Compare 1/7 to consecutive multiples of 1/9. This is easily done by converting the fractions to a common denominator of LCM(7, 9) = 63:
1/9 = 7/63
2/9 = 14/63
while
1/7 = 9/63
Then 1/7 falls between 1/9 and 2/9, so 1/7 = 1/9 plus some remainder. In particular,
1/7 = 1/9¹ + 2/63.
We do the same sort of comparison with the remainder 2/63 and multiples of 1/9² = 1/81. We have LCM(63, 9²) = 567, and
1/9² = 7/567
2/9² = 14/567
3/9² = 21/567
while
2/63 = 18/567
Then
2/63 = 2/9² + 4/567
so
1/7 = 1/9¹ + 2/9² + 4/567
Compare 4/567 with multiples of 1/9³ = 1/729. LCM(567, 9³) = 5103, and
1/9³ = 7/5103
2/9³ = 14/5103
3/9³ = 21/5103
4/9³ = 28/5103
5/9³ = 35/5103
6/9³ = 42/5103
while
4/567 = 36/5103
so that
4/567 = 5/9³ + 1/5103
and so
1/7 = 1/9¹ + 2/9² + 5/9³ + 1/5103
Next, LCM(5103, 9⁴) = 45927, and
1/9⁴ = 7/45927
2/9⁴ = 14/45927
while
1/5103 = 9/45927
Then
1/5103 = 1/9⁴ + 2/45927
so
1/7 = 1/9¹ + 2/9² + 5/9³ + 1/9⁴ + 2/45927
One last time: LCM(45927, 9⁵) = 413343, and
1/9⁵ = 7/413343
2/9⁵ = 14/413343
3/9⁵ = 21/413343
while
2/45927 = 18/413343
Then
2/45927 = 2/9⁵ + remainder
so
1/7 = 1/9¹ + 2/9² + 5/9³ + 1/9⁴ + 2/9⁵ + remainder
Then the base 9 expansion of 1/7 is
0.12512..._9
Answer:
good u?
Step-by-step explanation:
Answer:
Both ratios reduce to the same ratio 3/50, so the restocking fee is proportional.
Step-by-step explanation:
For the $200, the restocking fee is $12, so the ratio of the restocking fee to the price of the item is 12/200.
For the $150, the restocking fee is $9, so the ratio of the restocking fee to the price of the item is 9/150.
Now we find out if the ratios 12/200 and 9/150 are equal.
12/200 = 3/50
9/150 = 3/50
Both ratios reduce to the same ratio 3/50, so the restocking fee is proportional.
13. Is 18
15. Is 86
17 is 5
19 is 15
21 is 24
23 is 29
