SHREE BALAJI CLASSES

Complement of a Number    Number System    Types of Number system In our previous article, we had discussed Convert any number into Decimal Number. Now, In this article we can easily understand how to convert Decimal Number into other Number Note : The Rule is very simple. Any number which you want convert Decimal to required format. Just divide by its base to this number and remainder is taken from bottom to top. Let’s understand with some examples Convert Decimal to Binary Ex 1. Convert (41) 10 into Binary Number Sol. 41 is divide by 2 because the base of binary number is 2       Integer quotient    Quotient      Remainder        41 / 2                       20                      1        20 / 2                       10                      0        10 / 2                       5                        0        5 / 2                         2                        1        2 / 2                         1                        0        1 / 2        

1. Condition :   This trick is used when we multiply quickly two numbers of two digits. Example.  21 × 59, 89 × 96 etc. Illustration 1:                                                                                                                       Illustration 2 Note : 2nd and 3rd part have only 1 digit. 

Complement of a Number    Number System    Types of Number system       In our previous article, we had discussed about different types of Number System. Now, In this article we can easily understand how to convert Any Number in to Decimal Number System. Convert Binary to Decimal – we convert binary to decimal by multiplying increasing power of two through right to left from decimal. If there is no decimal, we should start from the last digit and multiplying by increasing power of 2 up to first digit. If decimal occurs, then start from the first digit and multiply by decreasing power of 2 up to the last digit. Let’s understand with an example. Ex 1. (110111) 2 Sol. (1*2 5 ) + (1*2 4 ) + (0*2 3 ) + (1*2 2 ) + (1*2 1 ) + (1*2 0 )         (1*32) + (1*16) + (0*8) + (1*4) + (1*2) + (1*1)         32 + 16 + 0 + 4 + 2 + 1         (55) 10                    Ans. Ex 2. (1001.01) 2 Sol. (1*2 3 ) + (0*2 2 ) + (0*2 1 ) + (1*2 0 ) + (0*2 -1 ) + (1*2 -2 )         (1*8) +

           In our everyday lives, we use the decimal numbering system. These are digits 0 through 9. Every number expressed in the decimal system is a combination of these ten digits i.e. 360, 418, 086 etc. These numbers uses only digits 0 through 9. However, there is another system which is used in computers, called binary system.                 The binary system works in essentially the same way, with the only difference being that it only has two digits. These are visually expressed by the digits 0 and 1, and every number expressed in the binary system is a combination of 0 and 1.                 These numbers (0 and 1) are actually a representation of signals. In modern electronic technology, computer circuit has only two states, on or off. 0 represent off while 1 represent on. There are many other Number Systems i.e. Octal Number System, Decimal Number System, Hexadecimal Number System etc. Decimal Number System – In above discussion, we saw that it uses numbers through 0

Different Number Systems – There are some different Number System with correspondence base. Which will describe as follows-   Number System  Base  Representation  Binary Number System      2  (Number) 2  Decimal Number System      10  (Number) 10  Octal Number System      8  (Number) 8  Hexadecimal Number System     16   (Number) 16 Note : Any number can be in decimal form. So there is an another way to solve them quickly. Let’s understand with an example. Ex 1. (4064.10) 10   Sol. This Number can also be written as (4*10 3 ) + (0*10 2 ) + (6*10 1 ) + (4*10 0 ) + (1*10 -1 ) + (0*10 -2 ) Note that after decimal digits we will use decreasing power of 10 from left to right. Ex 2.   (1101.01) 2        Sol. This Number can also be written as (1*2 3 ) + (1*2 2 ) + (0*2 1 ) + (1*2 0 ) + (0*2 -1 ) + (0*2 -2 ) Exercise: From Question 1 to 5, expand with theirs correspondence base. 1.     (6529.89) 10 2.    (1164.54) 8 3.     (10011.01) 2 4.    (4301.44) 5 5.    (11111.01

