Question
To the nearest thousandth, what is the decimal form of nine-fourteenths?
Answers
GPT-4o mini
To convert the fraction nine-fourteenths (\(\frac{9}{14}\)) into decimal form, we can perform the division of 9 by 14.
Starting to divide:
1. 14 does not go into 9, so we write 0 and add a decimal point and a zero (making it 90).
2. 14 goes into 90 six times (since \(14 \times 6 = 84\)).
3. Subtract 84 from 90 which gives us 6.
4. Bring down another 0 to make it 60.
5. 14 goes into 60 four times (since \(14 \times 4 = 56\)).
6. Subtract 56 from 60 which gives us 4.
7. Bring down another 0 to make it 40.
8. 14 goes into 40 two times (since \(14 \times 2 = 28\)).
9. Subtract 28 from 40 which gives us 12.
10. Bring down another 0 to make it 120.
11. 14 goes into 120 eight times (since \(14 \times 8 = 112\)).
12. Subtract 112 from 120 which gives us 8.
13. Bring down another 0 to make it 80.
14. 14 goes into 80 five times (since \(14 \times 5 = 70\)).
15. Subtract 70 from 80 which gives us 10.
16. Bring down another 0 to make it 100.
17. 14 goes into 100 seven times (since \(14 \times 7 = 98\)).
18. Subtract 98 from 100 which gives us 2.
19. Bring down another 0 to make it 20.
20. 14 goes into 20 one time (since \(14 \times 1 = 14\)).
21. Subtract 14 from 20 which gives us 6 again and the process will repeat.
From the division, we find that:
\[
\frac{9}{14} = 0.642857\ldots
\]
This decimal goes on infinitely, but we round it to the nearest thousandth. The thousandth place is the third digit after the decimal point.
The digits are:
- First digit: 6
- Second digit: 4
- Third digit: 2
- Next digit (to determine rounding): 8
Since the next digit (8) is 5 or greater, we round the third digit (2) up to 3.
Thus, the decimal form of nine-fourteenths, rounded to the nearest thousandth, is:
\[
\boxed{0.643}
\]
Starting to divide:
1. 14 does not go into 9, so we write 0 and add a decimal point and a zero (making it 90).
2. 14 goes into 90 six times (since \(14 \times 6 = 84\)).
3. Subtract 84 from 90 which gives us 6.
4. Bring down another 0 to make it 60.
5. 14 goes into 60 four times (since \(14 \times 4 = 56\)).
6. Subtract 56 from 60 which gives us 4.
7. Bring down another 0 to make it 40.
8. 14 goes into 40 two times (since \(14 \times 2 = 28\)).
9. Subtract 28 from 40 which gives us 12.
10. Bring down another 0 to make it 120.
11. 14 goes into 120 eight times (since \(14 \times 8 = 112\)).
12. Subtract 112 from 120 which gives us 8.
13. Bring down another 0 to make it 80.
14. 14 goes into 80 five times (since \(14 \times 5 = 70\)).
15. Subtract 70 from 80 which gives us 10.
16. Bring down another 0 to make it 100.
17. 14 goes into 100 seven times (since \(14 \times 7 = 98\)).
18. Subtract 98 from 100 which gives us 2.
19. Bring down another 0 to make it 20.
20. 14 goes into 20 one time (since \(14 \times 1 = 14\)).
21. Subtract 14 from 20 which gives us 6 again and the process will repeat.
From the division, we find that:
\[
\frac{9}{14} = 0.642857\ldots
\]
This decimal goes on infinitely, but we round it to the nearest thousandth. The thousandth place is the third digit after the decimal point.
The digits are:
- First digit: 6
- Second digit: 4
- Third digit: 2
- Next digit (to determine rounding): 8
Since the next digit (8) is 5 or greater, we round the third digit (2) up to 3.
Thus, the decimal form of nine-fourteenths, rounded to the nearest thousandth, is:
\[
\boxed{0.643}
\]