Question

Rational vs Irrational

Categorize each example as rational or irrational

4.589
0.666...
1.732...
0.022022022022...
√5
√16

Answer 1

Place each number into the categories it belongs.

(some numbers will go into more than one category)

Natural Whole Integers Rational Irrational Real

√81 √3 0 -13 1.2

Answer 2

Express 1/6 as a repeating decimal.

Answer 3

choose the point that represents √18 on the number line.

R S Q P
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___ because it is in between the perfect squares ___ and ___

Answer 4

choose the point that represents √18 on the number line.
___ because it is in between the perfect squares ___ and ___.

R S Q P
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Answer 5

choose the point that represents √18 on the number line. (choose one)
___ because it is in between the perfect squares 16 and 25.

R S Q P
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Answer 6

for the inequality __ > 6, which numbers listed below make the inequality true?

√83
-2.6
0
√25

Answer 7

List the following numbers in order from least (top) to greatest (bottom).
√16
19/2
9.4
√80
8

Answer 8

(8*1000)+(6*100)+(2*10)+(4*1)+(3*1/100)

Answer 9

(8*1000)+(6*100)+(2*10)+(4*1)+(3*1/100) as a decimal number

Answer 10

Find two whole numbers a and b that satisfy the diagram

<----|--|------|--|---->
9 √a √b 10

a=80 b=100
a=100 b=94
a= 85 b=9.5

Answer 11

Convert 2.56¯¯¯¯¯ to a fraction

Answer 12

4.589 - rational (it can be expressed as a fraction: 4589/1000)
0.666... - rational (it can be expressed as a fraction: 2/3)
1.732... - irrational (non-repeating decimal with no pattern, approximates the square root of 3)
0.022022022022... - rational (it can be expressed as a fraction: 2/90)
√5 - irrational (non-repeating decimal with no pattern, approximates the square root of 5)
√16 - rational (it can be expressed as a whole number: 4)

Answer 13

Natural: 0, 1.2
Whole: 0
Integers: 0, -13
Rational: 0, 1.2
Irrational: √3
Real: √81, √3, 0, -13, 1.2

Answer 14

To express 1/6 as a repeating decimal, we divide 1 by 6:

0.166666...

The number 6 does not terminate or repeat, so we can represent 1/6 as the repeating decimal 0.166666...

Answer 15

To determine which point represents √18 on the number line, we need to find the perfect squares that √18 falls between.

Starting with perfect squares: 0, 1, 4, 9, 16, 25, ...

We can see that √18 falls between √16 (4) and √25 (5) on the number line.

Therefore, the point that represents √18 on the number line is between points Q and R:

R S Q P
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Answer 16

To determine which point represents √18 on the number line, we need to find the perfect squares that √18 falls between.

Starting with perfect squares: 0, 1, 4, 9, 16, 25, ...

We can see that √18 falls between √16 (4) and √25 (5) on the number line.

Therefore, the point that represents √18 on the number line is between points Q and R:

R S Q P
|-|-|-|-|-|-|-|-|-|

Answer 17

To choose the point that represents √18 on the number line, we look for the point that is in between the perfect squares 16 and 25.

Based on the given options, the point that represents √18 on the number line is Q.

Therefore, the correct choice is:

R S Q P
|-|-|-|-|-|-|-|-|-|

Answer 18

To determine which numbers from the list make the inequality __ > 6 true, we can plug them into the inequality and see if the statement holds.

√83 ≈ 9.1104
9.1104 > 6 (true)

-2.6 > 6 (false)

0 > 6 (false)

√25 = 5
5 > 6 (false)

Therefore, the only number that makes the inequality __ > 6 true from the given list is √83.

Answer 19

Ordering the numbers from least to greatest:
√16 = 4
19/2 = 9.5
9.4
√80 ≈ 8.944
8

The ordered list would be:
4, 8, 9.4, 9.5, 8.944

Answer 20

To evaluate the expression (8*1000)+(6*100)+(2*10)+(4*1)+(3*1/100), we can simplify it step by step:

(8 * 1000) = 8,000
(6 * 100) = 600
(2 * 10) = 20
(4 * 1) = 4
(3 * 1/100) = 0.03

Adding all the simplified expressions together:

8,000 + 600 + 20 + 4 + 0.03 = 8,624.03

Therefore, the value of the expression is 8,624.03.

Answer 21

To express the expression (8*1000)+(6*100)+(2*10)+(4*1)+(3*1/100) as a decimal number, we can simplify it step by step:

(8 * 1000) = 8000
(6 * 100) = 600
(2 * 10) = 20
(4 * 1) = 4
(3 * 1/100) = 0.03

Adding all the simplified expressions together:

8000 + 600 + 20 + 4 + 0.03 = 8624.03

Therefore, the expression (8*1000)+(6*100)+(2*10)+(4*1)+(3*1/100) as a decimal number is 8624.03.

Answer 22

To find two whole numbers a and b that satisfy the given diagram, we need to consider the square roots (√a and √b) and the numbers marked on the diagram (9 and 10).

From the diagram, we can see that √a is located between 9 and √b, and √b is located between √a and 10.

Let's try the options provided:

1. a = 80, b = 100
√a = √80 ≈ 8.944, √b = √100 = 10
This satisfies the diagram since √a (approximately 8.944) is between 9 and √b (10), and √b (10) is between √a (approximately 8.944) and 10.

2. a = 100, b = 94
√a = √100 = 10, √b = √94 ≈ 9.695
This does not satisfy the diagram since √a (10) is not between 9 and √b (approximately 9.695).

3. a = 85, b = 9.5
Both a and b are not whole numbers. Therefore, they cannot satisfy the diagram.

Based on the options provided, the values a = 80 and b = 100 satisfy the diagram.

Answer 23

To convert the repeating decimal 2.56¯¯¯¯¯ to a fraction, we can follow these steps:

1. Assign a variable to the repeating part. Let x = 56.
2. Determine the number of repeating digits in x. In this case, there are two repeating digits.
3. Create an equation to represent the repeating decimal:
x = 0.56¯¯¯¯¯
4. Multiply both sides of the equation by a power of 10 that shifts the decimal to the left by the same number of places as the number of repeating digits. In this case, we need to multiply by 100:
100x = 56.56¯¯¯¯¯.
5. Subtract the original equation (step 3) from the equation in step 4:
99x = 56.
6. Solve for x by dividing both sides of the equation by 99:
x = 56/99.

Thus, the fraction equivalent of the repeating decimal 2.56¯¯¯¯¯ is 56/99.