Decimals and its Operations
Decimal number is an another way to write a fraction. For example, $ 4.25, $ 0.25, the number after the decimal or right side from the decimal is part of one dollar. It can also be written as \[\frac{25}{100}\] of a dollar. The base of decimal number system is 10 and Indo - Arabic number system is base 10 number system. Base 10 or decimal number system can always change the place value of the number by one spot, either multiplying or dividing by 10. It is more clear from the example given below:
Decimal point
The decimal point is the most important part of a decimal number. It is exactly to the right of the units position.
Like and Unlike Decimals
The decimals having the same number of digits to the right of decimal point are called like decimals, otherwise decimals are unlike. For example 10.52, 0.63, 258.69, 35.74 are like-decimals whereas 11.205, 4.23, 7.852, 14.00087 are unlike decimals.
Terminating and Non-Terminating and Repeating Decimals
If the decimal representation of a fraction \[\frac{p}{q}\] comes to an end then the decimal we obtain, is called terminating decimals. Important note: A fraction \[\frac{p}{q}\] is a terminating decimal, if prime factors of q are 2 and 5 only.
\[2\frac{3}{5}=2.6\] is a terminating decimal.
Non - terminating and repeating decimals: A decimal in which digit or a set of digits repeats periodically is called non - terminating and repeating decimals. For example, \[\frac{1}{3}=0.3333333.....=\text{ }0.\overline{3}\]and\[\frac{3}{11}=0.272727.......=0.\overline{27}\] are non-terminating and repeating decimals.
Find the terminating decimals from the following fractions:
\[\frac{23}{25},\frac{219}{175},\frac{337}{80},\frac{29}{198},\frac{19}{512}\]
(a) \[\frac{23}{25},\frac{219}{175},\frac{337}{80}\]
(b) \[\frac{337}{80},\frac{29}{198},\frac{19}{512}\]
(c) \[\frac{219}{175},\frac{337}{80},\frac{29}{198}\]
(d)\[\frac{23}{25},\frac{337}{80},\frac{19}{512}\]
(e) None of these
Answer: (d)
Explanation
The denominators of fractions are 25,175, 80,198, 512 and their prime factors are: \[25=5\times 5\]
\[175=5\times 5\times 7,\]\[80=2\times 2\times 2\times 2\times 5,\]\[198=2\times 3\times 3\times 11\]
\[512\text{ }=2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\]
Here we observe that the prime factors of 25, 80 and 512 have only 2 and 5.
Hence\[\frac{23}{25},\frac{337}{80},\frac{19}{512}\] are terminating decimal.
Express one second into hour.
(a) .0025 hours
(b) 1.0256 hours
(c) .00027 hours
(d) 1.000126 hours
(e) None of these
Answer: (c)
Explanation
One second \[=\frac{1}{60\times 60}=.00027\] hours
Which one of the following fractions is in ascending order?
(a) \[\frac{16}{19},\frac{11}{14},\frac{17}{22}\]
(b) \[\frac{11}{14},\frac{16}{19},\frac{17}{22}\]
(c) \[\frac{17}{22},\frac{11}{14},\frac{16}{19}\]
(d) \[\frac{16}{19},\frac{17}{22},\frac{11}{14}\]
(e) None of these
Answer: (c)
Explanation
\[\frac{16}{19}=0.842,\frac{17}{22}=0.773\And \frac{11}{14}=0.786.\]
\[\therefore 0.77<0.786<0.842\frac{17}{22}<\frac{11}{14}<\frac{16}{19}\]
The LC.M. of 3, 0.09 and 2.7 is:
(a) 2.7
(b) 1.27
(c) .027
(d) 0.27
(e) more... 
Introduction
We have already studied about different kinds of fraction and its properties. In this chapter we will study about some complex problems related to fractions.
Fraction and its Operations
Fractional number is defined as a part of whole.
It is represented as \[\frac{p}{q}\] where p & q are the integers and \[p\ne \]0
Here "p" is called the numerator & "q" is called the denominator of the rational number.
There are three circles given below showing the shaded parts of the circle. \[\frac{1}{2}\]of the circle is half of the whole circle, \[\frac{1}{4}\] of the circle is quarter (fourth) of the whole circle and \[\frac{3}{8}\] of the circle is three- eighth part of the whole circle.
