Asked by asd
Find a rational number between 2 and 2 1/4 using the method of adding the numbers together and dividing by 2. Write the answer as a mixed number.(1 point)
Answers
Answered by
GPT 3.5
To find a rational number between 2 and 2 1/4 using the method of adding the numbers together and dividing by 2, we can add 2 and 2 1/4:
2 + 2 1/4 = 2 + 9/4 = 8/4 + 9/4 = 17/4
Now, we divide 17/4 by 2:
(17/4)/2 = 17/4 * 1/2 = 17/8
Therefore, a rational number between 2 and 2 1/4 using this method is 17/8.
To write this as a mixed number, we divide 17 by 8:
17 ÷ 8 = 2 remainder 1
So, the mixed number form of 17/8 is 2 1/8.
2 + 2 1/4 = 2 + 9/4 = 8/4 + 9/4 = 17/4
Now, we divide 17/4 by 2:
(17/4)/2 = 17/4 * 1/2 = 17/8
Therefore, a rational number between 2 and 2 1/4 using this method is 17/8.
To write this as a mixed number, we divide 17 by 8:
17 ÷ 8 = 2 remainder 1
So, the mixed number form of 17/8 is 2 1/8.
Answered by
asd
Show an example of a rational number that is between 10−−√ and 11−−√
16/5
10/3
3.1
3.4
16/5
10/3
3.1
3.4
Answered by
GPT 3.5
To determine which of the given numbers is a rational number between √10 and √11, we need to evaluate each number and check if it falls within the given range.
Let's calculate each option:
√(10) ≈ 3.16227766017
√(11) ≈ 3.31662479036
a) 16/5 ≈ 3.2
b) 10/3 ≈ 3.33333333333
c) 3.1 (This number falls between √10 and √11)
d) 3.4 (This number falls between √10 and √11)
Therefore, both options c) 3.1 and d) 3.4 are rational numbers that fall between √10 and √11.
Let's calculate each option:
√(10) ≈ 3.16227766017
√(11) ≈ 3.31662479036
a) 16/5 ≈ 3.2
b) 10/3 ≈ 3.33333333333
c) 3.1 (This number falls between √10 and √11)
d) 3.4 (This number falls between √10 and √11)
Therefore, both options c) 3.1 and d) 3.4 are rational numbers that fall between √10 and √11.
Answered by
asd
How many irrational numbers are there between 11−−√ and 17−−√?
twenty-eight numbers
six numbers
four numbers
an infinite number
twenty-eight numbers
six numbers
four numbers
an infinite number
Answered by
GPT 3.5
To find the number of irrational numbers between the square roots of 11 and 17, we can determine the number of integers between the square roots and subtract them from the total number of numbers between the roots. Since integers are rational numbers, the remaining numbers will be irrational.
Let's calculate the square roots:
√(11) ≈ 3.31662479036
√(17) ≈ 4.12310562562
Now we need to find the number of integers between these two square roots. The integers within this range are 4 and 3, so there are two integers.
The total number of numbers between the square roots is 4 (including the square roots themselves) since we have 3.31662479036 <a< 4 < b< 4.12310562562.
Now we subtract the two integers from the total number of numbers:
4 - 2 = 2
Therefore, there are two irrational numbers between the square roots of 11 and 17.
Let's calculate the square roots:
√(11) ≈ 3.31662479036
√(17) ≈ 4.12310562562
Now we need to find the number of integers between these two square roots. The integers within this range are 4 and 3, so there are two integers.
The total number of numbers between the square roots is 4 (including the square roots themselves) since we have 3.31662479036 <a< 4 < b< 4.12310562562.
Now we subtract the two integers from the total number of numbers:
4 - 2 = 2
Therefore, there are two irrational numbers between the square roots of 11 and 17.