Tamara J. answered • 04/12/13

Math Tutoring - Algebra and Calculus (all levels)

Given:

average family net worth in country A (per family): $410,000 / family

number if families in country A: 6.1 X 10^{7} families

Country A's total family net worth is, thus, equal to the product of the number of families and each family's average net worth. That is,

Country A's total family net worth = (6.1 X 10^{7})·(410,000)

First, convert 410,000 into scientific notation noting that the decimal point in this number is at the very end or after the last digit (i.e., 410,000.00). When using scientific notation, the number part must be greater than 1 but less than 10 and the power of base 10 will depend on how many places you move the decimal. In the case of 410,000.00, we have to move the decimal point 5 places to the left to yield 4.1, since we made the number part smaller we have to make the power of base 10 bigger that power of base 10 being the # of places we moved the decimal point.

410,000.00 X 10^{0}

Notice that 10^{0} = 1, this is just to illustrate what is happening to the #. So when we move the decimal of the number 5 places to the left, thus decreasing the number, we have to increase the power of base 10 by the number of places we moved the decimal. Doing so we arrive at the following:

4.1 X 10^{5}

Therefore,

total family net worth = (6.1 X 10^{7})·(4.1 X 10^{5})

(6.1 X 10^{7})·(4.1 X 10^{5}) = (6.1 · 4.1) X (10^{7} · 10^{5})

= (25.01) X (10^{7+5})

= 25.01 X 10^{12}

Since the number part is not between 1 and 10, this expression is not in scientific notation. To convert it into such notation, we move the decimal place in the 25.01 one place to the left, which decreases the number so we have to increase the power of base 10 by one. That is,

25.01 X 10^{12} = 2.501 X 10^{13}

≈ 2.5 X 10^{13}

Thus, country A's total family net worth is $2.5 X 10^{13}