How to Write Terminating and Repeating Decimals as Fractions

This video tutorial covers the concepts of terminating and repeating decimals, explaining how to convert them into fractions. It begins with an introduction to the lesson objectives, followed by a detailed explanation of terminating decimals and their conversion to fractions. The video then explores repeating decimals, introducing the vinculum notation and demonstrating how to express these decimals as fractions. Mathematical proofs are provided to validate the patterns observed in repeating decimals. The tutorial concludes with complex examples and a summary of the key points discussed.

What is the main objective of the lesson on terminating and repeating decimals?

• To practice multiplication of decimals

• To explore the history of decimals

• To understand how to convert decimals into fractions

• To learn how to add and subtract decimals

Which of the following is a characteristic of a terminating decimal?

• It always ends with a zero

• It can be written as a fraction

• It has an infinite number of digits

• It cannot be simplified

How would you express 0.35 as a fraction in its simplest form?

• 3/5

• 1/2

• 7/20

• 35/100

What is a repeating decimal?

• A decimal with a repeating pattern of digits

• A decimal that ends after a few digits

• A decimal that cannot be converted into a fraction

• A decimal that is always greater than 1

What is the vinculum in the context of repeating decimals?

• A type of decimal that terminates

• A method to simplify fractions

• A symbol indicating a repeating pattern

• A mathematical operation

How can you express 0.5 repeating as a fraction?

• 5/10

• 1/3

• 5/9

• 1/2

What is the first step in converting a repeating decimal to a fraction using algebra?

• Multiply the decimal by 10 or 100

• Add a whole number to the decimal

• Divide the decimal by 2

• Subtract the decimal from 1

If a decimal has two repeating digits, what should you multiply by to start the conversion process?

• 10

• 100

• 5

• 1000

How would you express 3.4 repeating as a mixed number?

• 3 and 4/9

• 3 and 1/2

• 3 and 2/3

• 3 and 5/6

What is the fraction form of 11.090909 repeating?

• 11 and 1/12

• 11 and 1/9

• 11 and 1/11

• 11 and 1/10