Hey Bot, I need a little help with this question.
Using a number line, what whole number and rational number to the nearest half is 58−−√ between?(1 point)
To find the whole number and the rational number nearest to 58−−√, we can start by representing 58−−√ on a number line.
Since 58 is closer to 59 than to 57, let's start by locating 59 on the number line.
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Now, let's consider the numbers between 59 and 60. We can divide this region in half, and find the midpoint. The midpoint between 59 and 60 is 59.5.
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59.5
Since we are looking for the number nearest to 58−−√, the whole number closest to 58−−√ is 59 (as it is closer than 60), and the rational number nearest is 59.5.
Therefore, the whole number and rational number closest to 58−−√ is 59 and 59.5, respectively.
Nevermind bot
Alright, if you have any other questions or need assistance in the future, feel free to ask. Have a great day!
Using rational approximations, what is an inequality statement comparing 81−−√ and 8–√8? Enter <, >, or =.(1 point)
To compare 81−−√ and 8–√8 using rational approximations, we can first find the approximate values for each expression.
For 81−−√, the square root of 81 is exactly 9. So, 81−−√ = 9.
For 8–√8, we can approximate the square root of 8. Since 8 is between 4 and 9, we know that 8–√8 is between 2 and 3. A more accurate approximation can be found by taking the average: (2 + 3)/2 = 2.5. Therefore, the approximation for 8–√8 is 2.5.
Now, we can compare 9 and 2.5. Since 9 is greater than 2.5, the inequality statement is:
81−−√ > 8–√8
Express 8/11 as a repeating decimal. Mark the cycle of repeating digits with a bar.(1 point)
To express 8/11 as a repeating decimal, we can use long division.
0. (Quotient)
___________
11 | 8.00
0
___________
8.00 (Dividend)
-7.26 (First subtract)
___________
0.74 (Dividend after subtracting)
0.66 (Bring down next digit)
___________
0.08 (Dividend after subtracting)
0.00 (No more digits to bring down)
The division process ends here since there are no more digits to bring down. As we can see, the pattern 0.74 repeats. So, 8/11 as a repeating decimal is approximately 0.74 with the digit 74 repeating indefinitely. We can represent this as:
8/11 ≈ 0.74 with a bar over the digits 74: 0.74̅
Isn't it 0.72 ?
Apologies for the incorrect response. You're right, the correct decimal representation for 8/11 as a repeating decimal is 0.72̅.
Here's the correct long division:
0. (Quotient)
___________
11 | 8.00
7
___________
10.00 (Dividend)
- 9.90 (First subtract)
___________
0.10 (Dividend after subtracting)
0.00 (No more digits to bring down)
As we can see, the pattern 0.72 repeats. So, 8/11 is equal to the repeating decimal 0.72̅. Thank you for pointing out the error, and apologies for any confusion caused.