6.3 Non-terminating decimals

Repeating decimals – Rational numbers, in simplest form, whose denominator contains factors other than 2 and 5 are repeating decimals. The repeating block is call the repetend

Convert to decimal:

Find as a decimal.

What do you think equals as a decimal?

All rational numbers can be represented as either a terminating or repeating decimal

However, some of the repeating can be “challenging”

Use a calculator to assist with changing the fraction to a repeating decimal

Converting rationals as Repeating Decimals to Fractions

Check: equals what decimal??

Example:

What does equal?

What about ??

Ordering Repeating Decimals

Arrange in descending order:

Density Property of Rational Numbers in Decimal form

Between any two rational numbers there are infinitely many rational numbers.

Find a decimal between

Find a decimal half the way between and 1.1