Maharashtra Board Class 8 Maths Chapter 1 Rational and Irrational Numbers Set 1.3 Solutions

Question 1. Write the following rational numbers in decimal form.
(i) \( \frac{9}{37} \)
(ii) \( \frac{18}{42} \)
(iii) \( \frac{9}{14} \)
(iv) \( \frac{103}{5} \)
(v) \( -\frac{11}{13} \)
Answer:
(i) \( \frac{9}{37} \)
              0.243
   37)9.000
              -0
              ---
              90
              -74
              ---
              160
              -148
              ----
              120
              -111
              ----
                9
\(\therefore \frac{9}{37} = 0.243\)
(ii) \( \frac{18}{42} \)
\( \frac{18}{42} = \frac{3 \times 6}{7 \times 6} = \frac{3}{7} \)
                0.428571
     7)3.000000
                -0
                ---
                30
                -28
                ---
                 20
                -14
                ---
                 60
                -56
                ---
                 40
                -35
                ---
                 50
                -49
                ---
                 10
                 -7
                 --
                  3
\(\therefore \frac{18}{42} = \frac{3}{7} = 0.428571\)
(iii) \( \frac{9}{14} \)
              0.6428571
   14)9.0000000
              -0
              ---
              90
              -84
              ---
              60
              -56
              ---
              40
              -28
              ---
              120
              -112
              ----
               80
               -70
               ---
               100
               -98
               ---
                20
               -14
               ---
                 6
\(\therefore \frac{9}{14} = 0.6428571\)
(iv) \( \frac{103}{5} \)
           20.6
    5)103.0
         -10
         ---
           03
           -0
           ---
           30
           -30
           ---
            0
\(\therefore \frac{103}{5} = 20.6\)
\(\therefore -\frac{103}{5} = -20.6\)
(v) \( -\frac{11}{13} \)
                0.846153
   13)11.000000
                -0
                ----
                110
                -104
                ----
                 60
                 -52
                 ---
                 80
                 -78
                 ---
                 20
                 -13
                 ---
                 70
                 -65
                 ---
                 50
                 -39
                 ---
                 11
\(\therefore \frac{11}{13} = 0.846153\)
\(\therefore -\frac{11}{13} = -0.846153\)
In simple words: To express a rational number as a decimal, divide the numerator by the denominator using long division. If the fraction can be simplified, do so before dividing. For negative fractions, perform the division on the absolute values and then apply the negative sign to the result.

🎯 Exam Tip: When converting fractions to decimals, especially non-terminating ones, carry out the division to at least 3-4 decimal places or until a repeating pattern is observed. Always simplify fractions before performing long division for easier calculation. Remember to apply the correct sign for negative rational numbers.