## Reflection: Real World Applications Can You Buy the Xbox One? - Section 1: Start Up

Connection to Economics:

Part of the conversation here will be around the concept of hyperinflation. Students will be curious how so much money could be worth so little. I suggest giving very brief explanation and demonstration of how money could reach such a point. In Zimbabwe in 2006, 1.25 US Dollars = 1 Zimbabwe Dollar. However, after a series of changes in currency, the Zimbabwe dollar lost value exponentially.

Yugoslavia in the 1990's is another great example:

In the 1990's the Yugoslavian currency was the dinar. However, Yugoslavia underwent hyperinflation and kept switching dinar systems. Each switch had a catastrophic effect on the Yugoslavian capital. Anything they had saved or owned became worthless. Here is what happened:

In 1990, you would pay 10,000 old dinars to purchase  a dinar from 1990.

In 1992, you would have to pay 10 dinars from 1990 for a new dinar from 1992.

In 1993, you would have to pay 10^6 dinars from 1992 to buy a new dinar from 1993.

In 1994, you would have to pay 10^9 dinars from 1993 to buy a new dinar from 1994.

Again in 1994, you would have to pay 1.3 x 10^7 dinars from early 1994 to buy a new dinar from late 1994.

Altogether: 10^4 x 10^1  x 10^6 x 10^9 x 1.3 x 10^7 = 1.3 x 10^27

This means that 1.3 x 10^27 pre 1990 dinar = 1 dinar in 1994

So you would need to own 1,300,000,000,000,000,000,000,000,000 dinars in 1990 to be worth a single dinar in 1994. However, this number is enormous. The total world GDP is about 70,200,000,000,000. Just putting these numbers next to each other tells us that this hyperinflation would crush the world economy. If the world experiences this type of hyperinflation, the currency we had before the hyperinflation would be worth less than a dollar!

I ask them, "If the world GDP experienced this type of hyperinflation, what would the world GDP be worth after the hyperinflation took effect?"

To solve this, students might set up a ratio:

1.3 x 10^27 old dollars : 1 new dollar

7.02 x 10^14 old dollars : x new dollars

x = .00000000000054 dollars

To bring back a conversation about place value, I would ask "how many dollars is this?" Or "how many cents is this?"

Connection to Economics
Real World Applications: Connection to Economics

# Can You Buy the Xbox One?

Unit 2: Scale of the Universe: Making Sense of Numbers
Lesson 21 of 21

## Big Idea: Hyperinflation is a real world example that can be understood through exponents and scientific notation.

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### Shaun Errichiello

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