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)
Rational vs Irrational
Categorize each example as rational or irrational
4.589
0.666...
1.732...
0.022022022022...
√5
√16
23 answers
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
(some numbers will go into more than one category)
Natural Whole Integers Rational Irrational Real
√81 √3 0 -13 1.2
Natural: 0, 1.2
Whole: 0
Integers: 0, -13
Rational: 0, 1.2
Irrational: √3
Real: √81, √3, 0, -13, 1.2
Whole: 0
Integers: 0, -13
Rational: 0, 1.2
Irrational: √3
Real: √81, √3, 0, -13, 1.2
Express 1/6 as a repeating decimal.
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...
0.166666...
The number 6 does not terminate or repeat, so we can represent 1/6 as the repeating decimal 0.166666...
choose the point that represents √18 on the number line.
R S Q P
|-|-|-|-|-|-|-|-|-|
___ because it is in between the perfect squares ___ and ___
R S Q P
|-|-|-|-|-|-|-|-|-|
___ because it is in between the perfect squares ___ and ___
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
|-|-|-|-|-|-|-|-|-|
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
|-|-|-|-|-|-|-|-|-|
choose the point that represents √18 on the number line.
___ because it is in between the perfect squares ___ and ___.
R S Q P
|-|-|-|-|-|-|-|-|-|
___ because it is in between the perfect squares ___ and ___.
R S Q P
|-|-|-|-|-|-|-|-|-|
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
|-|-|-|-|-|-|-|-|-|
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
|-|-|-|-|-|-|-|-|-|
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
|-|-|-|-|-|-|-|-|-|
___ because it is in between the perfect squares 16 and 25.
R S Q P
|-|-|-|-|-|-|-|-|-|
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
|-|-|-|-|-|-|-|-|-|
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
|-|-|-|-|-|-|-|-|-|
for the inequality __ > 6, which numbers listed below make the inequality true?
√83
-2.6
0
√25
√83
-2.6
0
√25
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.
√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.
List the following numbers in order from least (top) to greatest (bottom).
√16
19/2
9.4
√80
8
√16
19/2
9.4
√80
8
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
√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
(8*1000)+(6*100)+(2*10)+(4*1)+(3*1/100)
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.
(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.
(8*1000)+(6*100)+(2*10)+(4*1)+(3*1/100) as a decimal number
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.
(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.
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
<----|--|------|--|---->
9 √a √b 10
a=80 b=100
a=100 b=94
a= 85 b=9.5
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.
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.
Convert 2.56¯¯¯¯¯ to a fraction
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.
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.
3 answers