Equivalent Fraction
Some fractions may look different, but they are equal and therefore, they are called equivalent fractions. It is obtained by multiplying its numerator and denominator by a non - zero numbers. Suppose \[\frac{a}{b}\] be a fraction (where a and b are co-prime and \[b\ne 0),\]then the equivalent fraction is: \[\frac{a}{b},\frac{2\times a}{2\times b},\frac{12\times a}{12\times b},\frac{23a}{23b},\frac{1202\times a}{1202\times b}\]
After reducing the above, we get the result as \[\frac{a}{b}\]
Rocky merry and John want to divide a chocolate equally among themselves when only two of them are present there. Find their respective share and also find the share of chocolate taken by the girls.
Solution:
The chocolate is divided into three parts given by \[=\frac{1}{3}\] of whole chocolate.
There are two girls in the group, so the share of both the girls \[=\frac{2}{3}\] part of the chocolate.
Properties of Fraction
Property I
Multiplication by the same number with numerator and denominator of the fraction results the same fraction, i.e. \[\frac{a}{b}=\frac{a\times c}{b\times c}\] (Where, a, b and c are integers and \[c\ne 0)\] Shaded part of the circle given below are half \[\left( \frac{1}{2} \right)\]of the circle and they are equal to \[\frac{2}{4}\And \frac{3}{6},\] But ^V are ^P1^^11111^ half of the circle. Therefore, \[=\frac{2}{4}=\frac{3}{6}.\]
The above given figures represents half of the circle in different ways.
Property II
For every two fractions with equal denominators, the larger fraction is the fraction with the larger numerator.
\[\frac{a}{c}>\frac{b}{c}if\,a>b.\](Where a, b and c are integers and\[c\ne 0)\]
Property III
For every two fraction with equal numerators, the larger fraction is the fraction with the smaller denominator.
\[\frac{a}{b}>\frac{a}{c},\]if \[b<c\](Where a, b and c are integers and c is not equal to 0)
Comparison of the Fraction
Sometime we need to compare two fractions to find which is larger or smaller. The following are ways to compare fractions: Decimal Method of Comparing Fractions The method to more... 
Simplifying Arithmetic Expressions
To simplify arithmetic expression follow BODMAS RULE
The value of \[~24-52\left\{ 5-\overline{\left( 13-8 \right)} \right\}\div \left[ 8\text{ }\{5+\left( -7 \right)\times \left( -9 \right)\} \right]\] is ......
(a) 124
(b) \[-24\]
(c) \[-529\]
(d) \[-\left( -24 \right)\]
(e) None of these
Answer: (d)
Explanation
We have: \[24-52\left\{ 5-\left( 13-8 \right) \right\}\div \left[ 8\text{ }\{5\text{ }+\left( -7 \right)\times \left( -9 \right)\} \right]\]
\[=24-52\left\{ 5-5 \right\}\div \left[ 8\{5+63\} \right]\]
\[=24-52\times 0\div \left[ 8\text{ }x\text{ }68 \right]\]
\[=24-52\times 0\div 544\]
\[=24-52\times 0\]
\[=24\]
we can write 24 as \[-\left( -24 \right)\] also.
Pamela tries to use bracket for a mathematical expression "twenty four multiplied by twelve more than the difference of twenty three and five". The correct representation is.
(a) \[24\times \left\{ \left( 23-5 \right)+12 \right\}\]
(b) \[24\times \left\{ \left( 23-5 \right) \right\}+12\]
(c) \[24\times \left( 23-5+12 \right)\]
(d) \[24\times 23-5+12\]
(e) None of these
Answer: (a)
Explanation
The correct representation is \[24\times \left\{ \left( 23-5 \right)+12 \right\}\]
The value of \[29-2\left\{ 6-\left( 7-3 \right) \right\}+\left[ 3\times \{5+\left( -3 \right)\times \left( -2 \right)\} \right]\]is____.
