Using a number line, what whole number and rational number to the nearest half is 58 between?

Question

1. between 8.5 and 9
2. between 8 and 8.5
3. between 7 and 7.5
4. between 7.5 and 8

Answer 1

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.

Answer 2

Express 8/11 as a repeating decimal. Mark the cycle of repeating digits with a bar.

Answer 3

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.