1. Condition :   This trick is used when we multiply quickly two numbers near  a  multiple of a power of 10. Example.  211 × 209, 189 × 191 Illustration 1 :      207 × 211 Numbers       Working Base         Difference      207                    2 × 100                  +7    211                    2 × 100                  +11     Solution:  1st part  /   2nd part(2 digits)                     [Number of digits in the 2nd part = Number of 0s in the base]                            2 × ( 207 + 11 ) / 7 × 11 (2 digits)       2 × 218      /     77          436        /     77  Answer is    43677 Note:  1st part can either be 207 +11 or 211 +7   Illustration 2 :      191 × 187 Numbers       Working Base         Difference      191                     2 × 100                  -9    187                     2 × 100                  -13     Solution:  1st part  /   2nd part(2 digits)                     [Number of digits in the 2nd part = Num

Why does lightning flash ? During a storm, flashes of lightning followed by thunder, light up the sky like fireworks. It is an impressive and sometimes frightening spectacle. The flash occurs for several reasons. As the air heat and cools, it expands and contracts, and this cause changes in the movement of air and pressure.The water droplets at the top of a cloud have a positive electrical charge, while those at the bottom of a cloud are negatively charged.    When the clouds are low enough, the negative charge in the water droplets attract a positive charge from the Earth. As a result, electrical energy is released with a flash. This causes the air to be heated tremendously high temperature, which in turn, causes the air to expand suddenly with an explosive noise that we call thunder. Though thunder and lightning occur at the same time, we see lightning first, and then hear thunder, because light travels faster than sound.

1. Condition :   This trick is used when we multiply quickly three numbers near  a  same power of 10. Example.  103 × 112 × 108   Illustration 1 :      107 × 102 × 105 Numbers       Base         Difference      107               100        +7 (let a=7)  102               100        +2 (let b=2)  105               100        +5 (let c=5) Solution:  1st part /   2nd part  /  3rd part                        (Number of digits in the 2nd and 3nd part =Number of 0s in the base)                            formula: 107+b+c  /  a×b+b×c+c×a  /  a×b×c 107+2+5  /  7×2+2×5+5×7   /  7×2×5       114     /     14+10+35     /    70       114     /            59            /    70  Answer is   1145970      Note:  1st part can either be   107+b+c  or  102+a+c  or   105+a+b Illustration 2 :      102 × 109 × 106  Numbers            Base            Difference       102                    100                  +2 (let a=2)   109                   

Global Warming  Global warming is the process when the earth heats up and the temperature rises. This happens when there is an increase in the production of gases like carbon dioxide, water vapour, nitrous oxide and methane, which are known as greenhouse gases. These greenhouse gases trap heat and light from the sun in the Earth's atmosphere, and this in turn increases the temperature and causes global warming. Did you know that since the beginning of the 20th century, the average temperature of the Earth has risen by 0.8 degree Celsius? Global warming hurts people, animals and plants . In fact, many cannot take the change, so they die out. Some Important Days to remember : September 16 - International Day for the preservation of the Ozone layer. June 5 - World Environment Day. April 22 - International Earth Day. March 23 - World Meteorological Day. March 22 - World Water Day.

Why do Stars Twinkle ? Out in space, stars do not twinkle. It is only when you look at them from Earth that they appear to do so. Stars are really very large but they are so far away from us that they seem to be just points of light.       Starlight comes towards Earth along a path through space that produces very little change in the light. However on Earth we see stars by looking through our planet's atmosphere, which is a thin shell of gases surrounding our planet. The Earth's atmosphere is in constant motion, with pockets of hot and cold air moving around constantly. Light rays bend differently in cold air and hot air. The motion of hot and cold air pockets causes the light rays from a star to move continuously too. In addition, the pockets of moving air also focus and defocus the starlight, so that its brightness keeps changing. Both of these effects together produce the sensation that we call 'twinkling' of stars .