The Number System Unit Test HELP ASAP
1. Which statement is true about the relationships between the number sets?(1 point)
Responses
A. Some irrational numbers are also integers.
B. All rational numbers are also integers.
C. Not all natural numbers are real numbers.
D. Whole numbers include all natural numbers and 0.
2. Which of the following is true about −9?(1 point)
Responses
A. It is an integer but not a rational number.
B. It is both an integer and a whole number.
C. It is a whole number but not an integer.
D. It is an integer but not a whole number.
1. D. Whole numbers include all natural numbers and 0.
2. B. It is both an integer and a whole number.
3. The cost of a gallon of gas, expressed strictly as a decimal, is $3.39910.
4. A. Fractions are always rational numbers.
What is a rational number with a denominator of 7 that is between 7–√
and 8–√
. Write your answer as an improper fraction.(1 point)
wrong
A. It is an integer but not a rational number.
1. Which statement is true about the relationships between the number sets?(1 point)
Responses
A. Some irrational numbers are also integers.
B. All rational numbers are also integers.
C. Not all natural numbers are real numbers.
D. Whole numbers include all natural numbers and 0.
2. Which of the following is true about −9?(1 point)
Responses
A. It is an integer but not a rational number.
B. It is both an integer and a whole number.
C. It is a whole number but not an integer.
D. It is an integer but not a whole number.
3. A sign in a gas station advertises gas at the rate of $3.39910 per gallon. How many dollars does a gallon cost, writing the price strictly as a decimal?(1 point)
4. Which set of numbers is always rational?(1 point)
Responses
A. fractions
B. positive numbers
C. decimals
D. integers
Sorry. For number 3 I meant:
A sign in a gas station advertises gas at the rate of $3.39 9/10 per gallon. How many dollars does a gallon cost, writing the price strictly as a decimal?(1 point)
If the gas is advertised at a rate of $3.39 9/10 per gallon, it means the cost is $3.39 + 9/10.
To write it as a decimal, we can convert the fraction 9/10 to a decimal by dividing 9 by 10: 9 ÷ 10 = 0.9.
Therefore, the cost of a gallon of gas, written strictly as a decimal, is $3.39 + 0.9 = $3.39 + $0.9 = $4.29.
5. The height of an equilateral triangle equals √3/2 times the side length. Using 7/4 for the square root of 3, what is the approximate height in meters of an equilateral triangle with a side length of 8 meters?(1 point)
6. The diagonal of a square equals 2–√ times the side length. Using 1.4 for the square root of 2, what is the approximate length in feet from one corner to an opposite corner of a square park that is 700 feet on a side?(1 point)
5. The height of an equilateral triangle equals √3/2 times the side length. To find the approximate height in meters of an equilateral triangle with a side length of 8 meters, we can substitute the value of √3/2 using the given approximation.
Height = (√3/2) * side length
= (7/4) * 8 meters
= 7 * 2 meters
= 14 meters
Therefore, the approximate height of the equilateral triangle is 14 meters.
6. The diagonal of a square equals 2 – √2 times the side length. To find the approximate length from one corner to an opposite corner of a square park that is 700 feet on a side, we can substitute the value of (√2) using the given approximation.
Length = (2 – √2) * side length
= (2 – 1.4) * 700 feet
= 0.6 * 700 feet
= 420 feet
Therefore, the approximate length from one corner to an opposite corner of the square park is 420 feet.
7. Using a number line, what whole number and rational number to the nearest half is 40−−√ between?(1 point)
40−−√ is between {blank} and {blank}
40−−√ is between 6 and 7 on the number line.
7. Using a number line, what whole number and rational number to the nearest half is 40−−√ between?(1 point)
40−−√ is between 6 and 7.
What is a rational number that √40 is between
To find a rational number between two values, we can take their average.
In this case, we want to find a rational number between √40 and a whole number. We know that √40 is between 6 and 7.
Taking the average of 6 and 7, we get (6 + 7)/2 = 13/2 = 6.5.
Therefore, a rational number that is between √40 and a whole number is 6.5.
what whole number and rational number to the nearest half is 40−−√ between?
The square root of 40, denoted as √40, is between two whole numbers on the number line.
To find the whole numbers to the nearest half between which √40 lies, we can take the square root of the closest perfect squares.
The closest perfect squares to 40 are 36 (6*6) and 49 (7*7).
Taking the square root of 36 gives us 6, and taking the square root of 49 gives us 7.
