Basics Concepts and Formulas - Decimal Fractions

ssc preparation, important competetion questions, current affairs of india, latest question asked in competetion papers,

Basics Concepts and Formulas - Decimal Fractions1. FractionsA fraction is an expression that indicates the quotient of two quantities.
Examples of fractions: $\frac{1}{2}$, $\frac{1}{3}$, $\frac{5}{7}$, $-\frac{8}{5}$ etc.
A fraction has two parts, Numerator and Denominator. Numerator is the number at the top of the fraction and denominator is the number at the bottom of the fraction.
For example, in the fraction $\frac{1}{4}$, $1$ is numerator and $4$ is denominator.
The denominator of a fraction cannot be zero.
Fractions can be denoted by using horizontal lines or diagonal lines. For example, $\frac{1}{4}$ and 1/4 represents the same.

2. Type of Fractions(a) Common Fraction
A common fraction (also known as Vulgar fraction and simple fraction) is a fraction in which both numerator and denominator are integers (Like other fractions, the denominator cannot be zero)

Examples: $\frac{2}{3}$, $\frac{7}{12}$, $-\frac{6}{5}$

(b) Decimal Fraction
A decimal fraction is a fraction in which denominator is an integer power of ten. (The term decimals are commonly used to refer decimal fractions).

Generally, a decimal fraction is expressed using decimal notation and its denominator is not mentioned explicitly.

Examples:

$\frac{1}{10}$ = .1

$\frac{1}{100}$ = .01

$\frac{17}{100}$ = .17

$\frac{4}{10000}$ = .0004

$\frac{121}{100}$ = 1.21

Decimal fractions can also be expressed using scientific notation with negative exponents.

Example: 4.193 × 10⁻⁷ is a decimal fraction which represents .0000004193

3. Generally, a zero is added to the left of the decimal point if a whole number is absent to draw the attention to the fact that the number is a decimal fraction.

For example, .1 and 0.1 represents the same

4. Annexing Zeros to the extreme right of a decimal fraction does not change its value.

Examples

0.4 = 0.40 = 0.400 = 0.4000, etc.
1.21 = 1.210 = 1.2100 = 1.21000, etc

5. If the numerator and denominator contain the same number of decimal places, we can remove the decimal sign.

Example

$\frac{1.2}{4.8}=\frac{12}{48}=\frac{1}{4}$

$\frac{0.03}{0.24}=\frac{3}{24}=\frac{1}{8}$

6. Conversion of a Decimal into Common FractionPut 1 in the denominator under the decimal point and annex with it as many zeros as is the number of digits after the decimal point. Now, remove the decimal point and reduce the fraction to its lowest terms.

Examples

0.5 = $\frac{5}{10}=\frac{1}{2}$

.75 = $\frac{75}{100}=\frac{3}{4}$

1.25 = $\frac{125}{100}=\frac{5}{4}$