Decimal Representations of Fractions

This video tutorial covers the conversion of rational numbers to decimals using long division. It explains the difference between terminating and repeating decimals, provides examples of decimal representation, and includes exercises for practice. The tutorial also discusses the patterns in repeating decimals and applies these concepts to real-world scenarios, such as splitting costs among friends.

What are the two types of decimal representations for rational numbers?

• Positive and negative

• Finite and infinite

• Terminating and repeating

• Whole and fractional

Which of the following fractions has a terminating decimal representation?

• 1/3

• 1/4

• 1/9

• 1/7

Which of the following fractions will have a repeating decimal representation?

• 1/2

• 1/5

• 1/6

• 1/10

What is the decimal representation of 3/4 using long division?

• 0.666...

• 0.333...

• 0.75

• 0.5

What is the decimal representation of 1/7 using long division?

• 0.142857...

• 0.2

• 0.125

• 0.333...

How can you determine if a decimal will repeat or terminate?

• By checking if the numerator is even

• By checking if the denominator has only 2 and 5 as prime factors

• By checking if the numerator is greater than the denominator

• By checking if the denominator is a prime number

If a fraction's denominator is 7, how many digits will its repeating decimal cycle have?

• 6

• 7

• 5

• 4

What happens to the decimal representation if the remainder in the division algorithm is zero?

• The decimal becomes negative

• The decimal becomes a whole number

• The decimal repeats

• The decimal terminates

In the context of splitting costs, if 5 people share $8 equally, how much does each person pay?

• $1.60

• $1.50

• $1.75

• $1.80

If two friends drop out of a trip, leaving 3 people to share $8, how much does each person pay?

• $2.65

• $2.68

• $2.66

• $2.67