Assign 18 

course Mth 151

??????????????assignment #018

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018. Base-10 Place-value Number System

Liberal Arts Mathematics I

10-21-2007

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14:37:41

`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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RESPONSE -->

8 * 10^2 + 3 * 10^1 + 6 * 10^0.

confidence assessment: 2

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14:38:03

836 means 8 * 100 + 3 * 10 + 6 * 1, or 8 * 10^2 + 3 * 10^1 + 6 * 10^0.

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RESPONSE -->

I used the powers.

self critique assessment: 2

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14:41:00

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

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RESPONSE -->

3 * 10^4 + 4 * 10^3 + 9 * 10^2 + 0 * 10^1 + 7 * 10^0

confidence assessment: 2

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14:42:08

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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RESPONSE -->

I used the powers but for the 7 I put 7 * 10^0

self critique assessment: 2

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14:45:56

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

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RESPONSE -->

3 * .00100 + 2 * .00010 + 6 * .00001

confidence assessment: 2

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14:46:26

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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RESPONSE -->

I did not put the 0s in.

self critique assessment: 2

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14:50:02

`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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RESPONSE -->

3 * 100 = 300

5 * 10 = 50

7 * 1 = 7

total 357

5 * 100 = 500

4 * 10 = 40

2 * 1 = 2

total 542

357 + 542 = 899

confidence assessment: 3

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14:50:39

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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RESPONSE -->

You work out the problems then add them together.

self critique assessment: 2

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14:53:03

`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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RESPONSE -->

4 * 100 = 400

7 * 10 = 70

8 * 1 = 8

total 478

5 * 100 = 500

6 * 10 = 60

4 * 1 = 4

total 564

478 + 564 =1042

confidence assessment: 3

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14:53:26

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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RESPONSE -->

Multiply out then add.

self critique assessment: 2

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Very good responses. Let me know if you have questions. &#