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Jacob's Algebra I-Help with C8-Exponents


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Sorry in advance if this is hard to read...I'm not sure how to convert the signs needed into this format. :)

 

My younger daughter is currently working through Jacob's Algebra I and is doing very well with this text. C8 covers exponents and we are fine except for one part of it. This text has her converting something like 81 x 10 (- 20) (the part in parentheses is meant to show that the 10 is to the power of negative 20) into scientific notation. She understands that she needs for the whole number in scientific notation to be between 1-9 and can convert this to 8. 1 x 10 (-19). It is this last part that has her confused. She knows that she just moved the decimal point one place to the left to go from 81 to 8. 1, but feels that the answer should be (-21) and not (-19) since she moved to the left. She wants to add the exponents (-20 and -1).

 

I have several other texts around the house and have looked through them, including an Algebra II book, but none of these seem to cover this. The conventional turn this number into scientific notation, both positive and negative, is covered along with the reversal (turn this scientific notation into the number it represents) but nothing on how to take something already set up to a power of 10 but that is not in scientific notation and put it into scientific notation.

 

Here is another one:

 

Set 2: 7d

 

Find each of the following powers. Express each answer in scientific notation.

 

d) (5 x 10 raised to 3) raised to negative 1

 

Her work is solid until the end. She raised 5 to the negative 1 and got 1/5. She raised 10 to the 3 to the negative 1 and got 10 to the negative 3. She turned 1/5 into a decimal of 0.2 and set this as x 10 to the negative 3. She knows now to move it into scientific notation, so she moved the 0.2 to 2 by moving the decimal point to the right one place, but this is where it falls apart for her. She thinks of this move to the right as a positive 1 so when adding exponents wants to add 1 + the -3 and getting an answer of 2 x 10 to the power of negative 2 and she should get negative 4. 

 

Answer 2 x 10 (-4)

 

How can I help her with this? 

 

I've tried showing her that if she converted 0.2 x 10 (-3) into a number that she would need for it to be written as 2 x 10 (-4) in order for those two numbers to be the same. 2 x 10 (-2) won't match this. She sees this, but she's frustrated with why moving to the left doesn't give her a negative and to the right doesn't give a positive in these problems. I'm wondering if there is another way to look at this that I'm unaware of...something to help it make sense to her. 

 

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Okay, she's not getting what the negative exponent means.

 

81 = 8.1 x 10^1

So, in your first example, 81 x 10^-20 = (8.1 x 10^1) x (10^-20) = 8.1 x (10^1 x 10^-20) --> so now she can add the exponents and get 8.1 x (10^-19).

The negative exponent means she has a small number. So, when she has something like 81, she's making that small number slightly bigger, thus making the exponent closer to 0.

 

In your later example, 0.2 = 2 x 10^-1 (dividing by 10). She needs to go back to what that negative exponent actually means.

 

That chapter in Jacobs is our next one - and we'll start it tomorrow or next week, so I can't be more helpful with the actual text (yet).

 

(I don't know if this will help or hurt, but Khan Academy has a bunch of videos on Scientific Notation. The first video I linked gets to the negative exponents around 11 1/2 minutes in.)

Edited by RootAnn
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