1. This is nothing more than scientific notation.  You understand that 5.678 X 10^3 is exactly the
    same as 5.678 X 1000 = 5678.  Whenever you see this type of notation with 10 raised to some
    power simply move the decimal the same amount of places as the exponent.  As above, no
    computation is needed at all simply move the decimal over 3 places and you will get the
    correct answer.  Note that when the exponent is negative that you will have to move the
    in the opposite direction.  So that 5.678 X 10^-3 = .005678.

2. If you understood the previous explanation you will easily see that your question simply asks
    what 2000 X 3000 equals.  So (2 X 10^3)(3 X 10^3) = 600000.  More importantly 600000 =
    6 X 10^6.  When you are given a problem of multiplication using scientific notation all you
    to do is multiply the whole numbers and add the exponents together.  2 X 3 = 6.  Just add
    those exponents and you have 6 X 10^6.  Division is similar except that you subract the
    denominator exponent from the numerator exponent.  So that 10 X 10^10 / 5 X 10^8 =
    2 X 10^2.

3. I'm rusty on converting base systems, but it is based on powers of the base. Each succeeding
    column of numbers represent another power of the base. We ordinarily use base 10.  You can
    find out precisely how to do this on any decent computer language website.

4. Whenever you are dealing with percentages, keep in mind that you are talking about a ratio.
    100 X % will always equal 1.  Dividing a percent by 100 will give you the decimal or fraction
    that you are really dealing with.  In your case you are adding 17.5%.  This equals .175.  To
    add this amount you can multiply .175(5000) and add it to 5000, but it is simpler to multiply
    1.175(5000) = 5875.  The reason for placing a 1 before the decimal is because the 1
    represents the original 100% of 5000.

5. This is beginning algebra.  You don't know the original cost and we will call this amount x.  You
    are told that it now costs 187.5 after 25% has been taken off.  The trick is in realizing that it is
    also 75% of the original cost. 

    .75x = 187.5,   x = 187.5 / .75 = 250

6. To solve this problem you need to know how much each share is worth.  You find this by
    dividing the total amount by the total number of shares and then multiplying this amount
    times each persons amount of shares.

    100000 / (8+3+4+5) = 5000    each share is worth 5000 so:
    Adam has 5 shares times 5000 = 25000
    Brenda = 40000
    Charlie = 15000
    Diana = 20000

7. 1:25000 is another ratio.  It means that every 1 unit on the map represents 25000 units in the
    real world.  It is easier to write it as the fraction 1/25000.  Our unknown is the real distance 
    versus the map distance.  We will let the real distance equal x.

     1(map distance)/25000(real distance) = 225mm(map distance)/x(real distance)

     1/25000 = 225/x ,  x = 225(25000) = 5625000.  That's a large number because we are using
     mm
     Dividing by 1000000 will give you km.  In this case 5.625 km.