To find a rational number with a denominator of 7 that is between 7–√ and 8–√, we can start by finding the decimal equivalents of these two numbers.
The decimal equivalent of 7–√ can be found by subtracting the square root of 2 from 7:
7 – √2 ≈ 7 – 1.41 = 5.59
Similarly, the decimal equivalent of 8–√ can be found by subtracting the square root of 2 from 8:
8 – √2 ≈ 8 – 1.41 = 6.59
Since we want to find a rational number with a denominator of 7 between these two decimals, we need to find a fraction that is between 5.59 and 6.59 when converted to decimal form.
To convert the fraction to a decimal, divide the numerator (19) by the denominator (7):
19 ÷ 7 ≈ 2.71
Since 2.71 falls between 5.59 and 6.59, the rational number 19/7 is a correct answer.
Therefore, the improper fraction 19/7 is the correct answer.
What is a rational number with a denominator of 7 that is between 7–√
and 8–√
. Write your answer as an improper fraction.
explain how 19/7 is the correct answer
1 answer
1 answer