Rewriting Fractions as Repeating Decimals Using Long Division

The video tutorial explains how to convert fractions into repeating decimals using long division. It addresses common misconceptions about rational numbers and demonstrates the process with examples like 1/3 and 7/11. The lesson emphasizes that repeating decimals are rational numbers and provides a step-by-step guide to identifying repeating patterns in long division.

What is a common misconception about repeating decimals when using a calculator?

• The calculator shows the exact repeating decimal.

• The calculator converts repeating decimals to fractions.

• The calculator cannot handle repeating decimals.

• The calculator stops and rounds the number.

Why is 2/3 considered a rational number despite being a repeating decimal?

• Because it terminates after a few digits.

• Because it is a whole number.

• Because it is an irrational number.

• Because it can be expressed as a fraction.

What is the repeating decimal representation of 1/3?

• 0.3

• 0.3 repeating

• 0.3333 repeating

• 0.3333

In the long division of 1/3, what pattern emerges?

• The remainder becomes zero.

• The remainder alternates between two numbers.

• The remainder repeats the same number.

• The remainder increases with each step.

What is the repeating decimal representation of 7/11?

• 0.63

• 0.6363 repeating

• 0.6363

• 0.63 repeating