1(Which statement is true about the relationships between the number sets?(1 point)
Responses
Whole numbers include all natural numbers and 0.
All rational numbers are also integers.
Some irrational numbers are also integers.
Not all natural numbers are real numbers.
2) Which of the following is true about −9?(1 point)
Responses
It is both an integer and a whole number.
It is an integer but not a whole number.
It is an integer but not a rational number.
It is a whole number but not an integer.
3) 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)
4) Which set of numbers is always rational?(1 point)
Responses
fractions
positive numbers
decimals
integers
5) he height of an equilateral triangle equals 3√2 times the side length. Using 74 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)
1) The statement "Whole numbers include all natural numbers and 0" is true.
2) It is both an integer and a whole number.
3) $3.399 per gallon
4) Fractions
5) The approximate height is 19.686 meters.
i need your help, please help :'(
Question
Which statement is true about the relationships between the number sets?(1 point)
Responses
All rational numbers are also integers.
Whole numbers include all natural numbers and 0.
Not all natural numbers are real numbers.
Some irrational numbers are also integers.
Which of the following is true about −9?(1 point)
Responses
It is an integer but not a whole number.
It is a whole number but not an integer.
It is both an integer and a whole number.
It is an integer but not a rational number.
1) The statement "Whole numbers include all natural numbers and 0" is true.
2) The statement "It is both an integer and a whole number" is true.
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)
Question
Which set of numbers is always rational?(1 point)
Responses
fractions
decimals
integers
positive numbers
The price of a gallon of gas in decimal form would be $3.399.
The set of numbers that is always rational is fractions.
The height of an equilateral triangle equals 3√2 times the side length. Using 74 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)
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)
The approximate height of an equilateral triangle with a side length of 8 meters, using 74 for the square root of 3, is 3*74*2 meters = 444 meters.
The approximate length from one corner to an opposite corner of a square park that is 700 feet on a side, using 1.4 for the square root of 2, is 700 * (2-√) feet = 700 * (2-1.4) feet = 700 * 0.6 feet = 420 feet.
Using a number line, what whole number and rational number to the nearest half is 40−−√ between?(1 point)
40−−√ is between
and
.
Using a number line, what whole number and rational number to the nearest half is 58−−√ between?(1 point)
Responses
between 8.5 and 9
between 8.5 and 9
between 7.5 and 8
between 7.5 and 8
between 7 and 7.5
between 7 and 7.5
between 8 and 8.5
between 8 and 8.5
40−−√ is between 6 and 6.5.
58−−√ is between 7.5 and 8.
Using rational approximations, what is an inequality statement comparing 81−−√ and 8–√8? Enter <, >, or =.(1 point)
The inequality is: 81−−√
8–√8.
Write 6,739 in expanded form.(1 point)
Responses
(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)
left parenthesis 9 times 1,000 right parenthesis plus left parenthesis 3 times 100 right parenthesis plus left parenthesis 7 times 10 right parenthesis plus left parenthesis 6 times 1 right parenthesis
(7×100)+(3×10)+(9×1)
81−−√ > 8−√8
6,739 in expanded form is: (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)
Convert 0.72¯¯¯¯¯ to a rational number in simplest form.(1 point)
Which of the following is a rational number between 5 and 514?(1 point)
Responses
26−−√
start root 26 end root
525
5 Start Fraction 2 over 5 end fraction
517
5 Start Fraction 1 over 7 end fraction
513
5 Start Fraction 1 over 3 end fraction
811 as a repeating decimal is 811.000...
To convert 0.72¯¯¯¯¯ to a rational number in simplest form, we can express it as 0.727272..., where the cycle of repeating digits is marked with a bar. This can be simplified as 8/11.
A rational number between 5 and 514 is 513.
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)
$$
To find a rational number with a denominator of 7 between 7–√ and 8–√, we need to find a fraction of the form n/7 such that n is between the values of 7–√ and 8–√.
7–√ ≈ 7 - 2.6 = 4.4
8–√ ≈ 8 - 2.8 = 5.2
Therefore, a rational number with a denominator of 7 that is between 7–√ and 8–√ is 19/7 in improper fraction form.
Describe the relationship between rational numbers and whole numbers. Are all rational numbers also whole numbers? Are all whole numbers also rational numbers? Give examples to support your answer.(4 points)
The relationship between rational numbers and whole numbers is that every whole number can also be considered a rational number. However, not all rational numbers are whole numbers.
A rational number can be defined as any number that can be expressed as the quotient or fraction of two integers, where the denominator is not zero. Whole numbers, on the other hand, are non-negative integers (including zero) without any fractional or decimal parts.
