Classify the following decimal fractions as terminating and non-terminating recurring decimals.

(1) 0.777… (2) 0.777

(3) 4.7182 (4)

(5) 9.165165 (6)

(7) 0.52888 (8)

(9)

(1) 0.777…

This number is non-terminating. Because the last digit 7 is repeating.

(2) 0.777

This number is terminating, because the number ends with 7, but not extending again three sevens.

(3) 4.7182

This is terminating, because the number is ending with 2 and not extending again.

(4)

This number is non-terminating, because 7182 is mentioned with a bar (‾). That says 7182 is repeating.

(5) 9.16516

This number is terminating, because the number is not extending after 9.16516.

(6)

This number is non-terminating, because 165 is mentioned with a bar (‾). That says 165 is repeating.

(7) 0.52888

This number is terminating, because the number is not extending after 0.52888.

(8)

This number is non-terminating, because 8 is mentioned with a bar (‾). That says 8 is repeating.

(9)

This number is non-terminating, because 136 is mentioned with a bar (‾). That says 136 is repeating.