1 Counting
One a piece of paper, “count” in base 8 over the following ranges and show the corresponding base 10 numbers to the side. You may find a number line useful for this activity.
- the base 10 numbers 0 to 24 (“0” to “30” in base 8)
- the base 10 numbers 56 to 72 (“70” to “110” in base 8)
2 Making Change 10
You need to give someone 43 cents using only dimes and pennies and using the least total number of coins possible.
- How many pennies?
- How many dimes?
3 Making Change 5
You are going to give someone 43 cents, this time only using pennies, nickels, and quarters, again using the least number of coins.
- How many pennies?
- How many nickels?
- How many quarters?
4 Making Change 3
Now imagine coins where still have pennies, but other coins are worth 3 times more than the next lowest coin. You want to give someone 43 cents.
- What are the values of the coins?
- How many of each coin type do you have?
5 Base 5 to Base 10
The number 1324 is a number in base 5. What is this number when written in base 10?
Challenging: the number 12.34 is a number in base 5, what is it in base 10?
6 Base 10 to Base 5
The number 216 is a number in base 10. What is this number when written in base 5?
7 English Language Representation
Answer the following questions using our english language representation. You do not need to show any work.
- What is two thousand added to three thousand (in words)?
- What is two thousand times three (in words)?
- What is two thousand times three thousand (in words)?
8 Scientific Notation Representation
Answer the following questions using mathematical notation. You may show work here.
- What is 2 \cdot 10^3 + 3 \cdot 10^3 ?
- What is 2 \cdot 10^3 \times 3 ?
- What is 2 \cdot 10^3 \times 3 \cdot 10^3 ?
9 Exponent rules
Show your math for computing the following without a calculator and without writing out all the zeros. (That is, use scientific notation to display the number.)
- 4 \cdot 10^{35} \times 2 \cdot10^{23}
- 4 \cdot 10^{35} \div 2 \cdot 10^{23}
10 Scientific Notation
The number 23.12 \cdot 10^3 is written entirely in base 5.
- What is this number when represented in base 10.
- Be sure some of your reasoning is visible on the page.
11 Strogatz Readings
Read Sections 1 (From Fish to Infinity) and 6 (Location, Location, Location) of The Joy of X in the link below. Answer the following questions in complete sentences.
- What conveniences does our number system provide?
- Why is the location of a number important?
If the library link doesn’t work here are two dropbox links: