Question
Without dividing, determine which of the following represent terminating decimals.
a.
b.
A. No, because the only factors of the denominator, 24 , are 2 and 5 .
B. No, the denominator of the simplified fraction contains a factor other than 2 or 5 .
C. Yes, because the only factors of the denominator, 24 , are 2 and 5 .
D. Yes, the only factors of the denominator of the simplified fraction are 2 or 5 .
b. Is
A. Yes, the only factors of the denominator of the simplified fraction are 2 or 5 .
B. No, because the only factors of the denominator, 28 , are 2 and 5 .
C. Yes, because the only factors of the denominator, 28 , are 2 and 5 .
a.
b.
A. No, because the only factors of the denominator, 24 , are 2 and 5 .
B. No, the denominator of the simplified fraction contains a factor other than 2 or 5 .
C. Yes, because the only factors of the denominator, 24 , are 2 and 5 .
D. Yes, the only factors of the denominator of the simplified fraction are 2 or 5 .
b. Is
A. Yes, the only factors of the denominator of the simplified fraction are 2 or 5 .
B. No, because the only factors of the denominator, 28 , are 2 and 5 .
C. Yes, because the only factors of the denominator, 28 , are 2 and 5 .
Ask by Ball Murphy. in the United States
Mar 22,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Solution
Step 1: Determine the condition for terminating decimals
A fraction in lowest terms
Step 2: Analyze
-
Simplify the fraction:
-
Factorize the denominator:
-
Conclusion:Since the denominator
contains (a prime other than or ), the fraction does not represent a terminating decimal. Correct Answer for (a):
B. No, the denominator of the simplified fraction contains a factor other thanor .
Step 3: Analyze
-
Simplify the fraction:
-
Factorize the denominator:
-
Conclusion:The denominator
is composed solely of the prime , hence the fraction represents a terminating decimal. Correct Answer for (b):
A. Yes, the only factors of the denominator of the simplified fraction areor .
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Extra Insights
To determine if a fraction represents a terminating decimal, we look at its denominator after simplification. A fraction will have a terminating decimal if the only prime factors of its denominator are 2 and/or 5.
For
For
In summary,
Now, let’s dig deeper into these fascinating concepts!
An interesting tidbit is that terminating decimals have a close relationship with powers of 10! Since our decimal system is base 10, any fraction that can be expressed in the form
When it comes to problem-solving, one common mistake is failing to fully simplify the fraction! Before you check the denominator’s prime factors, make sure you’ve simplified the fraction completely. It’s essential because a fraction that seems to have a denominator with only 2’s and 5’s at first glance may contain other factors in its unsimplified form—leading you down the wrong path towards identifying whether it’s terminating!
