Simple and Decimal Fractions
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Solved Examples
Study MaterialSolved Examples – Simple and Decimal Fractions
Solved examples help students understand the practical application of fractions and decimal concepts in competitive examinations. These examples are designed from basic to advanced level and cover important concepts frequently asked in SSC, Banking, Railway, CAT, CDS, NDA, UPSC, and placement aptitude tests.
Topics Covered in Solved Examples
- Decimal Fractions
- Fraction to Decimal Conversion
- Decimal to Fraction Conversion
- Addition and Subtraction of Decimals
- Multiplication and Division of Decimals
- Recurring Decimals
- Comparison of Fractions
- Mixed Recurring Decimal Conversion
- Approximation Techniques
- Algebraic Simplification
Example 1: Decimal Fraction Representation
Question: Convert the following fractions into decimal form:
(a) 1/10
(b) 7/1000
Solution:
(a) 1/10 = 0.1
(b) 7/1000 = 0.007
Therefore:
1/10 = 0.1 and 7/1000 = 0.007
Example 2: Decimal to Fraction Conversion
Question: Convert 0.25 into a vulgar fraction.
Solution:
0.25 = 25/100
Divide numerator and denominator by 25:
= 1/4
Therefore:
0.25 = 1/4
Example 3: Decimal to Fraction Simplification
Question: Convert 2.008 into a fraction.
Solution:
2.008 = 2008/1000
Divide numerator and denominator by 8:
= 251/125
Therefore:
2.008 = 251/125
Example 4: Addition of Decimal Fractions
Question: Find:
12.45 + 7.356 + 0.9
Solution:
Arrange decimals properly:
12.450
7.356
0.900
Total = 20.706
Therefore:
Answer = 20.706
Example 5: Subtraction of Decimal Fractions
Question: Find:
15.8 − 4.257
Solution:
15.800 − 4.257
= 11.543
Therefore:
Answer = 11.543
Example 6: Multiplication by Power of 10
Question: Evaluate:
5.9632 × 100
Solution:
Move decimal point two places to the right.
5.9632 × 100 = 596.32
Therefore:
Answer = 596.32
Example 7: Multiplication of Decimal Numbers
Question: Find:
0.2 × 0.02 × 0.002
Solution:
Ignore decimal points initially:
2 × 2 × 2 = 8
Total decimal places:
1 + 2 + 3 = 6
Therefore:
0.2 × 0.02 × 0.002 = 0.000008
Example 8: Division of Decimal Fraction
Question: Find:
0.0204 ÷ 17
Solution:
Ignore decimal point initially:
204 ÷ 17 = 12
Dividend contains 4 decimal places.
Therefore:
0.0204 ÷ 17 = 0.0012
Example 9: Division by Decimal Fraction
Question: Find:
0.00066 ÷ 0.11
Solution:
Multiply both numerator and denominator by 100:
= 0.066 ÷ 11
= 0.006
Therefore:
Answer = 0.006
Example 10: Comparison of Fractions
Question: Arrange the following in descending order:
3/5, 6/7, 7/9
Solution:
Convert into decimal form:
3/5 = 0.6
6/7 = 0.857
7/9 = 0.777...
Therefore:
6/7 > 7/9 > 3/5
Example 11: Pure Recurring Decimal
Question: Convert 0.333... into fraction.
Solution:
For pure recurring decimals:
0.333...
= 3/9
= 1/3
Therefore:
0.333... = 1/3
Example 12: Pure Recurring Decimal Conversion
Question: Convert 0.535353... into a fraction.
Solution:
Repeating digits = 53
Number of repeating digits = 2
Fraction = 53/99
Therefore:
0.535353... = 53/99
Example 13: Mixed Recurring Decimal
Question: Convert 0.1666... into fraction.
Solution:
0.1666...
= (16 − 1)/90
= 15/90
= 1/6
Therefore:
0.1666... = 1/6
Example 14: Annexing Zeros
Question: Does adding zeros after decimal change the value?
Solution:
No.
0.8 = 0.80 = 0.800
All values are equal.
Example 15: Algebraic Identity Simplification
Question: Find:
99 × 101
Solution:
99 × 101
= (100 − 1)(100 + 1)
Using identity:
(a − b)(a + b) = a² − b²
= 100² − 1²
= 10000 − 1
= 9999
Example 16: Approximation Technique
Question: Approximate:
19.98 × 5.02
Solution:
19.98 ≈ 20
5.02 ≈ 5
Therefore:
20 × 5 = 100
Important Exam Tips
- Practice decimal and recurring decimal conversions regularly.
- Memorize common fraction-decimal equivalents.
- Always count decimal places carefully during multiplication.
- Use approximation in lengthy calculations.
- Apply algebraic identities for faster simplification.
- Use decimal conversion for quick fraction comparison.
- Align decimal points properly during addition and subtraction.
Practicing solved examples regularly improves calculation speed, conceptual clarity, and accuracy in solving Simple and Decimal Fraction questions in competitive examinations.