Understanding Fractions and Decimals

The video tutorial explores the properties of the fraction 23/6, determining its rationality and converting it to a decimal. It explains why 23/6 is a rational number and not an irrational one. The tutorial demonstrates the long division process to convert the fraction into a repeating decimal, 3.83 repeating. It also compares 23/6 to pi, concluding that it is not an approximation for pi. Finally, the video evaluates several statements about the fraction, confirming which are true and which are false.

Which of the following is a characteristic of a rational number?

• It is always an irrational number.

• It cannot be expressed as a fraction.

• It is always a whole number.

• It can be expressed as a fraction with integers.

What is the first step in converting the fraction 23/6 into a decimal?

• Add a decimal point to 23.

• Subtract 6 from 23.

• Divide 23 by 6 using long division.

• Multiply 23 by 6.

When converting 23/6 to a decimal, what pattern emerges?

• The decimal does not repeat.

• The decimal repeats with the digit 8.

• The decimal repeats with the digit 3.

• The decimal terminates after two digits.

Which statement is true about the decimal form of 23/6?

• It is an irrational number.

• It is exactly equal to 3.83.

• It terminates after a few digits.

• It repeats with the digit 3.

What is the repeating part of the decimal representation of 23/6?

• 8

• 6

• 3

• 83

Why is 23/6 not used as an approximation for pi?

• Because it is less than pi.

• Because it is exactly equal to pi.

• Because it is greater than pi.

• Because it is not approximately 3.14.

Which fraction is commonly used as an approximation for pi?

• 23/6

• 22/7

• 21/8

• 24/7

What is the difference between 3.83 and 3.83̅?

• 3.83 is a terminating decimal, while 3.83̅ is a repeating decimal.

• Both are repeating decimals.

• 3.83̅ is a terminating decimal.

• 3.83 is a repeating decimal.

Which of the following is true about the decimal 3.83̅?

• It is approximately equal to 3.83.

• It is exactly equal to 3.83.

• It is greater than 3.83.

• It is less than 3.83.

How many of the six statements about the fraction 23/6 are true?

• One

• Two

• Four

• Three