Math Is Fun Forum

morik

Member

Registered: 2005-11-23

Posts: 16

More questions from me...

A few more bugging questions from my maths mod....
It isn't so much the answers (I can do them on a calculator easily), I have to show the method of working them.
Answers and/or method of working out for any of these would be much appreciated

1. Express 5.678 x 10³ as a whole number i.e without the index.

2. Calculate 2 x 10³ x 3 x 10³. Express the answer both as a whole number and by using indices.

3. What is 250/10 in hexadecimal?

4. A computer is advertised for sale at £5000 plus VAT at 17.5%. What is the total price payable?

5. A computer monitor is advertised as "25% off, price now £187.50". What was the price before the discount?

6. A lottery win of £100,000 is to be divided amongst 4 players who have won the following shares in the syndicate. Adam 5; Brenda 8; Charlie 3; Diana 4. How much does each player get?

7. An Ordinance Survey map is printed at a scale of 1:25000. A walker measures a distance between two points on the map and finds that it is 225mm. What is the actual distance across the ground? Give your answer using a suitable unit of measure.

Last edited by morik (2005-11-24 03:56:30)

irspow

Guest

Re: More questions from me...

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.

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: More questions from me...

Very good, irspow. Feel free to join up as a member any time you want, as it will let you upload images, use a signature and avatar, stop other people from stealing your name and post in all the boards, including the secret one that you can't even see. I hung around as a guest for a while, but being a member is much more fun. [Edit: People from everywhere will flock to admire my skills of persuasion. Well, maybe they won't. But they should. ]

Back to morik, in question 3, hexadecimal notation is just base 16. The numbers count 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F, 10 and so on.

For the actual calculation, it is simpler to leave it in base 10. 250/10 is obviously 25.

To convert 25 into base 16, just split it into powers of 16. 25 has one 16 in it, so the 16^1 digit is 1. Left over is 9, so the units digit is 9. Therefore, 25(dec) = 19(hex)

Fun Fact: 31(oct) = 25(dec)
Hallowe'en = Christmas!

---

Why did the vector cross the road?
It wanted to be normal.