Therefore, √40 is between 6 and 7.
To the nearest half, this can be expressed as √40 ≈ 6.5.
So the whole number to the nearest half is 7, and the rational number to the nearest half is 6.5.
Good. So... 40−−√ is between what and what?
Apologies for the confusion in my previous response. I made an error in explaining the range of values.
The square root of 40, denoted as √40, is between two whole numbers on the number line.
The closest perfect squares to 40 are 36 (6*6) and 49 (7*7).
Therefore, √40 is between the whole numbers 6 and 7.
So 40−−√ is between 6 and 7.
no, it's supposed to be between a whole number AND a rational number to the nearest half
Apologies for the misunderstanding.
To find a rational number to the nearest half that √40 is between, we need to find the whole number and the rational number that are closest to √40.
√40 is approximately 6.32455532034.
The closest whole number to √40 is 6.
To find the rational number to the nearest half, we need to determine if √40 is closer to 6 or to 7.
Since √40 is closer to 6, the rational number to the nearest half that √40 is between is 6.5.
Therefore, √40 is between the whole number 6 and the rational number 6.5 to the nearest half.
8. Using a number line, what whole number and rational number to the nearest half is 58−−√ between?(1 point)
Responses
A. between 7 and 7.5
B. between 8.5 and 9
C. between 8 and 8.5
D. between 7.5 and 8
To find the whole number and rational number to the nearest half that 58−−√ is between, we need to locate its approximate value on a number line.
√58 is approximately 7.61577.
The closest whole number to √58 is 8.
To find the rational number to the nearest half, we need to determine if √58 is closer to 8 or to 9.
Since √58 is closer to 8, the rational number to the nearest half that √58 is between is 8.5.
Therefore, 58−−√ is between the whole number 8 and the rational number 8.5 to the nearest half.
The correct answer is D. between 7.5 and 8.
Using rational approximations, what is an inequality statement comparing 81−−√ and 8–√8? Enter <, >, or =.(1 point)
To compare 81−−√ and 8–√8 using rational approximations, we can approximate the square roots.
The square root of 81 is 9, and the square root of 8 is approximately 2.828.
Therefore, 81−−√ is greater than 8–√8.
The inequality statement comparing them is:
81−−√ > 8–√8
Using rational approximations, what is an inequality statement comparing √81 and √88? Enter <, >, or =.(1 point)
Using rational approximations, we can find that the square root of 81 is exactly 9, and the square root of 88 is approximately 9.38042.
Therefore, √81 is less than √88.
The inequality statement comparing them is:
√81 < √88
Write 6,739 in expanded form.(1 point)
Responses
(7×100)+(3×10)+(9×1)
left parenthesis 7 times 100 right parenthesis plus left parenthesis 3 times 10 right parenthesis plus left parenthesis 9 times 1 right parenthesis
(6×1,000)+(7×100)+(3×10)+(0×1)
left parenthesis 6 times 1,000 right parenthesis plus left parenthesis 7 times 100 right parenthesis plus left parenthesis 3 times 10 right parenthesis plus left parenthesis 0 times 1 right parenthesis
(6×1,000)+(7×100)+(3×10)+(9×1)
left parenthesis 6 times 1,000 right parenthesis plus left parenthesis 7 times 100 right parenthesis plus left parenthesis 3 times 10 right parenthesis plus left parenthesis 9 times 1 right parenthesis
(9×1,000)+(3×100)+(7×10)+(6×1)
(6×1,000)+(7×100)+(3×10)+(9×1)
Express 811 as a repeating decimal. Mark the cycle of repeating digits with a bar.(1 point)
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To express 811 as a repeating decimal, we can divide 811 by the number 999, since 999 is the largest three-digit number and will produce a repeating decimal.
811 ÷ 999 = 0.811811811...
The cycle of repeating digits is 811, and we can mark it with a bar over the top, giving us:
0.¯811¯
Express 8/11 as a repeating decimal. Mark the cycle of repeating digits with a bar.(1 point)
To express 8/11 as a repeating decimal, we can perform long division.
When we divide 8 by 11, the decimal part starts repeating after the first digit.
8 ÷ 11 = 0.727272...
The cycle of repeating digits is 72, so we can mark it with a bar over the top, giving us:
0.¯72¯
Convert 0.72¯¯¯¯¯
to a rational number in simplest form.(1 point)
To convert 0.72¯¯¯¯¯ to a rational number in simplest form, we can use the concept of repeating decimals.