(a) 58
(b) -59
(c) 57
(d) 59
(e) None of these
Answer: (a)
If \[P=45-\left[ 5+\{60-\left( 39-8 \right)\} \right]\]and \[Q=-12+\left[ 25-2\{16-9\} \right]\] than then \[\left| P \right|+\left| Q \right|=?\]\[\left| P \right|+\left| Q \right|=?\]
(a) 10
(b) \[-10\]
(c) 20
(d) 12
(e) None of these
Answer: (d)
Explanation
\[p=45-[5+\{60-(39-8)\}]=45-[5+\{60-31\}]\]
\[=45-\left( 5+29 \right]=45-34=11\]and \[Q=-12+\left[ 25-\{2\left( 16-9 \right)\} \right]\]
\[=-12+\left[ 25-\{2\times 7\} \right]=-12+\left[ 25-14 \right]=-12+11=-1\]
Hence \[\left| P \right|+\left| Q \right|=\left| 11 \right|+\left| -1 \right|=11+1=12\]
There are two integers X and Y such that 5 and T are their additive inverse respectively then \[\left| X \right|+\left| Y \right|+\left| S \right|+\left| T \right|\] is equal to
(a)\[\left| X \right|\]
(b) \[\left| Y \right|+\left| S \right|\]
(c)\[2\left( \left| X \right|+|Y| \right)\]
(d) \[\left| X \right|+\left| Y \right|\]
(e) None of these
Answer: (c)
Explanation
Here, \[\left| S \right|=\left| X \right|\]and \[\left| T \right|=\left| Y \right|\]hence,
\[\left| X \right|+\left| Y \right|+\left| S \right|+\left| T \right|\]\[=\left| X \right|+\left| Y \right|+\left| X \right|+\left| Y \right|=2\left( \left| X \right|+|Y| \right)\]
If\[P=\left[ 29-\left( -2 \right)\{6-\left( 7-3 \right)\} \right]\]and \[Q=\left[ 3\times \{5+\left( -3 \right)\times \left( -2 \right)\} \right]\]then P - Q is equal to
(a) 10
(b) 1
(c) -1
(d) 2
(e) None of these
Answer: (b)
Absolute value of an Integer
Absolute value of an integer defined as follows:
\[\left| a \right|=\left\{ \begin{matrix} a,if & a>o \\ -a,if & a>0 \\ \end{matrix} \right.\]
For example:\[\left| 12 \right|=12,\left| -12 \right|=-\left( -12 \right)=12\]\[\left\{ because\text{ }\left( -12 \right)<0 \right\}\] 
Properties of Integers
There are four properties of Integers
Properties of Addition
Closure Property
The sum of two integers is always an integer.
For any two integer's p and q, \[\Rightarrow p+q\] is an integer.
For example \[\left( -\text{ }4 \right)+3=\left( -\text{ }1 \right),\] Which is an integer.
Commutativity
Sum of two integers is commutative.
For any two integers p and q,\[~\Rightarrow p+q=q+p,\] for example \[7+\left( -6 \right)=1\]and \[\left( -\text{ }6 \right)+7=1,\] therefore \[7\text{ }+\text{ }\left( -\text{ }6 \right)\text{ }=\text{ }\left( -6 \right)+7\]
Associativity
We addition of integers is associative. For any three integers p, q and r, \[p+\left( q+r \right)=\left( p+q \right)+r,\]
\[\left( -4 \right)+\left\{ \left( -8 \right)+6 \right\}=\left\{ \left( -4 \right)+\left( -8 \right) \right\}+6\]
Solution:
L.H.S \[=\left( -4 \right)+\left\{ \left( -\text{ }8 \right)+6 \right\}R.H.S=\left\{ \left( -4 \right)+\left( -8 \right) \right\}+6\]
\[=(-4)+(-2)=(-12)+6=(-6)=(-6)\]
Additive Identity
Additive identity is the number which when added to an integer gives the same integer. In case of addition "0" is the identity for integers. For example:
(i) \[~\left( -8 \right)+0=\left( -8 \right)\]
(ii) \[~0+\left( -37 \right)=\left( -37 \right)\]
(iii) \[31+0=37\]
Additive Inverse
The additive inverse of an integer is that integer which when added to the given integer gives the additive identity \[0.\left( -p \right)\] is the additive inverse of p, i.e. \[p+\left( -p \right)\] = 0. We get the additive inverse by taking the negative of the given integer. For example ( - 10) is additive inverse of 10 and 20 is the additive inverse of (-20)
Properties of Subtraction
Closure Property
Integers are closed under subtraction. If a and b are two integers then a - b is also an integer.
For example
(i) \[7-9=-2\] is an integer
(ii) \[\left( -8 \right)-\left( -15 \right)=7\] is an integer
Subtraction is neither Commutative nor Associative
For any two numbers a and \[b,a-b\ne b-a\] and for any three integers a, b, c we have \[a-(b-c)\ne (a-b)-c\]
(i) \[9-3\ne 3-9\]
(ii) \[9-(3-2)\ne (9-3)-2\]
A bird is flying at the height of 750 m above the lake surface. At a particular point it is exactly above a fish swimming 120 m below the lake surface. What is the vertical separation between bird and fish?
(a) 150m
(b) 350m
(c) 870m
(d) 630m
(e) Data is insufficient
Answer: (c)
Explanation
Distance between bird and fish | 750 m|+|-120 m| = 750 m+120 m = 870 m
Therefore, option (C) is correct and rest of the options is incorrect. more... 
