Understanding 0.3 Repeating as One-Third

The video tutorial demonstrates that 0.3 repeating is equal to one-third by expressing it as an infinite sum and using geometric series. It explains converting decimals to fractions and powers of one-tenth, and employs the multiply, shift, and subtract method to solve the equation, ultimately proving the equivalence of 0.3 repeating and one-third.

What is another way to express 0.3 repeating?

• 0.3 with a bar over the 0

• 0.333

• 0.33

• 0.3 with a bar over the 3

How is 0.3 repeating initially expressed in the video?

• As a whole number

• As an infinite sum

• As a fraction

• As a finite sum

What is the first step in converting decimals to fractions?

• Writing decimals as whole numbers

• Expressing decimals as fractions

• Adding decimals together

• Multiplying decimals

What is the common ratio in the geometric series discussed?

• 1.0

• 0.3

• 0.03

• 0.1

What method is used to determine the sum of the geometric series?

• Division and multiplication

• Multiply, shift, and subtract

• Addition and subtraction

• Integration and differentiation

What is the result of multiplying the first equation by the common ratio?

• 0.1S

• 0.3S

• 0.03S

• 0.9S

What happens to the terms when the second equation is subtracted from the first?

• All terms remain

• Only the last term remains

• All terms cancel out

• Only the first term remains

What is the final value of S after solving the equation?

• One-fifth

• One-third

• One-fourth

• One-half

What does the final result demonstrate about 0.3 repeating?

• It is equal to one-third

• It is equal to one-fifth

• It is equal to one-half

• It is equal to one-fourth

What is the purpose of dividing both sides of the equation by 0.9?

• To eliminate decimals

• To find the value of S

• To simplify the equation

• To convert to fractions