What is the base 7 representation of the number 275?
21201 is the base 3 representation of what number?
I'm having trouble with both questions. Can someone help me out? I tried using the internet but I was still confused.
+c*7^2 +b^7^1 + a^7^0
c*49 + b*7 + a
5*49 = 245 so c = 5
275 - 245 = 30
so b = 4 and 30-28 = 2 so a = 2
so
542
===========================
check
5*49 + 4*7 + 2 = 245 + 28 + 2 = 275
so
5 4 2 is it
What you want to do is represent 275 as powers of 7
So
7^3 = 343 ,we don't have to go that high
7^2 = 49
275/49 = 5 with remainder of 30
30/7 = 4 with remainder of 2
then 275 = 5(7^2) + 4(7) + 2
= 5427
if 21201 is a base 3 number
= 2(3^4) + 1(3^3) + 2(3^2) + 0(3^1) + 1(3^0)
= 162 + 27 + 18 + 0 + 1
= 208 in base 10
21201
is
1*3^0
0*3^1
2*3^2
1*3^3
2*3^4
= 2*81 + 1*27 + 2*9 +0*3 + 1*1
= 162 + 27 +18 + 0 + 1
= 208
I am still so confused.. why did you do that?
Hey, I was so pleased that we agreed
remember our old tens system is
just 0 through 9 times 10^n in each spot starting on the right with 10^0 which is one
so 549 is
5*10^2 + 4*10 + 9*10^0 = 500 + 40 + 9
we are used to that but other cultures might use 7 instead of 10
then a three digit number would be
a*7^2 + b*7^1 + c*7^0
or
a*49 + b*7 + c*1
now a , b and c must be 0,1,2 -.... 6
just like in the ten system they must be
0 , 1 , 2 ..... 8, 9
so the biggest I can make with 3 digits in 7 system is
666
which would be
6*49 + 6*7 + 6
or
294 + 42 + 6 = 342
now for example the biggest I can put in the second spot with 0 on the right is 42 (not 90) and in the left spot with zeros on the right 294 (not 900)
so
600 in seven system would be 294
6*7^2 = 294 :)
Of course, I'm here to help! Let's tackle each question one by one.
1. To find the base 7 representation of the number 275, we need to convert it from its decimal form (base 10) to base 7. Here's how you can do it step by step:
First, divide the number 275 by 7. The quotient is 39 with a remainder of 2.
Next, divide the quotient 39 by 7 again. The new quotient is 5 with a remainder of 4.
Continue this process, dividing each quotient by 7 until the quotient is 0.
The remainders, in reverse order, form the base 7 representation of the number. In this case, it is 425.
So, the base 7 representation of 275 is 425.
2. Now, let's move on to the second question. We need to find the decimal (base 10) equivalent of the number given in base 3 representation.
To do this, we will multiply each digit of the base 3 number by the corresponding power of 3 and sum them all up.
In the given base 3 number 21201, we can calculate its decimal value as follows:
- The rightmost digit (1) is multiplied by 3^0 (which is 1), so it gives us 1.
- The second rightmost digit (0) is multiplied by 3^1 (which is 3), so it gives us 0.
- The next digit (1) is multiplied by 3^2 (which is 9), so it gives us 9.
- The next digit (2) is multiplied by 3^3 (which is 27), so it gives us 54.
- The leftmost digit (2) is multiplied by 3^4 (which is 81), so it gives us 162.
Finally, we add all these values together: 1 + 0 + 9 + 54 + 162 = 226.
Therefore, the base 10 equivalent of the base 3 number 21201 is 226.
I hope this explanation helps you understand how to solve these types of questions!