Rational vs irrational

Question

Categorize Each example as rational or irrational
.66666666666666666...
.022022022022022022...
1.732...
4.589
16
5

Answer 1

.66666666666666666... - Rational (repeating decimal)
.022022022022022022... - Rational (repeating decimal)
1.732... - Irrational (√3)
4.589 - Rational (terminating decimal)
16 - Rational (whole number)
5 - Rational (whole number)

Answer 2

Place each number into the categories it belongs. (Some numbers will go into more than one category)
Natural
Whole
Integers
Rational
Irrational
Real
-13,0,81,3,1.2222...

Answer 3

Natural: 0, 3, 81
Whole: 0, 81
Integers: -13, 0, 3, 81
Rational: 0, 1.2222...
Irrational: None
Real: -13, 0, 81, 3, 1.2222...

Answer 4

Express 1/6 as a repeating decimal

Answer 5

To express 1/6 as a repeating decimal, we can use long division.

When we divide 1 by 6, we get a quotient of 0 and a remainder of 1. We then bring down a zero and divide 10 by 6, which gives us a quotient of 1 and a remainder of 4. We repeat this process until we identify a repeating pattern.

```
0.1
-----
6 | 1.000000...
- 0
-----
10
- 6
-----
40
- 36
-----
40
- 36
-----
40
- 36
-----
400
- 36
-----
400
- 36
-----
40
```

The division continues indefinitely, and we can see that the pattern "40" repeats without end. Therefore, 1/6 can be expressed as the repeating decimal 0.1666666... (The dots indicate that the digit 6 repeats indefinitely).