# Homework Help: Unit Prefixes

1. Aug 18, 2009

### bumblebeeliz

1. The problem statement, all variables and given/known data

(1.4 x 106 m/s)2 - (3.5x104 m/s)2

2. Relevant equations

3. The attempt at a solution

We square them and then do we subtract them? Which would equal to:

(1.4 x 106 m/s)2 - (3.5x104 m/s)2
(1.96 x 1012 m2/s2) - (1.22x108 m2/s2)
(1.95878 x 104 m2/s2 )

Is this correct?

2. Aug 18, 2009

### Staff: Mentor

OK, except for a decimal mistake in one of your numbers.
No. How did you get this? (What's 1012 - 108? To subtract, rewrite the numbers so they have the same exponent.)

3. Aug 18, 2009

### bumblebeeliz

I thought we could subtract the exponent. I am not sure how to re-write the numbers and make them have the same exponent.

4. Aug 18, 2009

### Staff: Mentor

Not when you are subtracting the numbers. Look what happens if you do:
102 - 101 ≠ 101
(100 - 10 = 90, not 10!)

102 - 101 = 10x101 - 1x101 = (10-1)x101 = 90

1000 = 1x103 = 10x102 = 100x101

5. Aug 18, 2009

### bumblebeeliz

I see what you mean, but I am really not sure how to apply it in my situation. I basically factor it?

But for some reason it is really not clicking how I am supposed to apply it.

I looked at some resources online and somebody suggested to divide them to allow the subtraction:

1.4 x 1012 / 3.5 x 108 = 0.4 x 104

Last edited: Aug 18, 2009
6. Aug 18, 2009

### Staff: Mentor

Not sure what you mean by "factoring". Here's the trick. If you reduce the exponent by 1, then you must increase the number by a factor of 10 (since this is base 10). Which just means move the decimal point to the right by 1.

1.96 x 1012 = 19.6 x 1011 = 196 x 1010 = 1960 x 109

And so on...

When you divide two numbers, then you can just subtract the exponents. But you're subtracting two numbers.

Note: I'm taking your first expression, where you subtract the two numbers, as given. So this is really a math question, not a physics question, since you haven't described the problem you're trying to solve. If you're not sure whether you should be subtracting or dividing, then describe the complete problem you're trying to solve.

7. Aug 18, 2009

### bumblebeeliz

Ah! Its all about the tricks for beginners. Much better :)

= 19600 x 108 - 1.22x108
= 19598.7 x 108

or

= 1.959878 x 1012

8. Aug 18, 2009

### bumblebeeliz

One more question:

1.95978 x 1012/ 0.02

97.989 x 1012 /2

48.969 x 1011

4.9 x 1012

Is this correct? So when you divide, the exponent drops?

9. Aug 18, 2009

### Staff: Mentor

Careful. That "/2" shouldn't be there.

1.95978 x 1012/ 0.02 = (1.95978/ 0.02) x 1012 = 97.989 x 1012

Note that the denominator didn't have an exponent:
0.02 = 0.02 x 100

10. Aug 18, 2009

### bumblebeeliz

Sorry, I meant this below: (scratch the first line)

97.989 x 1012 /2

48.969 x 1011

4.9 x 1012

(next time ill post the whole problem..sorry)

11. Aug 18, 2009

### Staff: Mentor

No. The exponent doesn't change; just divide the numbers:
97.989 x 1012 /2 = (97.989/2) x 1012 = 48.969 x 1012

12. Aug 18, 2009