The numbers we use in arithmetic are all Decimal numbers. Different number systems are defined using the remainders that numbers yield on division by base. A decimal is a number that is written using base 10 system. The 10 digits we use to represent the numbers in decimal system, that are 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 form a set of possible remainders, we get dividing any number by 10. The position or place values in decimal number system are all powers of 10. 
A decimal number can be expressed in verbal, decimal and expanded form.
Example:
Verbal Form 
Forty three and fifteen hundredths 

Decimal Form 
 43.15 
Expanded Form 
4 Tens + 3 Ones + 1 Tenths + 5 Hundredths 40.0 + 3.0 + 0.1 + 0.05 
For example, the number 72.86 is read shortly as 'Seventy two point eight six'. The digits to the left of decimal point 72 form the integer part and the numbers to the left of it 86 (86 hundredths) form the decimal part. The digit 0 is written in front of the decimal point for decimal numbers less than 1 as in 0.572.
→ Read More The place value chart used for integers is extended to include decimal place values. Let us place the decimal number 85.743 in Decimal place value chart to write the different forms of the number.
Word Form  Eight five and seven hundred forty three thousandths 
Decimal Form  85.743 
Expanded Form  8 Tens + 5 Ones + 7 Tenths + 4 Hundreds + 3 Thousands 80.0 + 5.0 + 0.7 + 0.04 + 0.003 
 If the immediate digit to the right is $\geq$ 5, one is added to the digit in the rounding place.
 If the immediate digit to the right is < 5, the digit in the rounding place is retained.
Solved Examples
Solution:
Hence, the number is rounded to the hundredth as 125. 75
Solution:
Hence, the number is rounded to the tenth as 89.2
Let us add 25.8, 17.423 and 8.76
The numbers are lined up as follows
25. 800 (Zeros appended in Hundredths and Thousandths places) 17. 423 8. 760 (Zero appended in Thousandths place)  51. 983 (The three numbers added to get the sum) 
In case of signed numbers, rules applicable to integers are applied to decimals as well.
 If the two numbers added are of the same sign, find the sum and take the common sign.
 If the two numbers added are of the opposite sign, find the difference and take the sign of the number whose absolute value is larger.
 While adding more than two numbers, group the numbers by sign, find the sum in each group and add these two numbers to get the sum of given numbers.
Examples:
4.5 + 7.82 = 12.32
10.84 + ( 4.62) = 15.46
84.6 + (12.78) = 71.82
6.02  2.48 + 3.25  0.25  1.46 = (6.02 + 3.25) + (2.48  0.25  1.46) = 9.27 + (4.19) = 5.08
Examples:
 7.05  (4.85) = 7.05 + 4.85 = 11.9
  13.72  (+ 7.63) =  13.72  7.63 =  21.35
  24.84  (10.62) = 24.84 + 10.62 = 14.22
Let us multiply 46.75 and 8.2
46.75 (The number has two decimal places) x 8.2 (The number has one decimal place)  9350 374000  383.350 < The decimal is placed counting three places from the right end. 
Ignoring the trailing zero, we can write 46.75 x 8.2 = 383.35
The sign rules are applied as applied to multiplying integers.
 4.25 x 0.72 = 3.06 + times + = +
 2.43 x  0.02 = 0.0486  times  = +
 72.5 x 3 = 217.5 + times  = 
Let us divide 482.4 by 12
Decimal by decimal division is done by suitably multiplying the dividend and the divisor in order to make the divisor an integer.