Understanding Base Systems and Conversions

This video tutorial explains how to write base-10 numbers in different bases, focusing on the decimal system as an example of a positional-base system. It introduces the concept of different bases, such as base-5, and explains how to determine place values in these systems. The tutorial then demonstrates how to convert numbers from base-10 to other bases using the remainder method, with detailed examples converting numbers to base-2 and base-6.

What is the primary characteristic of a positional-base system?

• The number of digits is always ten.

• The position of a digit determines its value.

• It uses only even numbers.

• It is based on the number 100.

In a base-5 system, which of the following is NOT a valid digit?

• 0

• 3

• 5

• 4

What is the first step in the remainder method for converting base 10 to another base?

• Subtract the base from the number.

• Find the highest power of the base that divides the number.

• Multiply the number by the base.

• Add the base to the number.

When converting 83 from base 10 to base 2, what is the highest power of 2 used?

• 2^4

• 2^7

• 2^6

• 2^5

In the conversion of 83 to base 2, what is the remainder when 83 is divided by 64?

• 17

• 21

• 15

• 19

What is the base-2 representation of the number 83?

• 1010011

• 1110001

• 1010101

• 1101011

When converting 2,973 from base 10 to base 6, what is the highest power of 6 used?

• 6^3

• 6^4

• 6^5

• 6^2

In the conversion of 2,973 to base 6, what is the remainder when 2,973 is divided by 1,296?

• 381

• 165

• 216

• 144

What is the base-6 representation of the number 2,973?

• 21,433

• 21,344

• 20,543

• 22,134

Which step is NOT part of the remainder method for base conversion?

• Repeat until the remainder is smaller than the base.

• Multiply the remainder by the base.

• Write down the remainder.

• Divide the number by the base.