NUMBER BASES 2

                   

       You are welcome to the second part of Number Bases and final post on Number bases as and I presume you might have done alot of practice questions after the last Lesson. If you have not read the last lesson, please visit this link and even more in your textbook. I hope to serve you better when you send in your comments and contribution in the comment box below. 

    Converting decimal numbers to bicimals has been a problem to all of us. So I decided to lay down some rules to follow so that it will be easy for you to remember with PRACTICE, you tend to get used to it. You know Mathematics is all about practice when you practice it gets sticked to your brain as the Shangai Maths whiz they will tell you more. Please if you dont get some rules call my attention to it.

          RULES TO CONVERT FROM DECIMALS TO BICIMALS

·         Separate the whole number values from the decimals. 

E.g 1.625 = 1 + 0.625

      6.75 = 6 + 0.75

·         If the whole number is not up to 2 since we are changing from decimals(fractions) to bicimals, there is no need to divide repeatedly by 2. If it’s 2 or more than 2 do not hesitate to do repeated division as it is done below:

2	6
2	3  r 0
2	1  r 1
2	0 r  1

Note that “r” means remainder  and we take the values of the r from the bottom. So we have “110.???”.

·       Finally take the decimal numbers “0.625” or “0.75” and multiply it by 2. Take the whole number you got from there and add it to the 110.??? You got in the first instance. Continue to multiply the number after the decimal number by two until you have “0” there. See the illustration below:

0.75  2  1.50                                      Ans = 110.1?

0.50  2   1.00                                     Ans = 110.11

As you can observe we have double zeros at the end of the “1.” So our mutiplication ends there.

Do This

Convert the following below from decimal(fraction) to bicimal:

1.    6.75

        Ans: 110.11

( Congrats to those those of you that got it in the previous post)  

Addition, Substraction, Multiplication and Division of Number Bases

1.    In base five, 424 + y + 203 = 2001

Find the missing number “y”?

Solution

Add 424 and 203 together in base five. If you cant see the solution below:

               424    

             +203         

                        1132_five

NOTE: When we sum numbers together and they are more than 5 take the multiples and leave the remainder.

i.e 4 + 3 = 7

5	7
	1 r 2

  We write the 2 and take the 1 towards the next value toward our left and continue with what the addition.

Hence:  y + 1132 = 2001

             Y = 2001 1132

              y 314_five

                             NO.2
 A man bought 37_eight measures of rice at $42_eight per measure and 63_eight measures of beans $56_eight per measure. Calculate the total amount of money spent in octag?

Step1: multiply $42 by $37

Step2: multiply $63 by $56

Step3: Add the result of the two together

Answer: 6510_eight

Please indicate if you didnt get this right.

                     

                              NO. 3

If 123_n = 251₆ find n?

      1 * n² +2 *n¹  + 3 *n⁰ = 2 * 6² + 1* 6¹ + 5 *6⁰

           n² + 2n + 3 72+ 6 +5

          n² + 2n + 3  83

          n² + 2n + 3 - 83 = 0

          n² + 2n - 80 = 0   

        (n + 10) (n-8) = 0

           Hence:

                        n= -10 or n =8

n  - 10 Since the base of a number is never negative

Therefore: n = 8

This ends everything on Number bases. Your contribution is highly welcomed. To contribute fill in the comment box or follow me on facebook.