REVised Physics Questions...?

Question

solve the following and put in scientific notation:

(can somebody give me an example of how to do this, so then maybe i can do them by myself?) thats all i ask... plz and thx

1.) 6.6 x 10^-8 divided by 3.3 x 10^-4

2.) 7.4 x 10^10 divided by 3.7 x 10^3

3.) 2.5 x 10^8 divided by 7.4 x 10^2

4.) (2.67 x 10^-3) - (9.5 x 10^-4)

5.) (1.56 x 10^-7) + (2.43 x 10^-8)

6.) (2.5 x 10^-6) x (3.0 x 10^-7)

7.) (1.2 x 10^-9) x (1.2 x 10^7)

8.) (2.3 x 10^4) x (2.0 x 10^-3)

solve for x:

17.) 3x divided by y = 6g divided by b

18.) d = t divided by x

19.) 2x^2 divided by 3 = dg

20.) 2 times the square root of x divided by c =y

Answer 1

When you multiply and divide numbers written in scientific notation, you do the numbers in front together, and handle the exponents separately.  I'll do the first- you do the rest.

6.6 x 10^-8    ÃƒÂ·  3.3 x 10^-4 = (6.6 ÷ 3.3) x (10^-8 ÷ 10^-4)

=2.0 x 10^(-8 - -4)

=2.0 x 10^(-8 + 4)

=2.0 x 10^-4

For multiplication, add the exponents.  For division, subtract the exponents (top - bottom).  Sometimes you get double negatives, so be careful to do it properly.

When you add and subtract numbers in scientific or exponential notation, you need to have the same exponent - so one of the numbers may need to be changed to match the exponent of the other.  Always change the number with the smaller exponent.  I'll do #5

1.56 x 10^-7 + 2.43 x 10^-8  (the -8 exponent is the smaller one, so I will make it into -7

2.43 x 10^-8

=something x 10^-7

since the exponent got more positive, it got bigger, so the front number will get smaller by moving the decimal once.

0.243 x 10^-7

So putting it together

1.56 x 10^-7 + 0.243 x 10^-7

=(1.56+0.243) x 10^-7

=1.803 x 10^-7 (may need to be rounded 1.80 depending on the rules forced upon you by your teacher)

17 3x/y = 6g/b  multiply both sides by y/3 to get the x alone

18 d = t/x  multiply both sides by x/d...

19 2x^2/3 = dg

First multiply both sides by 3/2, then take the square root of both sides (don't forget the ±)

20 2√x/c=y (I'm assuming the c is outside the √)

multiply both sides by c/2, then square both sides.

Good luck!

Answer 2

to do a multiplication/division problem (number 1)

(6.6 x 10^-8) / (3.3 x 10^-4 )

by rearranging the operations via algebra you can get:

(6.6/3.3) x (10^-8 / 10^-4) = 2 x (10^-8 / 10^-4)

then if you know the rules for doing algebra with exponentials, you can get straight to the answer by  doing (-8 - -4) = -4:

2 x 10^-4

which is the answer for number 1

to do the addition/subtractions problems is a bit different. first you want to change each number so that it has the same value in the exponential

(2.67 x 10^-3) - (9.5 x 10^-4) = (26.7x10^-4) - (9.5 x 10^-4)

then you can use the distributive law in reverse to take the exponential out

(26.7x10^-4) - (9.5 x 10^-4) = (26.7-9.5)x10^-4

= 17.2 x 10^-4

which is the answer for number 4.