Using a number line, what whole number and rational number to the nearest half is 58 between?
1. between 8.5 and 9
2. between 8 and 8.5
3. between 7 and 7.5
4. between 7.5 and 8
To determine which whole number and rational number to the nearest half is 58 between, we can look for the pair of numbers on the number line that sandwich 58.
Option 1: 58 is greater than 8.5 but less than 9.
Option 2: 58 is greater than 8 but less than 8.5.
Option 3: 58 is not between 7 and 7.5.
Option 4: 58 is not between 7.5 and 8.
Therefore, the whole number and rational number to the nearest half that 58 is between is 8 and 8.5.
Thus, the correct answer is option 2: between 8 and 8.5.
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 divide 8 by 11 using long division:
0.72
------------
11 | 8.00
The first step is to determine how many times 11 can go into 80. The quotient is 7.
0.72
------------
11 | 8.00
-7.70
-----
30
Next, we bring down the next digit, which is 0, and divide 11 into 300. The quotient is 27.
0.727
------------
11 | 8.00
-7.70
-----
30
- 27
-----
30
Since the remainder is 30 and the divisor is 11, we need to bring down the next digit (0) and continue dividing.
0.7272
------------
11 | 8.00
-7.70
-----
30
- 27
-----
30
- 27
-----
30
Since the remainder is 30 and the divisor is 11, we bring down the next digit (0) and continue dividing.
0.72727
------------
11 | 8.00
-7.70
-----
30
- 27
-----
30
- 27
-----
30
- 27
-----
30
The pattern 72 repeats, so we can express 8/11 as a repeating decimal:
8/11 = 0.72̅
Therefore, the decimal representation of 8/11 is 0.72 with a bar over the 2 indicating that the digits 72 repeat.
To determine which whole number and rational number is nearest to 58 between the given options, let's consider each interval using a number line.
1. Between 8.5 and 9:
58 is closer to 9 than 8.5, so it is not the correct option.
2. Between 8 and 8.5:
58 is greater than both 8 and 8.5, so it is not the correct option.
3. Between 7 and 7.5:
58 is greater than both 7 and 7.5, so it is not the correct option.
4. Between 7.5 and 8:
58 is closer to 7.5 than 8, so it is the correct option.
Therefore, the whole number and rational number to the nearest half that 58 is between is between 7.5 and 8.