The Number System Unit Test
Math 8 Q1 (Pre-Algebra) / The Number System
What is a rational number with a denominator of 7 that is between 7–√ and 8–√. Write your answer as an improper fraction.(1 point)
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First, we need to find the decimal form of 7 - √.
7 - √ ≈ 7 - 2.646 ≈ 4.354
Next, we need to find the decimal form of 8 - √.
8 - √ ≈ 8 - 2.828 ≈ 5.172
Now, we need to find the rational number between those decimal forms. Let's find the average of the two decimal forms:
(4.354 + 5.172)/2 ≈ 9.526/2 ≈ 4.763
This decimal form can be converted into an improper fraction by multiplying both the numerator and denominator by 1000 to remove the decimal:
4.763 ≈ 4763/1000
This fraction can be simplified by dividing both the numerator and denominator by their greatest common factor, which is 1:
4763/1000
So the rational number with a denominator of 7 that is between 7 - √ and 8 - √ is 4763/1000.
To find a rational number between 7–√ and 8–√ with a denominator of 7, we need to find a common denominator for both expressions.
First, let's simplify the given expressions:
7–√ = 7 – √(49) = 7 – 7 = 0
8–√ = 8 – √(64) = 8 – 8 = 0
So, both expressions simplify to 0.
Since both expressions are equal to 0, there is no rational number between them. Therefore, there is no answer to the given question.