Introduction
Integers are the set of all positive and negative numbers including zero. They are denoted by Z, i.e. z= {........, -4, -3, -2, -1, 0, 1, 2, 3, 4 ..........}
All the natural numbers are integer but converse is not true. e.g. 2000005 is a natural number and integers. On contrary (-5) is an integer but not a natural number.
Similarly whole numbers are integer and converse is not true. 
Hypertext Transfer Protocol (HTTP)
HTTP is the most important protocol used in WWW. It is a protocol that allows transferring the information on the World Wide Web between clients and servers. The main purpose of the HTTP is publishing and retrieving of the Web pages. The latest version of HTTP is HTTP/I.I. The original version of HTTP is HTTP 1.0. The main feature of HTTP 1.0 is that it uses a separate connection to the same server for every document.
Web Servers
A web server is a computer application that delivers web pages using HTTP over the World Wide Web. Basically it is responsible for accepting HTTP requests from clients or web browser. It also processes the requests send by the client and then sends the HTTP response back to the client.
Hyperlink
Hyperlink allows linking another place in the same document or another document. It also allows to link with the World Wide Web. A user just needs to click on hyperlink to go for relevant destination.
Hypertext
Hypertext is a kind of text that contains the reference of other text that exists in the same or other electronic document or the World Wide Web. A reader can immediately access the relevant information by just clicking or pressing the key on hypertext.
Working with the CD-Player
Now a day CD players are easily available in number of varieties and users are more confused about it. A CD player which you have opted for, contains basically three main features- a tracking device, derive motor, laser and a lens system. Basically derive motor needs pace not more than 200 rpm, but some time it needs approx 500 rpm also. Whereas the tracking device adjust the laser assembly and thus makes it possible for laser and lens system to work in a proper manner for the data which is stored on the CD (Compact Disk).
E-mail
Email (Electronic mail) is a digital correspondence that provides the facility to send and receive text messages, picture files and any other file to and from anyone with an e-mail address. E-mail is fast, easy and inexpensive. Email is a formal conversation. It should be point to point and well written. In current market there are many service providers who provide free e-mail services on the Internet, such as www.gmail.com, www.yahoo.com, www.hotmail.com and www.msn.com. The first part of the email address is a user name. The second part or domain name defines the Internet provider where the mail is sent. The two parts are separated by '@' sign (pronounced as "at the rate"). The domain name is followed by an extension that indicates the type of organization to which the network belongs.
The following is an example of an email address:
Steve@gmail.com
To send mail:
Introduction to Microsoft Internet Explorer
IE (Internet Explorer) is one of the most popular Internet browser that was developed by Microsoft. The first version of IE was IE1 that was launched in 1995. Microsoft continually works on the enhancement of IE. Currently Microsoft is working on IE 9. The IE 8 is the latest version of IE. The IE2, IE3, IE4, IE5, IE6 and IE 7 are the older version of IE. For performing various tasks on the Internet you can use the explorer toolbar.
The following list shows the description of each button:
HTML is a markup language that is used for developing website. HTML is developed by......................
(A) W3C
(B) Tim Berner-Lee
(C) Dennis Ritchie
(D) Microsoft
(E) None of these
Answer: (b)
Explanation
Correct Option:
(B) HTML language is developed by Tim Berner-Lee at Consiel European pour la Research Nuclear (CERN) to enable the researchers to share their research papers with the help of Internet.
Incorrect Options:
Therefore, option (B) is correct and rest of the options is incorrect.
Generally all the browsers are supporting HTML but basically the HTML is used by...............................
(A) Mosaic Browser
(B) Internet Explorer
(C) Mozila
(D) Safari
(E) None of these
Answer: (a)
Explanation
Correct Option:
(A) Generally all the browsers are supporting HTML but basically the HTML is used by Mosaic Browser.
Incorrect Options:
Therefore, option (A) is correct and rest of the options is incorrect.
Which of the following statements is/are true?
(A) WWW is used for accessing any information on the Internet
(B) Newsgroups and E-mails are not a part of the Web
(C) With the help of hyperlinks the Web links one Internet site to another
(D) All of these
(E) None of these
Answer: (d)
Explanation
Correct Option:
(A) All of the options are correct.
Incorrect Options:
Therefore, option (A) is correct and more... 
Web Page
For accessing any information on the Internet, the system WWW (World Wide Web) is used. It's one of the graphical parts of the internet. The WWW consists of files or Web pages that contain information and links to resources throughout the Internet.
You can surf or browse the Web in several ways:
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