# Calculating the GDP per person?

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• Dec 13th 2010, 10:54 AM
jebus197
Calculating the GDP per person?
A country has a population of 61 million and a Gross National Product (GNP) of 4.3 trillion euros. (You should use the UK and US versions of million and trillion.)
Which of the following gives the GNP per person in scientific notation correct to 3 s.f.?

Select one:

$7.049x10^4$
$7.05x10^19$
$7.05x10^4$
70500
$0.705x10^5$

Again any explanation would be welcome. I can get the GDP per person simply enough by using Google to divide 4.3 trillion by 61 million

I did this like this:(4.3 x (10^12)) / (6.1 x (10^5)) = 7 049 180.33. But this is where I get lost. How do you round this number off to 3 Sf and what's the right answer?

• Dec 13th 2010, 11:00 AM
Unknown008
I don't know what you did to your population because a million is 10^6, hence

$61\ million = 61\times 10^6$

When you round off to 3 sf, you keep only the first 3 digits from the left. Here are examples:
36841 to 3sf becomes : 36800
514.52 to 3 sf becomes : 515
0.01655 to 3 sf becomes : 0.0166

If you have a digit less than 5 to the right of the last number you are taking in the rounded figure, you round down. If the digit is instead equal to 5 or is larger than 5, you round up.

Can you work out the solution to your problem now? (Smile)
• Dec 13th 2010, 11:28 AM
jebus197
Dang you like asking questions don't you lol? Let's see if I get the calculation right first (4.3 x 10^12) / (6.1 x 10^7) is the same as 4.3 billion divided by 61 million. This gives an answer of 704 918.033 (seven hundred and 4 thousand nine, one, eight point zero, three, three.)

But erm... no I'm stuck again. Do I count the 0.33. I don't get it.
• Dec 13th 2010, 11:38 AM
Unknown008
It's stronger than me, sorry (Itwasntme)

But no, it's not $6.1\times10^6$ but $61\times10^6$

This would give you 70 491.8033

Now, in standard form, it will become $7.049 180 33 \times 10^x$

Can you deduce the value of x? (Just to see if you understand the concept of standard form)

Next, you take the first 3 digits, since you are rounding to 3 sf.

$7.049 \times 10^x$

I left the 4th digit to enable us to know whether to round UP or round DOWN. The digit is 9, it is larger than 5, and hence, you round UP to become:

$7.05 \times 10^x$
• Dec 13th 2010, 12:01 PM
jebus197
(4.3 x 10^12) / (6.1 x 10^7) is the same as 4.3 billion divided by 61 million. This gives an answer of 70 491.8033 Moving the decimal place 4 places to the left gives 7.04918033 x $10^4$

Taking the first 3 numbers (the first 3 significant figures reading left to right) gives 7.04 and since the next number after this is larger than 5 (in this case it's a 9) we round the last of the 3 digits up to give 7.05 x $10^4$

Did I get it right?
• Dec 13th 2010, 12:02 PM
Unknown008
This time yes (Clapping)