assignments 1819

course Mth 151

???~?ZG????????assignment #018

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018. Base-10 Place-value Number System

Liberal Arts Mathematics I

12-13-2007

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20:33:40

`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: 3

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20:36:17

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

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RESPONSE -->

3*10,000+4*1,000+9*100+0*10+7*1

confidence assessment: 3

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20:38:37

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

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RESPONSE -->

0*1+0*.01+3*.001+2*.0001+6*.00001

confidence assessment: 3

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20:47:17

`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 -->

step 1:(3 * 10^2 + 5 * 10^1 + 7 * 10^0)

+(5 * 10^2 + 4 *10^1 + 2 * 10^0)

step 2:(3*10^2+5*10^2) + (5*10^1+4*10^1) + (7*10^0+2*10^0)

step 3(add) :(8+10^2)+(9*10^1)+(9*10^0)

step4: 899

confidence assessment: 3

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21:04:05

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

step 2: 9*10^2 +13*10^1 +12*10^0

step3: 12*10^0

2*10^0 +10^1

step 4: 9*10^2 +13*10^1+1*10^1+2*10^0=

9*10^2+14*10^1 +2*10^0

step 5:14*10^1=

10*10^1+4*10^1=

10^2+4*10^1

step 6: 9*10^2 +1*10^2 +4*10^1 +2*10^0=

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

step 7: 10*10^2=10^3

step 8: 1042

confidence assessment: 2

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assignment #019

019. Place-value System with Other Bases

Liberal Arts Mathematics I

12-13-2007

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21:22:29

`q001. There are 5 questions in this set.

The preceding calculations have been done in our standard base-10 place value system. We can do similar calculations with bases other than 10.

For example, a base-4 calculation might involve the number 3 * 4^2 + 2 * 4^1 + 1 * 4^0. This number will be expressed as 321{base 4}.

What would this number be in base 10?

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RESPONSE -->

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

= 3*16+2*4+1*1

=48+8+1

= 57

confidence assessment: 3

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21:26:04

`q002. What would the number 213{base 4} be in base 10 notation?

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RESPONSE -->

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

= 2*16+1*4+3*1

= 32 +4 +3

=39

confidence assessment: 3

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21:47:30

`q003. Suppose we had a number expressed in the form 6 * 4^2 + 7 * 4^1 + 3 * 4^0. This number isn't quite in the form needs to be if it is to be expressed in base 4. This is because we have the numbers 6 and 5, which exceed 4. How would this number be expressed without using any numbers 4 or greater?

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RESPONSE -->

7*4^1

4*4^1+3*4^1

4^2+3*4^1

6=4+2

6*4^2= 4*4^2+2*4^2

4*4^2=4^3

6*4^2+7*4^1+3*4^1

=( 4*4^2+2*4^2)+(4*4^1+3*4^1) +(3*4^0)

=1*4^3+3*4^2+3*4^1+3*4^0

=1333

confidence assessment: 1

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22:03:08

`q004. What would happen to the number 1333{base 4} if we added 1?

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RESPONSE -->

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

= 1*4^3+3*4^2+3*4^1+4*4^0

4*4^0=4^1

=1*4^3+3*4^2+1*4^1+0*4^0

=1*4^3+3*4^2+4*4^1+0*4^0

4*4^1=4^2

=1*4^3+3*4^2+1*4^2+0*4^1+0*4^0

=1*4^3+4*4^2+0*4^1+0*4^0

4*4^2=4^3

=1*4^3+1*4^3+0*4^2+0*4^1+0*4^0

=2*4^3+0*4^2+0*4^1+0*4^0

=2000

confidence assessment: 2

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22:08:24

`q005. How would the decimal number 659 be expressed in base 4?

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RESPONSE -->

the 4th power is 4^4= 256

2*256=2*4^4

659+2*4^4+2*4^3+1*4^2+0*4^1+3*4^0

confidence assessment: 1

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