Understanding Base Conversion

The video tutorial explains how to determine the base in which the number 333 is equal to 171 in base 10. It starts by reviewing base 10 place values and then explores different bases, starting with base 5, which results in 93 in base 10. The tutorial then tries base 7, successfully converting 333 to 171 in base 10, concluding that the correct base is 7.

What is the place value of the digit '7' in the number 171 in base 10?

• One's place

• Ten's place

• Hundred's place

• Thousand's place

How can 171 in base 10 be expressed in expanded form?

• 1 * 100 + 7 * 10 + 1 * 1

• 1 * 10 + 7 * 10 + 1 * 1

• 1 * 1000 + 7 * 100 + 1 * 10

• 1 * 10 + 7 * 1 + 1 * 0

Why must the base for 333 be smaller than 10?

• Because the leftmost digit in 333 is larger than in 171

• Because 333 is a smaller number than 171

• Because the leftmost digit in 333 is smaller than in 171

• Because 333 is a larger number than 171

What is the result of converting 333 in base 5 to base 10?

• 171

• 93

• 49

• 333

What is the place value of the rightmost digit in base 5?

• 5 cubed

• 5 to the zero

• 5 to the first

• 5 squared

What is the result of converting 333 in base 7 to base 10?

• 171

• 333

• 49

• 93

What is the place value of the middle digit in base 7?

• 7 to the zero

• 7 to the first

• 7 cubed

• 7 squared

What is the value of 3 * 49 in base 10?

• 21

• 3

• 49

• 147

What is the correct base for 333 to equal 171 in base 10?

• Base 5

• Base 6

• Base 8

• Base 7

What is the value of 3 * 7 in base 10?

• 49

• 3

• 21

• 147