Upper Elementary Challenge Math Bases Problems

Warmup: In the number 7342, the 3 stands for 3 groups of 100 = 300. What does the 7 stand for?

In base 6, the number 543 means something very different than 543 in base 10. In 543 base 6, the number 5 means 5 groups of 36 or 180. What does the number 4 stand for?

Level 2: The base 10 number 23 is turned into base 6. Translate the base 10 number 23 into base 6.

Level 3: What are the first 12 columns for base 2?

• 0, 1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010, 1011

• 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12

• A, B, C, D, E, F, G, H, I, J, K, L

• 2,048 1,024 512 256 128 64 32 16 8 4 2 1

Genius Level: It was mentioned to a person who uses base 2 that the United States has 100 senators. The person who uses base 2 drew a picture as shown below and asked: You have only this many senators? Why did he think that the United States has a total of 4 senators?

• Because 100 in base 2 is equal to 4 in Base 10

• Because 100 in base 2 is equal to 2 in Base 10.

• Because 100 in base 2 is equal to 8 in Base 10.

• Because 100 in base 2 is equal to 1 in Base 10.

Warmup: The base 10 columns are shown below. What is the missing column? Base 10 columns: ? 10,000 1,000 100 10 1

Level 1: Fill in the missing base 5 column. Base 5 columns: 625 125 ? 5 1

Level 2: Translate the base 5 number 121 into base 10.

Level 3: How many groups of 25 are in 37?

Level 3: How many groups of 5 are in 12?