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word math problem

A family refers to a group or more people related by birth, marriage, or adoption who reside together. In 2000, in country A, the average family net worth was 460,000, and there were about 6.9x10^7 families. Calculate the total net worth in the country A in 2000

Country A’s total family net worth is  blank       -dollars.

(use scientific notation. Use the multiplication symbol in the math palette as needed. Round to the nearest tenth as needed.)

Help me please

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2 Answers

Remember your scientific notation?

107 = 10,000,000  so 6.9 * 10,000,000 =69,000,000 families.

now we have x(amount of net worth per family) divided by 69,000,000 we get the average 460,000

so x = 31740000000000 dollars

This is a question testing you on your knowledge of scientific notation. In science you typically deal with really really big numbers or really really small numbers. 

For example, if you are talking about the number of people who live in a country... there might be 69,000,000. The whole idea of scientific notation is to make a shortcut for writing numbers with a lot of zeros in them. If we were to write 69,000,000 in scientific notation we would simply move the decimal directly to the right of the whole number 6.9 then we would count how many times we moved the decimal point and which becomes our exponent when multiplying by 10... x 10. So now we know what they mean when they say 6.9 x 107... it means 69,000,000.

Now there are two ways to solve this problem. I'll show you the long way which you may understand a little easier than the shortcut first. 

First, remove scientific notation (write the number out) and rewrite the problem and see if it makes sense: 

A family refers to a group or more people related by birth, marriage, or adoption who reside together. In 2000, in country A, the average family net worth was 460,000, and there were about 69,000,000 families. Calculate the total net worth in the country A in 2000

Now it should make a bit more sense. Each family makes about 460,000 so how much do 69,000,000 families make? Just multiply the numbers out. $31,740,000,000,000 See what I mean about big numbers? Lets rewrite that in scientific notation by moving the decimal point directly to the right of the 3 and counting how many place values we moved the decimal. 31,740,000,000,000 = 3.174x1013


Now I promised you the shortcut way:

Write both numbers which you intend to multiply in scientific notation form:

4.6x10x 6.9x107 

Multiply the front ends together, don't worry about the x10 parts

4.6 x 6.9 = 31.74

Now we ADD the exponents together when writing the scientific notation

31.74x105+7 = 31.74x1012

But wait! That doesn't match our original answer... do you see why? The decimal point is not directly to the right of the 3. If we move the decimal point one more space over we will have to bump the exponent up one value. Let's see if our answers match after trying that.

3.174x1013 

Look at that! It works. Hope that helps :) 

 

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