問題
問1．次の数を有理数であるか無理数であるか答えなさい．
(1) \(-3.3\)
(2) \(107\)
(3) \(\displaystyle \frac{4}{\pi}\)
(4) \(\displaystyle \frac{17}{31}\)
(5)\(1-\sqrt{3}\)
(6) \(5\sqrt{2}+\sqrt{7}\)
(7) \( \displaystyle \sqrt{2}-\frac{2}{\sqrt{2}}\)
(8) \(0.0051\)
問2．次の小数を分数で表しなさい．
(1) \(2.\dot5\)
(2) \(3.\dot1\dot4\)
(3) \(2.\dot1\dot9\)
(4) \(0.\dot3\dot8\)
(5) \(0.\dot61\dot5\)
(6) \(1.3\dot0\dot1\)
(7) \(5.0\dot1\dot3\)
(8) \(1.\dot10\dot2\)
(9) \(0.1\dot02\dot5\)
問3．次の分数を小数で表せ．
(1) \(\displaystyle \frac{5}{3}\)
(2) \(\displaystyle \frac{9}{8}\)
(3) \(\displaystyle \frac{15}{7}\)
(4) \(\displaystyle \frac{9}{5}\)
(5) \(\displaystyle \frac{11}{6}\)
解答
問1．
(1) 有理数
(2) 有理数
(3) 無理数
(4) 有理数
(5) 無理数
(6) 無理数
(7) 有理数
(8) 有理数
問2．
問3．
(1) \(\displaystyle \frac{5}{3}=1.\dot6\cdots \text{(答)}\)
(2) \(\displaystyle \frac{9}{8}=1.125\cdots \text{(答)}\)
(3) \(\displaystyle \frac{15}{7}=2.\dot14285\dot7\cdots \text{(答)}\)
(4) \(\displaystyle \frac{9}{5}=1.8\cdots \text{(答)}\)
(5) \(\displaystyle \frac{11}{6}=1.8\dot3\cdots \text{(答)}\)