Understanding Repeating Decimals and Geometric Series

The video tutorial explains how to represent the repeating decimal 0.4008 as an infinite geometric series. It demonstrates the process of identifying the common ratio and using the formula for the sum of an infinite geometric series to express the repeating decimal as a fraction. The tutorial also covers simplifying the fraction to its simplest form.

What is the repeating decimal discussed in the video?

• 0.4800

• 0.408

• 0.8400

• 0.4008

How is the repeating decimal 0.4008 expressed as an infinite series?

• By adding 0.4008 repeatedly

• By adding 0.00004008 repeatedly

• By adding 0.4008 and shifting the decimal

• By adding 0.4008 and multiplying by 10

What is the common ratio used in the geometric series representation of 0.4008?

• 0.1

• 0.01

• 0.0001

• 0.001

What is the significance of the common ratio in a geometric series?

• It determines the last term

• It determines the pattern of the series

• It determines the sum of the series

• It determines the first term

What is the formula for the sum of an infinite geometric series?

• a / (1 + r)

• a * (1 + r)

• a * (1 - r)

• a / (1 - r)

What is the fraction representation of the repeating decimal 0.4008?

• 4008/1000

• 4008/10000

• 4008/9999

• 4008/999

What is the simplified form of the fraction 4008/9999?

• 1336/3333

• 1336/3330

• 1333/3336

• 1330/3336

What mathematical concept allows the repeating decimal to be expressed as a fraction?

• Fibonacci series

• Harmonic series

• Geometric series

• Arithmetic series

What operation is performed to simplify the fraction 4008/9999?

• Division by 2

• Division by 4

• Division by 3

• Division by 5

What is the purpose of expressing a repeating decimal as a geometric series?

• To find its decimal expansion

• To find its square root

• To express it as a whole number

• To express it as a fraction