Fractions: Fractions is a number which can be represented as numerator and denominator, i.e, its reciprocal of integers. Fractions can be represented in different forms:
Decimals: Decimal number is a number which always uses 10 as its base and it is most widely used to solve the complex problems. It is denoted with a dot (.) in between it. Decimal numbers do not necessarily contain a decimal point; 563, 5.63, and -563 are all decimal numbers.
Numerator is the top part of the fraction. Denominator is the down part. if numerator is greater then denominator then value will be more compared to denominator is greater then the numerator. The different ways of representation of numerator and denominator can be seen below:
Types of Fractions
Fraction are classified into 3 types:
Proper fraction: Numerator is less then denominator
Example: $\frac{3}{4}$
Improper fraction: Numerator is greater then or equal to denominator
Example: $\frac{3}{2}$ or $\frac{2}{2}$
Mixed fraction: Mixed fraction consist of whole number.
Example: 5($\frac{2}{4}$)
The fractions which contains equal numerator and denominator are called equal fractions.
Example
Conversions
Decimal to fractions
The following are the steps to be followed for conversion of decimal to fractions:
1) Write the decimal
2) Count the number of digits where the decimal point is.
3) Then depending on that divide the number by 10,100-------
4) Cancel if they are any divisible terms
5) Remain it like fractions
Fractions to decimals
The following are the steps to be followed for conversion of fraction to decimal.
1) Write the fraction
2) Divide the numerator total with denominator
3) Now represent the fraction like a decimal.
To simplify the fraction we need to make the numerator and denominator simple i.e, cancel the divisible terms in numerator and denominator and make it simple.
Example
Simplify $\frac{50}{100}$
Given fraction is $\frac{50}{100}$
Numerator = 50
Denominator = 100 = 50x2
$\frac{50}{100}$
Numerator = 50
Denominator = 100 = 50x2
Decimal and Place Values with Decimals
Decimals can be represented by converting fractions to decimals.
Example
The decimals 0.7, 0.64, and 0.037 can be expressed as the decimal fractions $\frac{7}{10}$, $\frac{64}{100}$, and $\frac{37}{1,000}$. They are all terminating decimals. These fractions can equally be expressed as the percentages 30%, 51%, and 2.3%.
The unit places of any decimal number are denoted by using positions tenths place, hundredths place, thousands place etc.
Tenths place, Hundredths place and Thousandths place:
The tenths place in any decimal number lies immediately after dot (.) Tenths place can be determined by making 10 parts between any two consequent numbers.