First, let's represent 0.72¯¯¯¯¯ as x:
x = 0.727272...
Now, we can multiply both sides of the equation by 100 to eliminate the repeating decimal:
100x = 72.727272...
Next, we subtract the original equation from the multiplied equation:
100x - x = 72.727272... - 0.727272...
99x = 72
Dividing both sides of the equation by 99:
99x/99 = 72/99
x = 8/11
Therefore, the rational number representation of 0.72¯¯¯¯¯ in simplest form is 8/11.
Which of the following is a rational number between 5 and 514
?(1 point)
Responses
525
5 Start Fraction 2 over 5 end fraction
513
5 Start Fraction 1 over 3 end fraction
517
5 Start Fraction 1 over 7 end fraction
26−−√
To determine which of the options is a rational number between 5 and 514, we need to consider their types.
- The number 525 is an integer, not a rational number.
- 5 Start Fraction 2 over 5 end fraction is a rational number, but it is equal to 5.4 which is greater than 5 and not between 5 and 514.
- The number 513 is an integer, not a rational number.
- 5 Start Fraction 1 over 3 end fraction is a rational number, but it is less than 5 and not between 5 and 514.
- The number 517 is an integer, not a rational number.
- √26 is an irrational number, not a rational number.
Based on the options given, there is no rational number between 5 and 514.
Which of the following is a rational number between 5 and 5 1/4
?(1 point)
Responses
525
5 Start Fraction 2 over 5 end fraction
513
5 Start Fraction 1 over 3 end fraction
517
5 Start Fraction 1 over 7 end fraction
26−−√
To determine which of the options is a rational number between 5 and 5 1/4, we need to consider their values.
- The number 525 is an integer, not a rational number.
- 5 Start Fraction 2 over 5 end fraction is a rational number, but it is equal to 5.4, which is greater than 5 1/4.
- The number 513 is an integer, not a rational number.
- 5 Start Fraction 1 over 3 end fraction is a rational number, but it is less than 5 1/4.
- The number 517 is an integer, not a rational number.
- √26 is an irrational number, not a rational number.
Based on the options given, there is no rational number between 5 and 5 1/4.
Which of the following is a rational number between 5 and 5/14
?(1 point)
Responses
5 2/5
5 1/3
5 1/7
26−−√
To determine which of the options is a rational number between 5 and 5/14, we need to consider their values.
- The number 5 2/5 is a rational number, but it is greater than 5 and not between 5 and 5/14.
- The number 5 1/3 is a rational number, but it is greater than 5 and not between 5 and 5/14.
- The number 5 1/7 is a rational number, but it is greater than 5 and not between 5 and 5/14.
- √26 is an irrational number, not a rational number.
Based on the options given, there is no rational number between 5 and 5/14.
Which of the following is a rational number between 5 and 5 1/4
?(1 point)
Responses
5 2/5
5 1/3
5 1/7
26−−√
To determine which of the options is a rational number between 5 and 5 1/4, we need to consider their values.
- The number 5 2/5 is a rational number, but it is greater than 5 1/4 and not between 5 and 5 1/4.
- The number 5 1/3 is a rational number, but it is greater than 5 1/4 and not between 5 and 5 1/4.
- The number 5 1/7 is a rational number, but it is greater than 5 1/4 and not between 5 and 5 1/4.
- √26 is an irrational number, not a rational number.
Based on the options given, there is no rational number between 5 and 5 1/4.
wrong! 5 1/7 is less than 5 1/4
Apologies for the mistake. You are correct.
To clarify, among the given options, the number 5 1/7 is indeed less than 5 1/4 and therefore falls between 5 and 5 1/4.
So, the correct answer is: 5 1/7 is a rational number between 5 and 5 1/4.
To find a rational number with a denominator of 7 that is between 7–√ and 8–√, we can convert the given numbers into decimal approximations and consider the rational numbers with a denominator of 7 within that range.
7–√ is approximately 5.07107.
8–√ is approximately 6.14214.
Considering rational numbers with a denominator of 7 within the range, we have:
5/7 ≈ 0.71429
6/7 ≈ 0.85714
Therefore, a rational number with a denominator of 7 that is between 7–√ and 8–√ is 6/7.
Apologies for the incorrect response.
To find a rational number with a denominator of 7 between 7–√ and 8–√, we need to consider the numbers 7–√ and 8–√ in decimal form.