Assignment 18 qa

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course Mth 151

05/06/20111209

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

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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: there are six 1’s, three 10’s, and eight 100’s. it will also be: 8*10^2 + 3*10 + 6*1

confidence rating #$&*:3

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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):n/a

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Self-critique Rating:3

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Question: `q002. How would we write 34,907 in terms of powers of 10?

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Your solution:that would be: that would be: seven 1’s, zero 10’s, nine 100’s, four 1000’s and three 10,000. It would also be 3 * 10000 + 4 * 1000 + 9 * 100 + 7 * 1

confidence rating #$&*:

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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):n/a

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Self-critique Rating:3

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Question: `q003. How would we write .00326 in terms of powers of 10?

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Your solution: we can write this like: .001* 3 + .0001 * 2 + .00001 * 6

confidence rating #$&*:

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

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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):n/a

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Self-critique Rating:a

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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:we would do: ( 100 * 3 + 10 * 5 + 1 * 7) + ( 100 * 5 + 10 * 4 + 1 * 2)

confidence rating #$&*:3

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

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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):n/a

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Self-critique Rating:3

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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: we could write that like: (4 * 10^2 + 7 * 10^1 + 8 * 10^0) + (5 * 10^2 + 6 * 10^1 + 4 * 10^0)

confidence rating #$&*:3

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

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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.

STUDENT SOLUTION

(4 x 10^2 + 5 x 10^2) + (7 x 10^1 + 6 + 10^1) + (8 x 10^0 + 4 x 10^0)

adds up to

9 x 10^2 + 13 x 10^1 + 12 x 10^0 = 1042

INSTRUCTOR RESPONSE

You got

9 x 10^2 + 13 x 10^1 + 12 x 10^0 = 1042

But this isn't in its final powers-of-10 notation.

13 * 10^1 isn't a legal expression. Since 13 is greater than 9, you would use the fact that 13 * 10^1 = 10^2 + 3 * 10^1 to write this in correct notation.

Your expression would then become

9 x 10^2 + 10^2 + 3 x 10^1 + 12 x 10^0

Also 12 * 10^0 = 10^1 + 2 * 10^0, so your expression is equivalent to

9 x 10^2 + 1 * 10^2 + 3 x 10^1 + 10^1 + 2 x 10^0

When we add the like powers of 10 we find that 9 * 10^2 + 10^2 = 10 * 10^2, which is 10^3.

Since 3 * 10^1 + 10^1 = 4 * 10^1.

your final expression should be

10^3 + 4 * 10^1 + 2 * 10^0.

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Self-critique (if necessary): was not aware that we had to simplify the terms

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Self-critique Rating:3

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