116,579 views
16 votes
16 votes
Convert repeating decimal to a rational number (limit repeating decimals to

thousandths).
21.) 0.6=
22.) 1.25 =
23.) 0.45

User Abdullah Dibas
by
3.2k points

1 Answer

10 votes
10 votes

21) You most likely mean the number 0.666…. If x = 0.666…, then

10x = 6.666…

10x - x = 6.666… - 0.666…

9x = 6

x = 6/2 = 2/3

22) You either mean 1.2555… (only 5 repeats) or 1.252525… (both 2 and 5 repeat).

If x = 1.2555…, then

10x = 12.555…

100x = 125.555…

100x - 10x = 125.555… - 12.555…

90x = 113

x = 113/90

Otherwise, if x = 1.252525…, then

100x = 125.252525…

100x - x = 125.252525… - 1.252525…

99x = 124

x = 124/99

23) You either mean 0.4555… or 0.454545….

If x = 0.4555…, then

10x = 4.555…

100x = 45.555…

100x - 10x = 45.555… - 4.555…

90x = 41

x = 41/90

Otherwise, if x = 0.454545…, then

100x = 45.454545…

100x - x = 45.454545… - 0.454545…

99x = 45

x = 45/99 = 5/11

User Hafizur Rahman
by
3.1k points