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So, let’s count in base 6 • Digits allowed: 0, 1, 2, 3, 4, 5 • There is no such thing as 6 • When we read a number such as 213 6 , we don’t say “two hundred thirteen.” We say instead “two-one-three, base 6.”

So, let’s count in base 6

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So, let’s count in base 6. Digits allowed: 0, 1, 2, 3, 4, 5 There is no such thing as 6 When we read a number such as 213 6 , we don’t say “two hundred thirteen.” We say instead “two-one-three, base 6.”. Count! In base 6. 1, 2, 3, 4, 5, - PowerPoint PPT Presentation

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Page 1: So, let’s count in base 6

So, let’s count in base 6

• Digits allowed: 0, 1, 2, 3, 4, 5• There is no such thing as 6• When we read a number such as 2136,

we don’t say “two hundred thirteen.” We say instead “two-one-three, base 6.”

Page 2: So, let’s count in base 6

Count! In base 6• 1, 2, 3, 4, 5,• 10, 11, 12, 13, 14, 15,• 20, 21, 22, 23, 24, 25,• 30, 31, 32, 33, 34, 35,• 40, 41, 42, 43, 44, 45,• 50, 51, 52, 53, 54, 55,• 100, 101, 102, 103, 104, 105, 110

Page 3: So, let’s count in base 6

Compare base 6 to base 10

• Digits 0 - 9• New place value after 9

in a given place• Each place is 10 times

as valuable as the one to the right

• 243 = 2 • (10 • 10) + 4 • 10 + 3 • 1

• Digits 0 - 5• New place value after 5

in a given place• Each place is 6 times

as valuable as the one to the right.

• 243base 6 = 2 • (6 • 6) + 4 • 6 + 3 • 1or 99 in base 10

Page 4: So, let’s count in base 6

In base 6, write the first five place values.

_____ _____ _____ _____ _____1296 216 36 6 1 64 63 62 61 60

cube flat long unit

Page 5: So, let’s count in base 6

Compare Base 6 to Base 10

312 =

3 • 100 + 1 • 10 + 2 • 1

312base 6 =

3 • 36 + 1 • 6 + 2 • 1 =116 in base 10

Page 6: So, let’s count in base 6

How to change from Base 10 to Base 6.

• Suppose your number is 325 in base 10.• We need to know what our place values will

look like.• _____ _____ _____ _____

6•6•6 6•6 6 1

Now, 6•6•6 = 216. 216 = 1000 in base 6.

Page 7: So, let’s count in base 6

Base 10 to Base 6

• ___1__ _____ _____ _____ 6•6•6 6•6 6 1

• Now, 325 - 216 = 109. Since 109 is less than 216, we move to the next smaller place value: 6 • 6 = 36.

• 109 - 36 = 73. Since 73 is greater than 36, we stay with the same place value.

Page 8: So, let’s count in base 6

Base 10 to Base 6

• __1___ ___3__ _____ _____6•6•6 6•6 6 1

• We had 109: 109 - 36 - 36 - 36 = 1. We subtracted 36 three times, so 3 goes in the 36ths place.

• We have 1 left. 1 is less than 6, so there are no 6s. Just a 1 in the units place.

Page 9: So, let’s count in base 6

Base 10 to Base 6

• __1___ ___3__ __0___ __1___6•6•6 6•6 6 1

• Check: 1 • 216 + 3 • 36 + 1 • 1 = 325

Page 10: So, let’s count in base 6

Count! In base 16 1, 2, 3, 4, 5, 6, 7, 8, 9, a,

b, c, d, e, f

10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 1a, 1b, 1c, 1d, 1e, 1f

20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 2a, 2b, 2c, 2d, 2e, 2f

Page 11: So, let’s count in base 6

In base 16, write the first five place values.

______ _____ _____ _____ _____ 65,536 4096 256 16 1 164 163 162 161 160

Page 12: So, let’s count in base 6

In base 5, write the first five place values.

_____ _____ _____ _____ _____ 625 125 25 5 1 54 53 52 51 50

cube flat long unit

Page 13: So, let’s count in base 6

In base 2, write the first five place values.

_____ _____ _____ _____ _____ 16 8 4 2 1 24 23 22 21 20

Page 14: So, let’s count in base 6

Let’s Look at Adding and Subtracting in Alphabitia

• If we use the Alphabitian numerals, do our rules for addition and subtraction hold true?

• Warm up: tell me one more and one less of each• AB• CAD• B0B• AA0• DD• Use manipulatives or drawings to explain your answers.

Page 15: So, let’s count in base 6

Let’s add in Alphabitia BCD

+ DB

BCD is DB is BCD + DB is

Page 16: So, let’s count in base 6

You try:

B0B+ABC

Use the manipulatives or draw pictures to help explain your answer.

Page 17: So, let’s count in base 6

Let’s subtract CBD

- ADC =

CBD is ADC is CBD - ADC is

Page 18: So, let’s count in base 6

You Try…

D00-B0B

B0A-BD

Page 19: So, let’s count in base 6

You try: Use manipulatives or drawings to explain

BBC - A0C

A0A0D - BCA

Page 20: So, let’s count in base 6

First Exam Scheduled• Wednesday, February 13th• Cover material from: • Textbook: 1.2, 1.3, 1.4, 1.7, 2.3, 3.1, 3.2• Explorations: 1.1, 1.4, 1.7, 2.8, 2.9, 3.1, 3.6• Notes/Problems from class• Sample test questions on line next Monday.

Page 21: So, let’s count in base 6

Homework for Monday• Exploration 2.9:

Part 1: for Base 6, 2, and 16, do #2; Part 3: #2, 3; Part 4: #1, 2, 4.

• Read Textbook pp. 109-118 • Do Textbook Problems pp. 120 - 121:

15b,c, 16b,d, 17a,i, 18b,f, 19, 29