Question 1160703
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Problem 1


In Roman numerals, we have
L = 50
X = 10
I = 1 ... this says "upper case i is equal to one"


We start with L = 50 and add on X = 10 to get LX = L+X = 50+10 = 60. So LX = 60.


Then we add on another ten
LXX = LX+X = 60+10 = 70
LXX = 70


Finally we add on II to represent two
LXXII = LXX+II = 70+2 = 72
<font color=red size=4>LXXII = 72</font>


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Problem 2


Here are some more Roman numerals to have on a reference sheet or memorize.
C = 100
D = 500


Writing DC means D+C = 500+100 = 600. The order matters because CD = 500-100 = 400. Think of it like how roman numeral IV means 5-1 = 4. If you list the smaller number first, then you subtract. Otherwise you add.


Therefore, DCII represents 602 
DCII = D+C+I+I = 500+100+1+1 = 602.


<font color=red size=4>Answer = DCII</font>


Here is a useful tool to help check your answer
<a href = "https://www.romannumerals.org/converter">https://www.romannumerals.org/converter</a>
This tool can be used for problem 1 as well.


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Problem 3


When we write something in base 10, like the number 937, we are really saying 900+30+7. This further can be broken down or written as 9*100+3*10+7*1. At this point, we have the coefficients 9,3,7 multiplied with descending powers of 10 (hence the name base 10).


9*100+3*10+7*1 is the same as 9*10^2+3*10^1+7*10^0. The exponents over the 10s are counting down.


Here's another example of a base 10 number
58972 = 5*10,000 + 8*1,000 + 9*100 + 7*10 + 2*1
58972 = 5*10^4 + 8*10^3 + 9*10^2 + 7*10^1 + 2*10^0


Now with base 5, we just replace all those '10's with 5. Writing a number like 12 in base 5, we would say


{{{12[5] = 1*5^1 + 2*5^0}}}


{{{12[5] = 1*5 + 2*1}}}


{{{12[5] = 5 + 2}}}


{{{12[5] = 7[10]}}}
The subscripts represent which base we're working in. 


Here's how you count in base 5. You start at 0, then add 1 like you normally would in base 10. Then bump up to 2, then 3, etc etc, until you reach 5. You can't actually get to 5 since it does not exist in base 5. So we have this so far
0,1,2,3,4


The next number would be 10
0,1,2,3,4,10
The number {{{10[5]}}} is the same as 5 in base 10. It's a bit confusing considering how the numbers swap like that.


Then after 10, we continue to increase just like we normally do
0,1,2,3,4,10,11,12
We can see that the '12' is in the spot of where the 7 base 10 would go.



<font color=red size=4>Answer = 7</font>


Useful calculator to check your work
<a href = "https://www.unitconverters.net/numbers/base-5-to-base-10.htm">https://www.unitconverters.net/numbers/base-5-to-base-10.htm</a>


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Problem 4


I'm not sure what you mean by "place value oh thousands". 


If you mean just simply "thousands place" or "one thousands place", then that would be 5. It might help to erase the numbers to the left of the 5 to see that 2,345,562 turns into 5,562. The first 5 is representing 5 thousand. More technically, it is 5 copies of one thousand added together.


If you want the ten-thousands place, then the answer is 4. Erase everything to the left of the 4 to go from 2,345,562 to 45,562. We see the number is over fourty thousand at this point.


If you want hundred-thousands place, then the answer is 3


Place value chart:
<img src = "https://i.imgur.com/bkJ7MWk.png">
The values in the second row represent the digits from 2,345,562.
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