Examples:
- All whole numbers are rational numbers. For example, 3 is a whole number and can also be expressed as the rational number 3/1.
- Not all rational numbers are whole numbers. For example, the rational number 2/3 is not a whole number as it is not an integer and has a fractional part.
CAN SOME ONE BUT JUST THE ANCERS SO I DON'T NEED TO TRY TO DESIFER ALL OF THIS??!?! ^
Certainly! Here are the answers to the questions:
1) No, not all rational numbers are whole numbers. Whole numbers are a subset of rational numbers, but not all rational numbers are whole numbers. For example, 1/2 is a rational number but not a whole number.
2) Yes, all whole numbers are rational numbers. Since whole numbers can be expressed as fractions with a denominator of 1, they can also be considered rational numbers. For example, 5 can be written as 5/1.
3) An example of a rational number that is not a whole number is 3/4.
4) An example of a whole number that is also a rational number is 2.
that don't help
I apologize for any confusion caused. Here are the simplified answers to your questions:
Question 1: No, not all rational numbers are whole numbers. Example: 1/2 is a rational number but not a whole number.
Question 2: Yes, all whole numbers are rational numbers. Example: 5 can be expressed as the rational number 5/1.
Question 3: An example of a rational number that is not a whole number is 3/4.
Question 4: An example of a whole number that is also a rational number is 2.
what about 10-15 i can't find the ancer for them
Apologies for the confusion. Here are the answers to the remaining questions:
Question 10: A rational number with a denominator of 7 that is between 7–√ and 8–√ in improper fraction form is 12/7.
Question 15: The relationship between rational numbers and whole numbers is that every whole number can also be considered a rational number because whole numbers can be expressed as fractions with a denominator of 1. However, not all rational numbers are whole numbers. For example, 1/2 is a rational number but not a whole number, while 2/1 is a whole number and also a rational number.
Write 6,739 in expanded form.(1 point)
Responses
(9×1,000)+(3×100)+(7×10)+(6×1)
left parenthesis 9 times 1,000 right parenthesis plus left parenthesis 3 times 100 right parenthesis plus left parenthesis 7 times 10 right parenthesis plus left parenthesis 6 times 1 right parenthesis
(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)+(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
(6×1,000)+(7×100)+(3×10)+(0×1)
The expanded form of 6,739 is (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)
$$
To express 811 as a repeating decimal, we can divide 811 by 9 and observe the repeating pattern.
811 ÷ 9 = 90 with a remainder of 1.
We can see that the remainder is 1, and it repeats indefinitely after the decimal point. So, the repeating decimal representation of 811 is 90.1111... where the cycle of repeating digits is marked with a bar over the digit 1. Therefore, the expression is 90.1¯¯¯¯¯.
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 represent the repeating decimal as a fraction.
Let's denote x as 0.72¯¯¯¯¯.
Multiplying both sides of this equation by 100 gives us:
100x = 72.7272¯¯¯¯¯
Subtracting the original equation from the above equation eliminates the repeating portion:
100x - x = 72.7272¯¯¯¯¯ - 0.72¯¯¯¯¯
99x = 72
Dividing both sides of the equation by 99 yields:
x = 72/99
The fraction 72/99 can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 9:
x = (72 ÷ 9) / (99 ÷ 9)
x = 8/11
Therefore, the rational number representation of 0.72¯¯¯¯¯ is 8/11 in its simplest form.
Which of the following is a rational number between 5 and 514?(1 point)
Responses
525
5 Start Fraction 2 over 5 end fraction
26−−√
start root 26 end root
513
5 Start Fraction 1 over 3 end fraction
517
The rational number between 5 and 514 is 513.
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)
To find a rational number with a denominator of 7 between 7–√ and 8–√, we need to find a fraction of the form n/7 such that n is between the values of 7–√ and 8–√.
Let's calculate the approximate values of 7–√ and 8–√:
7–√ ≈ 7 - 2.65 ≈ 4.35
8–√ ≈ 8 - 2.83 ≈ 5.17
Therefore, a possible rational number with a denominator of 7 between 7–√ and 8–√ can be 29/7 in improper fraction form.
Using the numbers 3.14 and π as examples, describe the difference between rational and irrational numbers in 1–2 sentences.
A rational number can be expressed as a fraction or a ratio of two integers, such as 3.14 = 314/100. On the other hand, an irrational number, like π, cannot be expressed as a fraction and has an infinite, non-repeating decimal representation.
can you say that again but mix it up a bit
Sure!
A rational number, such as 3.14, can be written as a fraction with both the numerator and denominator as integers, like 314/100. However, an irrational number, like π, cannot be expressed as a fraction and has a decimal representation that neither terminates nor repeats.