course Mth 151
If your solution to stated problem does not match the given solution, you should self-critique per instructions at
http://vhcc2.vhcc.edu/dsmith/geninfo/labrynth_created_fall_05/levl1_22/levl2_81/file3_259.htm
.
Your solution, attempt at solution. If you are unable to attempt a solution, give a phrase-by-phrase interpretation of the problem along with a statement of what you do or do not understand about it. This response should be given, based on the work you did in completing the assignment, before you look at the given solution.
018. Base-10 Place-value Number System
Question: **** `q001. There are 5 questions in this set.
From lectures and textbook you will learn about some of the counting systems used by past cultures. Various systems enabled people to count objects and to do basic arithmetic, but the base-10 place value system almost universally used today has significant advantages over all these systems.
The key to the base-10 place value system is that each digit in a number tells us how many times a corresponding power of 10 is to be counted.
For example the number 347 tells us that we have seven 1's, 4 ten's and 3 one-hundred's, so 347 means 3 * 100 + 4 * 10 + 7 * 1.
Since 10^2 = 100, 10^1 = 10 and 10^0 = 1, this is also written as
3 * 10^2 + 4 * 10^1 + 7 * 10^0.
How would we write 836 in terms of powers of 10?
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Your solution:
836 = 8*10^2+3*10^1+6*10^0
Confidence Assessment:
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Given Solution:
836 means 8 * 100 + 3 * 10 + 6 * 1, or 8 * 10^2 + 3 * 10^1 + 6 * 10^0.
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Self-critique (if necessary):
Self-critique Rating:
Question: **** `q002. How would we write 34,907 in terms of powers of 10?
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Your solution:
34,907 = 34*10^3+9*10^2+7*10^0
Confidence Assessment:
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Given Solution:
34,907 means 3 * 10,000 + 4 * 1000 + 9 * 100 + 0 * 10 + 7 * 1, or 3 * 10^4 + 4 * 10^3 + 9 * 10^2 + 0 * 10 + 7 * 1.
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Self-critique (if necessary):
I started with 34 instead of the 3 separately. I also didn’t multiply the 0 and I did the multiplying on the last digit 7 wrong.
Self-critique Rating:
Question: **** `q003. How would we write .00326 in terms of powers of 10?
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Your solution:
0*0+0*0+0*0+3*10^2+2*10^1+6*1
Confidence Assessment:
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Given Solution:
First we note that
.1 = 1/10 = 1/10^1 = 10^-1,
.01 = 1/100 = 1/10^2 = 10^-2,
.001 = 1/1000 = 1/10^3 = 10^-3, etc..
Thus .00326 means
0 * .1 + 0 * .01 + 3 * .001 + 2 * .0001 + 6 * .00001 =
0 * 10^-1 + 0 * 10^-2 + 3 * 10^-3 + 2 * 10^-4 + 6 * 10^-5 .
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Self-critique (if necessary):
I was way off. I didn’t consider my decimals.
Self-critique Rating:
Question: **** `q004. How would we add 3 * 10^2 + 5 * 10^1 + 7 * 10^0 to 5 * 10^2 + 4 * 10^1 + 2 * 10^0?
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Your solution:
3*10^2=300 5*10^2=500
5*10^1= 50 4*10^1= 40
7*10^0= 7 2*10^0= 2
___________ ___________
357 + 542 = 899
Confidence Assessment:
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Given Solution:
We would write the sum as
(3 * 10^2 + 5 * 10^1 + 7 * 10^0) + (5 * 10^2 + 4 * 10^1 + 2 * 10^0) ,
which we would then rearrange as
(3 * 10^2 + 5 * 10^2) + ( 5 * 10^1 + 4 * 10^1) + ( 7 * 10^0 + 2 * 10^0),
which gives us
8 * 10^2 + 9 * 10^1 + 9 * 10^0. This result would then be written as 899.
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Self-critique (if necessary):
Self-critique Rating:
Question: **** `q005. How would we add 4 * 10^2 + 7 * 10^1 + 8 * 10^0 to 5 * 10^2 + 6 * 10^1 + 4 * 10^0?
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Your solution:
4*10^2=400 5*10^2=500
7*10^1= 70 6*10^1= 60
8*10^0= 8 4*10^0= 4
___________ ___________
478 + 564 = 1042
Confidence Assessment:
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Given Solution:
We would write the sum as
(4 * 10^2 + 7 * 10^1 + 8 * 10^0) + (5 * 10^2 + 6 * 10^1 + 4 * 10^0) ,
which we would then rearrange as
(4 * 10^2 + 5 * 10^2) + ( 7 * 10^1 + 6 * 10^1) + ( 8 * 10^0 + 4 * 10^0),
which gives us
9 * 10^2 + 13 * 10^1 + 12 * 10^0.
Since 12 * 10^0 = (2 + 10 ) * 10^0 = 2 * 10^0 + 10^1, we have
9 * 10^2 + 13 * 10^1 + 1 * 10^1 + 2 * 10^0 =
9 * 10^2 + 14 * 10^1 + 2 * 10^0.
Since 14 * 10^1 = 10 * 10^1 + 4 * 10^1 = 10^2 + 4 * 10^1, we have
9 * 10^2 + 1 * 10^2 + 4 * 10^1 + 2 * 10^0 =
10^10^2 + 4 * 10^1 + 2 * 10^0.
Since 10*10^2 = 10^3, we rewrite this as 1 * 10^3 + 0 * 10^2 + 4 * 10^1 + 2 * 10^0.
This number would be expressed as 1042.
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Self-critique (if necessary):
It is easier for me to set it up the way I am doing is this wrong?
you should do these in powers of 10, and should not use our familiar (and efficient) elementary-school algorithm where you put the numbers in columns, 'carry', etc.
Self-critique Rating: