#$&* course mth151 12/3/14 at 3 If your solution to stated problem does not match the given solution, you should self-critique per instructions at
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Given Solution: 836 means 8 * 100 + 3 * 10 + 6 * 1, or 8 * 10^2 + 3 * 10^1 + 6 * 10^0. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary):ok ------------------------------------------------ Self-critique Rating:ok ********************************************* Question: `q002. How would we write 34,907 in terms of powers of 10? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: 3*10,000+4*1000+9*100+0*10+7*1 3*10^4+4*10^3+9*10^2+0*10^1+7*10^0 confidence rating #$&*:3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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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. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary):ok ------------------------------------------------ Self-critique Rating:ok ********************************************* Question: `q003. How would we write .00326 in terms of powers of 10? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: 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 confidence rating #$&*:3 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Given Solution: First we note that .1 = 1/10 = 1/10^1 = 10^-1, .01 = 1/100 = 1/10^2 = 10^-2, .001 = 1/1000 = 1/10^3 = 10^-3, etc.. Thus .00326 means 0 * .1 + 0 * .01 + 3 * .001 + 2 * .0001 + 6 * .00001 = 0 * 10^-1 + 0 * 10^-2 + 3 * 10^-3 + 2 * 10^-4 + 6 * 10^-5 . &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary):ok ------------------------------------------------ Self-critique Rating:ok ********************************************* Question: `q004. How would we add 3 * 10^2 + 5 * 10^1 + 7 * 10^0 to 5 * 10^2 + 4 * 10^1 + 2 * 10^0? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: 3*10^2=300 5*10^1=50 7*10^0=7 5*10^2=500 4*10^1=40 2*10^0=2 800+90+9=899 or we could rearrange the problem first and groupd 100s, 10s, 1s (3*10^2+5*10^2) + (5*10^1+4*10^1) + (7*10^0+2*10^0) 8*10^2 + 9*10^1 + 9*10^0 800+90+9 899 confidence rating #$&*: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. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary):ok ------------------------------------------------ Self-critique Rating:ok ********************************************* 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? YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: (4*10^2+5*10^2) +(7*10^1+6*10^1) + (8*10^0+4*10^0) 9*10^2 + 13*10^1 + 12*10^0 we could go ahead and solve like this which would be.. 900+130+12=1042 however this isn't adding by just using the single powers of 10 since we have 13*10^1 and 12*10^0 these can be broken down 13*10^1 = 1*10^2 + 3*10^1 12*10^0 = 1*10^1 + 2*10^0 the equation would now look like (9*10^2 + 1*10^2) +(3*10^1 + 1*10^1) + 2*10^0 10*10^2 + 4*10^1 + 2*10^0 10*10^2=1*10^3 1*10^3 + 4*10^1 + 2*10^0 1000+40+2 1042 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. &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& Self-critique (if necessary):ok ------------------------------------------------ Self-critique Rating:ok ********************************************* Question: `q006. Write each of the following in expanded notation using the highest possible powers of 10, and explain your reasoning for each, using only expanded notation in your explanations: 14 * 10^3 4 * 10^4 + 14 * 10^3 8 * 10^3 + 17 * 10^2 + 21 * 10^1 + 15 * 10^0 YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: 14*10^3 it is not correct to multiply a number greater than 9 by a power of 10 14*10^3 would end up being 14000 which can be broken down further by saying 1*10^4 + 4*10^3 14*10^3= 1*10^4 + 4*10^3 which would be 10000+4000 14000 4*10^4 + 14*10^3 we already know that 14*10^3 needs to be broken down further and what we can rewrite it as 4*10^4 + 1*10^4 + 4*10^3 5*10^4 + 4*10^3 which would be 50000+4000 54000 8*10^3 + 17*10^2 + 21*10^1 + 15*10^0 we can already see that three of these need to be broken down into correct powers of ten since they are more than 9 17*10^2 = 1*10^3 + 7*10^2 21*10^1 = 2*10^2 + 1*10^1 15*10^0 = 1*10^1 + 5*10^0 the problem should be rewritten as (8*10^3 + 1*10^3) + (7*10^2 + 2*10^2) + (1*10^1 + 1*10^1) + 5*10^0 9*10^3 + 9*10^2 + 2*10^1 + 5*10^0 which would be 9000+900+20+5 9925 confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ********************************************* Question: `q007. Show how we would add 8 * 10^2 + 7 * 10^0 to 4 * 10^2 + 5 * 10^0, performing all steps in expanded powers of 10. YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY Your solution: (8*10^2 + 4*10^2) + (7*10^0 + 5*10^0) 12*10^2 + 12*10^0 12*10^2 = 1*10^3 + 2*10^2 12*10^0 = 1*10^1 + 2*10^0 we can rewrite as 1*10^3 + 2*10^2 + 1*10^1 + 2*10^0 1000 + 200 + 10 + 2 1212 confidence rating #$&*: ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ------------------------------------------------ Self-critique Rating:ok " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: " Self-critique (if necessary): ------------------------------------------------ Self-critique rating: #*&!