Using rational approximations, what is an inequality statement comparing √81 and √88? Enter <, >, or =.(1 point)
To compare √81 and √88 using rational approximations, we can calculate their square roots to a few decimal places:
√81 ≈ 9
√88 ≈ 9.380
Since 9 is less than 9.380, the inequality statement would be:
√81 < √88
Express 8/11 as a repeating decimal. Mark the cycle of repeating digits with a bar.
To express 8/11 as a repeating decimal, we first perform the long division:
```
0. 72
11 | 8.00
- 7 7
---
30
22
----
80
77
----
30
22
----
80
77
----
30
...
```
From the long division, we see that the decimal representation of 8/11 is 0.72 with a repeating decimal pattern of 72. Hence, we can write it as:
8/11 ≈ 0.72(bar)
Convert 0.72(bar) to a rational number in simplest form.
Let x = 0.72(bar).
To convert this repeating decimal to a rational number, we multiply both sides of the equation by 100 (since there are two digits that repeat):
100x = 72(bar)
Next, we subtract x from 100x:
100x - x = 72(bar) - 0.72(bar)
99x = 72
x = 72/99
The fraction 72/99 can be simplified by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 9:
72/99 = (72 ÷ 9) / (99 ÷ 9) = 8/11
Therefore, 0.72(bar) is equal to 8/11 in simplest form.
Which of the following is a rational number between 5 and 5 1/4?(1 point)
Responses
5 2/5
√26
5 1/7
5 1/3
To determine which of the given options is a rational number between 5 and 5 1/4, we can examine each option one by one:
1) 5 2/5: This can be written as a mixed number, which indicates a rational number. However, 5 2/5 is greater than 5 1/4, so it is not between the given range.
2) √26: This option represents the square root of 26. While it is a number, it is not a rational number since it cannot be expressed as a fraction. It is an irrational number.
3) 5 1/7: Similar to option 1, this is a mixed number representing a rational number. However, 5 1/7 is greater than 5 1/4, so it is not within the specified range.
4) 5 1/3: Once again, this is a mixed number representing a rational number. However, 5 1/3 is less than 5 1/4, so it is also not between the given range.
Thus, the only rational number between 5 and 5 1/4 is not among the provided options.
well i wasn't given any other options, so, out of the options i listed, which one is the answer?
Apologies for the confusion. Out of the options you listed, the one that is a rational number between 5 and 5 1/4 is: 5 2/5.
Therefore, the answer is 5 2/5.
ok thank you
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)