलिखित परिमेय संख्याओं के दशमलव प्रसार सांत है या असांत आवर्ती हैं:

$space 6 over 15$

Solution

space 6 over 15 space equals space fraction numerator 6 over denominator 3 cross times 5 end fraction space equals space 2 over 5 space equals fraction numerator 2 space straight x space 2 over denominator 5 space straight x space 2 end fraction space equals space 4 over 10

इस का प्रसार सांत दशमलव हैl

Question 34

बिना लंबी विभाजन प्रक्रिया किए बताइए कि निम्नलिखित परिमेय संख्याओं के दशमलव प्रसार सांत है या असांत आवर्ती हैं:

$space 35 over 50$

Solution

space 35 over 50 equals fraction numerator 35 over denominator 2 space cross times space 5 squared end fraction space equals space fraction numerator 35 space straight x space 2 space over denominator 2 squared space straight x space 5 squared end fraction space rightwards double arrow 70 over 10 squared

space 35 over 50

इस का प्रसार सांत दशमलव हैl

Question 35

Solution

space 77 over 210 space equals space fraction numerator 11 space x space 7 over denominator 2 space cross times space 3 space cross times space 5 space cross times space 7 end fraction space equals space fraction numerator 11 over denominator 2 space straight x space 3 space straight x space 5 end fraction

space 77 over 210

इस का प्रसार असांत आवर्ती दशमलव हैl

Question 36

Solution

left parenthesis straight i right parenthesis space space 13 over 3125 equals 13 over 5 to the power of 5 equals fraction numerator 13 cross times 2 to the power of 5 over denominator 2 to the power of 5 cross times 5 to the power of 5 end fraction space space space space space space space space space space space space space equals fraction numerator 416 over denominator left parenthesis 10 right parenthesis to the power of 5 end fraction equals 0.00416 left parenthesis ii right parenthesis space space space 17 over 8 equals 17 over 2 cubed equals fraction numerator 17 cross times 5 cubed over denominator 2 cubed cross times 5 cubed end fraction space space space space space space space space space space space space equals fraction numerator 2125 over denominator left parenthesis 10 right parenthesis cubed end fraction equals 2.125 left parenthesis iv right parenthesis space space space space 15 over 1600 equals fraction numerator 15 over denominator 2 to the power of 6 cross times 5 squared end fraction equals fraction numerator 15 cross times 5 to the power of 4 over denominator 2 to the power of 6 cross times 5 to the power of 6 end fraction space space space space space space space space space space space space space space space space space space equals fraction numerator 9375 over denominator left parenthesis 10 right parenthesis to the power of 6 equals 0.009375 end fraction

left parenthesis vi right parenthesis space space space space space fraction numerator 23 over denominator 2 cubed.5 squared end fraction equals fraction numerator 23 over denominator 2 cubed cross times 5 cubed end fraction equals fraction numerator 115 over denominator left parenthesis 10 right parenthesis cubed end fraction equals 0.115 left parenthesis viii right parenthesis space space space 6 over 15 equals 2 over 5 equals fraction numerator 2 cross times 2 over denominator 5 cross times 2 end fraction equals 4 over 10 equals 0.4 left parenthesis ix right parenthesis space space space space space 35 over 50 equals fraction numerator 35 over denominator 2 cross times 5 squared end fraction equals fraction numerator 35 cross times 2 over denominator 2 squared cross times 5 squared end fraction space space space space space space space space space space space space space equals fraction numerator 70 over denominator left parenthesis 10 right parenthesis squared equals 0.70 end fraction space