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Scientific Notation with a Calculator

Use technology to perform operations on numbers in scientific notation

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Practice Scientific Notation with a Calculator

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Teacher Contributed

Real World Applications – Algebra I

Topic

Dead Fish! How can we quantify all the dead fish in Norway?

Student Exploration

On New Year’s Eve of 2011, people were a little concerned with 20 tons of dead fish that had washed up to shore in Norway. Take a look at the picture on http://www.huffingtonpost.com/2012/01/03/dead-herring-in-norway_n_1181005.html?ref=green and see if you can quantify how much fish that is.

If you read the article, scientists were trying to figure out ways to clean up all of this dead fish the following day. In order to find ways to clean up this big mess, they had to quantify how much fish this could actually be. Let’s try to represent all of this dead fish using scientific notation.

Assuming that these were Atlantic herring, the approximate weight of one fish is about 1.05 kg. The article also claims that there were 40 tons of fish, but how can we represent this in terms that we can understand? How many fish is this really? If you’ve never seen 1 ton, you might not really know what that unit of measure means. 1 ton is equivalent to 2000 lbs. The nice thing about using scientific notation is that we can represent really big and really small numbers in a much easier way, rather than writing a bunch of zeros before and after decimals. In this case, we’re going to represent 2000 lbs as 2×103\begin{align*}2 \times 10^3\end{align*}. Since the article mentioned 20 tons of fish. So, that means that 20 tons×2000 lbs=40000 lbs\begin{align*}20 \ tons \times 2000 \ lbs = 40000 \ lbs\end{align*}, or 4×104 lbs\begin{align*}4 \times 10^4 \ lbs\end{align*}. If we also know that 1.05 kg is equivalent to 2.31 lbs, we can figure out how many fish we’re really talking about. If we divide 4×104 lbs\begin{align*}4 \times 10^4 \ lbs\end{align*} by 2.31 lbs, we get 1.73×104 fish\begin{align*}1.73 \times 10^4 \ fish\end{align*}! When we divide numbers with exponents, we divide 4 by 2.31, but kept the “×104\begin{align*}\times 10^4\end{align*}.” What does 1.73×104 fish\begin{align*}1.73 \times 10^4 \ fish\end{align*} look like? What does this mean?

If we were to convert back, we can just multiply it all. 1.73×10×10×10×10=17,300 fish\begin{align*}1.73 \times 10 \times 10 \times 10 \times 10 = 17,300 \ fish\end{align*}.

How accurate do you think the article was, in representing the amount of fish as “tens of thousands”? Do you think 17,300, as we have calculated, is an accurate representation? Do you think the given picture is an accurate representation? Why or why not?

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