Understanding Place Value
Consider the following number system (on the left in the table). Contrast this with the Base
5 Alphabet system we have been using (on the right in table).
• What characteristics are similar? What characteristics are different?
• What symbols would represent the basic place value blocks (i.e., flats, longs, units, etc.)
in each system?
• How many symbols will the system on the left eventually need?
• How many will the one on the right need?
• Is the system on the left a true place value system? Why or why not?
A
AA
AAA
AAAA
B
BA
B AA
B AAA
B AAAA
BB
BB A
BB AA
BB AAA
BB AAAA
BBB
BBB A
BBB AA
BBB AAA
BBB AAAA
BBBB
BBBB A
BBBB AA
BBBB AAA
BBBB AAAA
C
A
B
C
D
A0
AA
AB
AC
AD
B0
BA
BB
BC
BD
C0
CA
CB
CC
CD
D0
DA
DB
DC
DD
A00
Questions to Consider
Looking at Bases Other than 10 or 5
If I told you that a number system were base 12 –
• How many distinct symbols would be needed? Why?
• What would be the value of the largest symbol? Why?
• What would the numbers in the 3rd place value represent? Why?
Understanding Place Value
We have thrown around words like “place-value” and “base”. Write as clear a description of
what these things mean as possible. You don’t need to sum it up all in one sentence. You
could, instead, discuss the key elements that make up these ideas.