# Decimal Fractions: Basic Concepts, Solved Problems and Solutions

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**Basic Concept: **

1. Decimal Fractions: Fractions in which denominators are power of 10 are Known as Decimal Fractions.

Thus, 1/10 = 1 tenth = .1; 1/100 = 1 hundredth = .01;

99/100 = 99 hundredth = .99, etc

2. Conversion of a Decimal into Vulgar Fraction: Put 1 in the denominator under the decimal point and annex with it as many zeros as in the number of digits after the decimal point. Now, remove the decimal point and reduce the fraction to its lowest terms.

3. Comparison of Fractions: Suppose some fractions are to be arranged in ascending or descending order of magnitude. Then, convert each one of the given fractions in the decimal form, and arrange them accordingly.

**Solved Examples:**

1. Convert the following into vulgar fractions:

(i) 0.75 (ii) 3.004 (iii) .0056

Sol: (i) 0.75 = 75/100 = 3/4

(ii) 3.004 = 3004/1000 = 751/250

(iii) .0056 = 56/10000 = 7/1250

2. Find the products of:

(i) 2.1693 * 1.4

Sol: 21693 * 14 = 303702. Sum of decimal places = (4 + 1) = 5

Therefore 2.1693 * 1.4 = 3.03702

(ii) 0.4 * 0.4 * 0.4 * 0.004 * 40

Sol: 4 * 4 * 4 * 40 = 2560. Sum of decimal places = (1+2+3) = 6

Therefore 0.4 * 0.4 * 0.4 * 0.004 * 40 = 0.002560

3. Arrange the fractions 3/5, 4/7,8/9 and 9/11 in their descending order.

Sol: Clearly, 3/5 = 0.6, 4/7 = 0.571, 8/9 = 0.88, 9/11 = 0.818

Now, 0.88>0.818>0.6>0.571

Therefore 8/9>9/11>3/5>4/7.

**Homework Questions:**

1. Which of the following fractions is less than 1/5?

a. 8/35 b. 8/37 c. 8/39 d. 2/11

2. Which of the following fractions is nearest to 2/5?

a.4/5 b. 21/50 c. 20001/50000 d. 200001/500000

3. Which of the following fractions lies between 2/3 and 3/5?

a. 2/5 b. 1/3 c. 1/15 d. 31/50

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