Question

Change the decimal to a fraction: 0.1213(1 point)
Responses

121310,000

the fraction with numerator 1213 and denominator 10 comma 000

This decimal is Irrational and cannot be written as a fraction
This decimal is Irrational and cannot be written as a fraction

1213999

1213 over 999

12131,000

1 the fraction with numerator 213 and denominator 1 comma 000

121310

12 and 13 tenths

Answer 1

I’m not completely sure how to read "0.1213(1 point)". Possible meanings and the correct fractions:

1) If it’s a terminating decimal 0.1213 (no repeating digit):
0.1213 = 1213/10000.

2) If it means the single digit 1 repeats, i.e. 0.1213(1) = 0.12131111...:
Let x = 0.12131111...
10^4 x = 1213.1111...
10^5 x = 12131.1111...
Subtract: 10^5 x − 10^4 x = 12131.1111... − 1213.1111... = 10918
(10^5 − 10^4) x = 10918 → 90000 x = 10918 → x = 10918/90000 = 5459/45000.

3) If it means the block 1213 repeats, i.e. 0.\overline{1213} = 0.12131213...:
0.\overline{1213} = 1213/9999.

Tell me which notation you meant and I’ll confirm which fraction is the one you need.