Tip:
Highlight text to annotate it
X
This video is going to be about solving a word problem using scientific notation.
So here's the problem.
I'm going to start out with a basic fact:
one pound of the cold
is worth approximately
2.3 times 10 to the fourth
dollars.
And let's say
that I've got $3 billion and
I want to convert that into gold,
and I'm curious how much it's going to weigh.
So the first step is going to be to take that three billion
and convert it
into scientific notation. I'm gonna do that in two steps.
First I'll write the three billion
with all its zeros.
So that's going to be
3 followed by nine zeros.
And then, of course, that means that in scientific notation
it would be 3
times
10 to the ninth.
And I'll add a dollar sign.
So
I want to convert that into gold and I want to know how many pounds of gold.
So it's going to be
x pounds,
and those x pounds are going to be worth
3
times
10 to the ninth.
So what have I got here?
There's two equations.
In both equations I've got pound on one side
and dollars on the other side,
and if I take
any equation
and take the
left side of the equation and call a numerator and take the right side and call
that a denominator,
that fraction the results
is going to be equal to one because I've got the same thing
in the numerator int denominator. So let's make two fractions.
The first fraction
is going to be
one pound
over
2.3
times
10 to the fourth,
That's the fact I started with.
And the second fraction
is also going to have pounds in the numerator.
That's going to be x pounds,
and that's going to be over
the dollar value,
which is 3 times
10 to the ninth.
Now look what I have here.
Both of these factions, which I've set equal to each other, have
pounds in the numerators and dollars in the denominators. In other words,
I'm using the same
units for the numerators and the same units for the denominators,
and now I want to find out what x is.
So what I can do is multiply both sides by 3 times 10 to the ninth.
So I'm going to have 1 pounds
times
3
times 10 to the ninth, that's dollars,
over
2.3
times 10 to the fourth dollars.
And the right side of the equation...
well that 3 times 10 to the ninth would have just have canceled, so that's
x pounds.
x pounds.
Now this looks kind of clumsy,
but it's gonna cancel out very nicely.
You notice I have a dollar sign in the numerator and the denominator
of this
left-hand fraction.
Well, I'm gonna divide both of these
numbers, the numerator and the denomiantor, by 'dollars',
which means I'll cancel out my dollars.
I've got a pound sign on the left side of the equation and on the right side of the equation,
so I'm going to divide both sides the equation
by the pound sign.
So I can cancel out the pound signs.
And now what I've got... I'm just gonna rewrite this...
is the x all by itself,
and x
equals...
let's see...
3
times
10 to the ninth
over
2.3
times
10 to the fourth. I got rid of all my units.
And what I want to do is take this fraction and convert it
into
a single number in scientific notation, rather than a fraction.
So that means I'm going to take the 3
and divide it by 2.3. So let's do that down here.
3...
I'm sorry... 2.3
divided into 3...
I'll move the decimal point over and make that the same has 23
divided into 30.
23 into 30 goes one time.
One times 23 is 23.
I subtract and get a 7. I bring down a zero.
23 into 70
goes 3 times,
and 3 times 23 is 69. I've got a remainder of 1. I could keep
doing this,
but since I was doing with an approximate value of gold,
I think I'll stop here and call that "1.3".
So now I can take the fraction
and turn that into
1.3
times
some powerful of 10.
And let's see... the power of 10 will be...
I've got 10 to the ninth in the numerator,
10 to the fourth in the denominator,
so I'll subtract that 4
from the 9
and get 10 to the fifth.
So
the weight of my gold, my three billion dollars worth of gold,
is going to be 1.3 times 10 to the fifth,
and the unit I was dealing with is pounds.
is packed
So let's just convert that into a number of that we're more used to seeing,
the standard form.
So I'll take the 1, I've got 1.3, I'll take the 1 and
after the 1 I would want 5 decimal places. So the first place will be taken
up with the 3,
and then I need
4 more places.
I'll put those in as zeros.
So my three billion dollars
is going to weigh
130 thousand pounds.
Let's just go over the steps one more time.
When you're dealing with word problems like this,
you've got to start out with some basic conversion fact. In other words,
you've got two different kinds of units... I've got pounds of gold
and I've got dollars, and you have to know how they equate to each other.
So we can start out with that fact,
that one pound of gold
is 2.3 times 10 to the fourth dollars.
That's my first equation. My second equation is going to
involve an x, the thing I'm looking for.
And
what I know about it.
So what I knew
about my problem was that I have three billion dollars.
So I converted the three billion dollars into scientific notation,
and I said that
x pounds equaled that amount.
Then I set up two fractions.
Both of the fractions were equal to 1,
because I used
the left side of my first equation
over the right side of that equation,
and that was equal to the left side of the second equation over the right side
of the second equation.
Now I've got
2 fractions, both of them equal to one,
and I've made them equal to each other,
and now I'm just solving for the one unknown I have, which is x.
It looks a little sloppy because I've got all these units, but the units cancel out.
I end up with a value for x
and then
I take that, if it's in a fraction form,
and a simplify it into
scientific notation form, without a fraction, and then if I want
I convert that into standard form.
So that's basically the process.
Take care, I'll see you next time.