Using a number line, what whole number and rational number to the nearest half is 58−−√ between?(1 point)
Responses
between 8 and 8.5
between 8 and 8.5
between 8.5 and 9
between 8.5 and 9
between 7.5 and 8
between 7.5 and 8
between 7 and 7.5
The whole number and rational number to the nearest half that 58-√ falls between is between 7.5 and 8.
Using a number line, what whole number and rational number to the nearest half is 58−−√ between?(1 point)
Responses
between 8 and 8.5
between 8 and 8.5
between 8.5 and 9
between 8.5 and 9
between 7.5 and 8
between 7.5 and 8
between 7 and 7.5
Apologies for the confusion in my previous response. The correct answer is between 7.5 and 8.
Express 8 over 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:
0.727272...
First, we divide 8 by 11:
__0.7272 (first digit is 7)
11 | 8.0000
- 7.07 (7 times 11 equals 77)
10
- 9.09 (9 times 11 equals 99)
10
-9.09
10
From the long division, we see that the decimal representation of 8/11 is 0.727272... The cycle of repeating digits is 72, which is marked with a bar over them: 0.72̅.
Convert 0.72¯¯¯¯¯ to a rational number in simplest form
To convert the repeating decimal 0.72¯¯¯¯¯ to a rational number in simplest form, we can assign a variable to the repeating part of the decimal and solve for it.
Let x = 0.727272...
Now, we can multiply both sides of the equation by 100 to move the decimal point two places to the right:
100x = 72.727272...
Now, let's subtract the original equation from this equation to eliminate the repeating part:
100x - x = 72.727272... - 0.727272...
99x = 72
Dividing both sides of the equation by 99, we get:
x = 72/99
To simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 9:
x = (72 ÷ 9) / (99 ÷ 9)
x = 8/11
Therefore, the rational number in simplest form equivalent to the repeating decimal 0.72¯¯¯¯¯ is 8/11.
Which of the following is a rational number between 5 and 514?(1 point)
Responses
525
5 Start Fraction 2 over 5 end fraction
517
5 Start Fraction 1 over 7 end fraction
26−−√
start root 26 end root
513
A rational number is a number that can be expressed as a fraction, where both the numerator and denominator are integers.
Among the given options, the rational number between 5 and 514 is 5 1/7.