Using a number line, what whole number and rational number to the nearest half is 30−−√
between?(1 point)
30−−√ is between
and
To find the whole number and rational number to the nearest half that 30−−√ is between, we need to determine the numbers on the number line that are closest to it.
First, let's find the whole number to the nearest half. The whole number closest to 30−−√ is 5. This is because 5^2 is equal to 25, which is the closest perfect square to 30.
Next, let's find the rational number to the nearest half. The rational number closest to 30−−√ is 5.5. This is because (5.5)^2 is equal to 30.25, which is slightly larger than 30.
Therefore, 30−−√ is between 5 and 5.5 on a number line.
Express 711
as a repeating decimal. Mark the cycle of repeating digits with a bar.
To express 711 as a repeating decimal, we need to divide 711 by the number 9 (since it has only one digit).
711 ÷ 9 = 79 with a remainder of 6
Now, we can express the remainder of 6 as a fraction over 9:
6/9 = 2/3
So, when we divide 711 by 9, we get 79 and 2/3 as the result.
To express this as a repeating decimal, we write 79 and place a bar over the 3 to indicate that it repeats.
Therefore, 711 as a repeating decimal is 79.3¯, with the 3 repeating indefinitely.
Express 7/11
as a repeating decimal. Mark the cycle of repeating digits with a bar.
To express 7/11 as a repeating decimal, we perform long division:
0.63...
________________
11 | 7
-6
___
10
-9
___
1
The remainder after the first division is 1. We then bring down a zero and continue the division:
0.63...
________________
11 | 7.00
-6
___
10
-9
___
1
________________
11 | 10.00 (add a zero to bring down)
-9
___
10
- 9
___
1
Once again, we have a remainder of 1. We continue this process by bringing down another zero:
0.63...
________________
11 | 7.00
-6
___
10
- 9
___
1
________________
11 | 10.00
-9
___
10
- 9
___
1
________________
11 | 10.01 (add a zero to bring down)
- 9
___
10
- 9
___
1
We can see that the pattern repeats with a remainder of 1. Therefore, 7/11 expressed as a repeating decimal is 0.63¯, with the 63 repeating indefinitely.
Convert 0.09¯¯¯¯¯
to a rational number in simplest form.
To convert the recurring decimal 0.09¯¯¯¯¯ into a rational number, we can use the concept of geometric series.
Let x = 0.09¯¯¯¯¯
Then, 100x = 9.99¯¯¯¯¯
Subtracting the first equation from the second equation:
100x - x = 9.99¯¯¯¯¯ - 0.09¯¯¯¯¯
99x = 9.90¯¯¯¯¯
Now, multiply both sides by 1/99 to isolate x:
(1/99)*(99x) = (1/99)*(9.90¯¯¯¯¯)
x = 0.10¯¯¯¯¯
We can express 0.10¯¯¯¯¯ as a fraction by noting that it is equal to 10/99. This can be obtained by dividing 0.10¯¯¯¯¯ by 0.01:
0.10¯¯¯¯¯ = 10/99
So, 0.09¯¯¯¯¯ is equal to 10/99 when expressed as a rational number in simplest form.
Bot are you correct
I'm not risking it :]
To find the whole number and rational number to the nearest half that 30−−√ is between, we need to locate 30−−√ on a number line and then find the nearest whole number and rational number to its left and right.
First, let's find 30−−√ on the number line. If we estimate its value, we know that the square root of any perfect square is an integer. The closest perfect square to 30 is 25 (5^2), and the square root of 25 is 5. Therefore, the value of 30−−√ is slightly greater than 5.
On the number line, if 5 is represented by a dot, we can estimate the value of 30−−√ to be somewhere to the right of 5 and less than 6.
Now let's find the nearest whole number and rational number to the left and right of 30−−√.
To the left of 30−−√, the nearest whole number is 5, and the nearest rational number is 5.5 (5 + 0.5).
To the right of 30−−√, the nearest whole number is 6, and the nearest rational number is also 6.5 (6 + 0.5).
Therefore, the whole number and rational number to the nearest half that 30−−√ is between are:
- To the left: 5 and 5.5
- To the right: 6 and 6.5