Decimals & Fractions

Decimals:
Representation of fractions not having numerators and denominators is called decimals.
Example: 0.19, 0.589
Representation of decimals:

Decimals are represented by a period or decimal point. The period decreases by multiples of ten as we proceed towards right.
Example:  In 128.379, there are 3 tenths, 7 hundredths and 9 thousandths.
Repeating Decimals:
Decimal is another form of representing a fraction.  There are two parts in a decimal number. Part of the number before the decimal point is called integer part and the part of the number after the decimal part is called fractional part. When the fractional part of a number is repeated at regular intervals, we call it as a repeated decimal.
For example, 1/3 = 0.3333…. is a repeated decimal.
A rational number can either be represented as a terminating or repeated decimal.
1/9 = 0.1111…
1/8 = 0.125.
We call the repeating decimals as recurring decimals also.
Decimal word Problems:
Keith wants to following articles whose costs are given besides them.
Article Cost in $
DVD Player 59.95
DVD Holder 16.95
Personal Stereo 24.95
Discs (10 no’s) 20.00
Keith has $200 and wants calculate how much will he left with on buying these articles?
Problem solving strategy:
Step 1: Find what is asked for
Step 2: Analyze the data provided
Step 3: Compute
Step 4: Test the result obtained.
Solution:
Step 1: We need to calculate the amount left with (Involves subtraction of total from the Initial amount)
Step 2: Data is tabulated
Step 3: Computation: Sum of the cost of all the articles =$ 59.95 + $16.95 + $24.95 + $20= $121.85
Amount left with him after the purchase of these articles = $200 – $121.85 = $ 78.15
Step 4: Test the result: $121.85 + $78.15 = $200.00
Equivalent decimals:
In a decimal number, there are two parts. Part of the number before the decimal point is called integer part and the part of the number after the decimal part is called fractional part. The value of a number does not change even after we add any number of zeros before the integral part or after fractional part.
For example, 3.62= 00003.62000
Adding Decimals:
We follow two steps to add the decimal numbers
Step 1: Write the decimal number one below the other with decimal point lined up
Step 2: Add zeros so that the length of the decimal numbers are same.
Step 3: Add them normally with the decimal number aligned.
Example: 3.905 + 5.89
3.905
5.890
--------
9.795