Maharashtra Board Class 6 Maths Chapter 5 Decimal Fractions Set 15 Solutions

Question 1. Write the proper number in the empty boxes.
Answer:
(i) \( \frac{3}{5} = \frac{3 \times \boxed{2}}{5 \times \boxed{2}} = \frac{\boxed{6}}{10} = \boxed{0.6} \)
(ii) \( \frac{25}{8} = \frac{25 \times \boxed{125}}{8 \times 125} = \frac{\boxed{3125}}{1000} = 3.125 \)
(iii) \( \frac{21}{2} = \frac{21 \times \boxed{5}}{2 \times \boxed{5}} = \frac{\boxed{105}}{10} = \boxed{10.5} \)
(iv) \( \frac{22}{40} = \frac{11}{20} = \frac{11 \times \boxed{5}}{20 \times 5} = \frac{\boxed{55}}{100} = \boxed{0.55} \)
In simple words: To fill the empty boxes, we found an equivalent fraction with a denominator of 10, 100, or 1000, then converted it to a decimal. This involves multiplying both the numerator and denominator by the same number to reach the target denominator.

🎯 Exam Tip: Always ensure that when finding equivalent fractions, you multiply both the numerator and the denominator by the exact same non-zero number to maintain the fraction's value, which is crucial for accurate conversions.

Question 2. Convert the common fractions into decimal fractions:
(i) \( \frac{3}{4} \)
(ii) \( \frac{4}{5} \)
(iii) \( \frac{9}{8} \)
(iv) \( \frac{17}{20} \)
(v) \( \frac{36}{40} \)
(vi) \( \frac{7}{25} \)
(vii) \( \frac{19}{200} \)
Answer:
(i) \( \frac{3}{4} = \frac{3 \times 25}{4 \times 25} = \frac{75}{100} = 0.75 \)
(ii) \( \frac{4}{5} = \frac{4 \times 2}{5 \times 2} = \frac{8}{10} = 0.8 \)
(iii) \( \frac{9}{8} = \frac{9 \times 125}{8 \times 125} = \frac{1125}{1000} = 1.125 \)
(iv) \( \frac{17}{20} = \frac{17 \times 5}{20 \times 5} = \frac{85}{100} = 0.85 \)
(v) \( \frac{36}{40} = \frac{9}{10} = 0.9 \)
(vi) \( \frac{7}{25} = \frac{7 \times 4}{25 \times 4} = \frac{28}{100} = 0.28 \)
(vii) \( \frac{19}{200} = \frac{19 \times 5}{200 \times 5} = \frac{95}{1000} = 0.095 \)
In simple words: To convert a common fraction to a decimal, find an equivalent fraction whose denominator is 10, 100, or 1000. Then, write the numerator with the decimal point placed according to the number of zeros in the denominator.

🎯 Exam Tip: When converting fractions to decimals, always try to make the denominator a power of 10 (10, 100, 1000, etc.) as it simplifies the process and avoids division errors.

Question 3. Convert the decimal fractions into common fractions:
(i) 27.5
(ii) 0.007
(iii) 90.8
(iv) 39.15
(v) 3.12
(vi) 70.400
Answer:
(i) \( 27.5 = \frac{275}{10} \)
(ii) \( 0.007 = \frac{7}{1000} \)
(iii) \( 90.8 = \frac{908}{10} \)
(iv) \( 39.15 = \frac{3915}{100} \)
(v) \( 3.12 = \frac{312}{100} \)
(vi) \( 70.400 = 70.4 = \frac{704}{10} \)
In simple words: To convert a decimal to a common fraction, write the decimal number as the numerator without the decimal point. The denominator will be a power of 10 (10, 100, 1000, etc.) with as many zeros as there are digits after the decimal point.

🎯 Exam Tip: Count the number of digits after the decimal point carefully; this count directly determines the power of 10 (e.g., one digit means /10, two digits means /100) that forms the denominator of the common fraction.