Operations with Numbers in Scientific Notation 04:55 minutes

Video Transcript

Transcript Operations with Numbers in Scientific Notation

Mr. and Mrs. Fox, who live in a village, need a new home. So they hire a real estate agent to help them. The agent only has listings of foxholes that are located in a nearby town. But the Foxes don't want to live in town because Mr. Fox thinks it will be crowded. He’s an artist, and he needs lots of space to work on his paintings, but with the addition of many baby foxes, they're practically bursting out of their current situation, so they can’t be too picky.
The real estate agent assures them that, although the new foxhole is located in town, it’s really nice and very family friendly. The real estate agent also tells them that the village where they currently live has population density of 750 foxes per mi.² and is much more crowded than the town. Mr. and Mrs. Fox are not so easily convinced of this, so they ask exactly how many foxes live in their area?

Calculating the Population

To calculate this information, we have to multiply the density by the area. First, write the population density in scientific notation, and then multiply the density times the area. To do this, we can apply the Commutative Property and rearrange the equation. Ok, that looks easier to manage. Order matters, so first calculate the product of 10² x 10³. Since the bases are the same, we can just add the exponents, so that’s equal to 10⁵. Next, multiply the coefficients together. 7.5(3.2) = 24, so you can write the equation as 24 x 10⁵, or you can write it in scientific notation as 2.4 x 10⁶, or you can write it in standard form as 2,400,000. 2,400,000 – that’s a lot of foxes.

Calculating the Population Density

To persuade the foxes to buy the foxhole that's located in the town, the real estate agent bombards them with facts and figures. He tells them the town has an area of 3.8 x 10² mi.². Although he’s sold apartments to 95 foxes so far, there's still lots of space, but they should move quickly before the best locations are sold. He tells the Foxes that to understand what a good deal the new foxhole is, they should calculate the population density of the town. Let's help the Foxes.

To do this, first write the population in scientific notation. 95 = 9.5 x 10¹ to find the polulation density, divide the population by the area. Now rewrite the equation to make it easier to solve. That's better. Remember, order matters, so first simplify the exponents. When you divide bases raised to an exponent – subtract, this means subtract the exponent in the numerator from the exponent in the denominator: 1 - 2. now, divide the coefficients. Now we can write the equation in scientific notation: 2.5 x 10⁻¹
Since the exponent is negative, to write the number in standard form, move the decimal to the left one place value. The polpulation density of the nearby town is 0.25 foxes per square mile. Convinced the town is a good alternative to the village, the fox family packs up and moves. Although they have lots of space, the real estate agent forgot to mention just one small, but very important fact...