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

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CCSS.7.NS.A.2D

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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

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CCSS.7.NS.A.2D

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What is the first step in converting decimals to fractions?

• Writing decimals as whole numbers

• Expressing decimals as fractions

• Adding decimals together

• Multiplying decimals

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CCSS.HSA.SSE.B.4

What is the common ratio in the geometric series discussed?

• 1.0

• 0.3

• 0.03

• 0.1

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CCSS.HSA.SSE.B.4

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

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CCSS.HSA.CED.A.3

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

• 0.1S

• 0.3S

• 0.03S

• 0.9S

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CCSS.8.EE.C.8B

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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

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CCSS.7.EE.B.3

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

• One-fifth

• One-third

• One-fourth

• One-half

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CCSS.7.NS.A.2D

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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

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CCSS.6.EE.B.7

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

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CCSS.6.EE.B.7