Decimals:
Numbers representing fractions without having any numerator or denominator is called a decimal number.
Example: 0.567, 0.2, 0.49
Decimal Chart:
The value of a number in a decimal is decided by its place value.
0.345
3 represents three tenths = 3/10
4 represents four hundredths = 4/100
5 represents five thousandths = 5/1000
In engineering calculations, fractions are used extensively. As we know that, we can always express a fraction in terms of its corresponding decimal number. We have a ready reckoner that gives us corresponding converted values of a fraction.
1/64 = .015625 1/32 = .03125 3/64 = .046875 1/16 = .0625
5/64 = .078125 3/32 = .09375 7/64 = .109375 1/8 = .125
9/64 = .140625 5/32 = .15625 11/64 = .171875 3/16 = .1875
13/64 = .203125 7/32 = .21875 15/64 = .234375 1/4 = .25
17/64 = .265625 9/32 = .28125 19/64 = .296875 5/16 = .3125
21/64 = .328125 11/32 = .34375 23/64 = .359375 3/8 = .375
25/64 = .390625 13/32 = .40625 27/64 = .421875 7/16 = .4375
29/64 = .453125 15/32 = .46875 31/64 = .484375 1/2 = .5
33/64 = .515625 17/32 = .53125 35/64 = .546875 9/16 = .5625
37/64 = .578125 19/32 = .59375 39/64 = .609375 5/8 = .625
41/64 = .640625 21/32 = .65625 43/64 = .671875 11/16= .6875
45/64 = .703125 23/32 = .71875 47/64 = .734375 3/4 = .75
49/64 = .765625 25/32 = .78125 51/64 = .796875 13/16= .8125
53/64 = .828125 27/32 = .84375 55/64 = .859375 7/8 = .875
57/64 = .890625 29/32 = .90625 59/64 = .921875 15/16= .9375
61/64 = .953125 31/32 = .96875 63/64 = .984375
Multiplying decimals
In multiplication of decimal numbers, we follow two steps:
Step 1: Multiply the numbers without taking into consideration of decimal points
Step 2: Place the decimal point starting from right and moving as many digits as the sum of the number of digits in decimal part in both numbers towards left.
Example:
Dividing decimals:
We have two steps to follow.
Step 1: Convert both numerator and denominator into fractions
Step 2: Follow the rules of division of fractions.
Example: 14.4 ?0.12
Step 1: 14.4 = 144/10 and 0.12 = 12/100
Step 2: 144/ 10 ? 12/100 = 144/10 ?100/12 = 120
Subtracting decimals:
To subtract decimals one from the other we follow
Step 1: Write the numbers one below the other with decimal point coinciding
Step 2: Add zeros to make length of the numbers same
Step 3: Follow the laws of subtraction to subtract
Example:
0.56- 0.287
0.560
0.287
-------
0.213
Terminating decimals:
The word terminate means end. A decimal number with definite number of digits (ending) is called terminating decimal.
Example: 0.495. There are three digits after the decimal point.
All terminating decimals can be represented as a rational number.
Dewey Decimal System:
In public libraries, books are catalogued according to the subjects. Dewey Decimal System (DDC) is the most widely used system of classification for organizing books in libraries. In this system, integer part of the number gives us the specific subject and decimal part gives us the specific part of the subject.
For example:
In DDC, 512.12 represents a book on Algebra, 815.4 represents a book on 16th century Italian poetry.
