Which list shows fractions that always result in a terminating decimal for values of n > 0?
CLEAR SUBMIT
111, 1,121,11,331 ...,111𝑛
1
11
,
1
,
121
,
1
1
,
331
.
.
.
,
1
11
n
110, 1,100,11,000 ...,110𝑛
1
10
,
1
,
100
,
1
1
,
000
.
.
.
,
1
10
n
16, 1,36, 1216...,16𝑛
1
6
,
1
,
36
,
1
216
.
.
.
,
1
6
n
13, 1,9, 127...,13𝑛
1
,
9
,
12
7
.
.
.
,
1
3
n
The list that shows fractions that always result in a terminating decimal for values of n > 0 is:
110, 1,100, 11,000..., 110𝑛
To determine which list of fractions always results in a terminating decimal for values of n>0, we need to examine the denominator of each fraction.
A decimal terminates when the denominator is divisible only by 2 and/or 5.
Let's analyze each list:
1. 111, 1,121,11,331 ...,111𝑛 : The denominator in each fraction is always 1, so it will always result in a terminating decimal.
2. 110, 1,100,11,000 ...,110𝑛: The denominator in each fraction is a power of 10, which is divisible only by 2 and/or 5. Thus, it will always result in a terminating decimal.
3. 16, 1,36, 1216...,16𝑛: The denominator in each fraction is a power of 6, which is not divisible only by 2 and/or 5. Therefore, this list does not always result in a terminating decimal.
4. 13, 1,9, 127...,13𝑛: The denominator in each fraction is a prime number (13), which is not divisible only by 2 and/or 5. Hence, this list does not always result in a terminating decimal.
From the given lists, only List 1 (111, 1,121,11,331 ...,111𝑛) and List 2 (110, 1,100,11,000 ...,110𝑛) always result in terminating decimals for values of n>0.