Decimal Fraction - Study Mode
[#131] The value of $$left( {frac{{0.125 + 0.027}}{{0.5 imes 0.5 + 0.09 - 0.15}}}
ight)$$ xa0 xa0 is :
Correct Answer
(C) 0.8
Explanation
Solution: Given expression : $$eqalign{
& frac{{0.125 + 0.027}}{{0.5 imes 0.5 + 0.09 - 0.15}} cr
& = frac{{{{left( {0.5}
ight)}^3} + {{left( {0.3}
ight)}^3}}}{{{{left( {0.5}
ight)}^2} + {{left( {0.3}
ight)}^2} - left( {0.5 imes 0.3}
ight)}} cr
& = left( {frac{{{a^3} + {b^3}}}{{{a^2} + {b^2} - ab}}}
ight) cr
& = frac{{left( {a + b}
ight)left( {{a^2} - ab + {b^2}}
ight)}}{{left( {{a^2} - ab + {b^2}}
ight)}} cr
& = (a + b) cr
& = left( {0.5 + 0.3}
ight) cr
& = 0.8 cr} $$
[#132] The fraction equivalent to $$frac{2}{5}$$% is :
Correct Answer
(C) $$frac{1}{250}$$
Explanation
Solution: $$frac{2}{5}$$% = $$frac{2}{5}$$ × $$frac{1}{100}$$ = $$frac{1}{250}$$
[#133] The value of $$left[ {35.7 - left( {3 + frac{1}{{3 + frac{1}{3}}}}
ight) - left( {2 + frac{1}{{2 + frac{1}{2}}}}
ight)}
ight]$$ xa0 xa0 xa0 is :
Correct Answer
(A) 30
Explanation
Solution: Given expression : $$eqalign{
& = 35.7 - left( {3 + frac{1}{{frac{{10}}{3}}}}
ight) - left( {2 + frac{1}{{frac{5}{2}}}}
ight) cr
& = 35.7 - left( {3 + frac{3}{{10}}}
ight) - left( {2 + frac{2}{5}}
ight) cr
& = 35.7 - frac{{33}}{{10}} - frac{{12}}{5} cr
& = 35.7 - left( {frac{{33}}{{10}} + frac{{12}}{5}}
ight) cr
& = 35.7 - frac{{57}}{{10}} cr
& = 35.7 - 5.7 cr
& = 30 cr} $$
[#134] The value of $$frac{{{{left( {0.06}
ight)}^2} + {{left( {0.47}
ight)}^2} + {{left( {0.079}
ight)}^2}}}{{{{left( {0.006}
ight)}^2} + {{left( {0.047}
ight)}^2} + {{left( {0.0079}
ight)}^2}}}$$ xa0 xa0 xa0 is :
Correct Answer
(C) 100
Explanation
Solution: Given expression : $$ = frac{{{a^2} + {b^2} + {c^2}}}{{{{left( {frac{a}{{10}}}
ight)}^2} + {{left( {frac{b}{{10}}}
ight)}^2} + {{left( {frac{c}{{10}}}
ight)}^2}}}$$ Where a = 0.06, b = 0.47 and c = 0.079 $$eqalign{
& = frac{{100left( {{a^2} + {b^2} + {c^2}}
ight)}}{{left( {{a^2} + {b^2} + {c^2}}
ight)}} cr
& = 100 cr} $$
[#135] Solve 3899 ÷ 11.99 - 2379 ÷ 13.97 = ?
Correct Answer
(C) 155
Explanation
Solution: = 3899 ÷ 11.99 - 2379 ÷ 13.97 = 3899 ÷ 12 - 2380 ÷ 14 ≈ 325 - 170 = 155