Which statement is true about the relationships between the number sets?(1 point)
Responses
Not all natural numbers are real numbers.
Not all natural numbers are real numbers.
Whole numbers include all natural numbers and 0.
Whole numbers include all natural numbers and 0.
All rational numbers are also integers.
All rational numbers are also integers.
Some irrational numbers are also integers.
Not all natural numbers are real numbers.
Which of the following is true about −9?(1 point)
Responses
It is both an integer and a whole number.
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 whole number.
It is a whole number but not an integer.
It is a whole number but not an integer.
It is an integer but not a rational number.
It is both an integer and a whole number.
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)
$3.39910 per gallon can be written as $3.40 per gallon.
Which set of numbers is always rational?(1 point)
Responses
decimals
decimals
positive numbers
positive numbers
fractions
fractions
integers
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 height of an equilateral triangle is given by the formula: height = side length * √3/2.
Using √3 = 74, we have:
height = 8 * √3/2 = 8 * 74/2 = 296/2 = 148 meters.
Therefore, the approximate height of an equilateral triangle with a side length of 8 meters is 148 meters.
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 diagonal of a square is given by the formula: diagonal = side length * √2.
Using √2 = 1.4, we have:
diagonal = 700 * √2 = 700 * 1.4 = 980 feet.
Therefore, the approximate length from one corner to an opposite corner of a square park that is 700 feet on a side is 980 feet.
Using a number line, what whole number and rational number to the nearest half is 40−−√ between?(1 point)
40−−√ is between
and
To find the whole number and rational number to the nearest half that 40−−√ is between, we can approximate the value of 40−−√.
Since the square root of 40 is approximately 6.32, and the square root of 41 is approximately 6.40, we can conclude that 40−−√ is between 6.32 and 6.40.
To find the nearest half, we round 6.32 down to 6.5 and 6.40 up to 6.5.
Therefore, 40−−√ is between 6.5 and 6.5.
Using a number line, what whole number and rational number to the nearest half is 58−−√ between?(1 point)
Responses
between 8 and 8.5
between 8 and 8.5
between 8.5 and 9
between 8.5 and 9
between 7 and 7.5
between 7 and 7.5
between 7.5 and 8
To find the whole number and rational number to the nearest half that 58−−√ is between, we can approximate the value of 58−−√.
Since the square root of 58 is approximately 7.62, and the square root of 59 is approximately 7.68, we can conclude that 58−−√ is between 7.62 and 7.68.
To find the nearest half, we can round 7.62 down to 7.5 and 7.68 up to 7.5.
Therefore, 58−−√ is between 7.5 and 7.5.
Using rational approximations, what is an inequality statement comparing 81−−√ and 8–√8? Enter <, >, or =.(1 point)
The inequality is: 81−−√
8–√8.
To compare 81−−√ and 8–√8 using rational approximations, we can simplify the square roots:
81−−√ can be approximated as 9, since the square root of 81 is exactly 9.
8–√8 can be approximated as 2.83, since the square root of 8 is approximately 2.83.
Therefore, the inequality statement is: 9 > 2.83.
Write 6,739 in expanded form.(1 point)
Responses
(9×1,000)+(3×100)+(7×10)+(6×1)
(6×1,000)+(7×100)+(3×10)+(9×1)
(6×1,000)+(7×100)+(3×10)+(0×1)
(7×100)+(3×10)+(9×1)
(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)
To express 811 as a repeating decimal, we can divide 811 by 990, as the numerator should be less than the denominator:
811 ÷ 990 = 0.818181...
The repeating decimal for 811 is 0.818181..., with the cycle of repeating digits marked with a bar over the "81".
Convert 0.72¯¯¯¯¯ to a rational number in simplest form.
To convert 0.72¯¯¯¯¯ to a rational number in simplest form, we can use the fact that repeating decimals can be represented as fractions.
Let's denote x = 0.72¯¯¯¯¯ and multiply both sides of the equation by 100 to eliminate the repeating part:
100x = 72.72¯¯¯¯¯
Now, we can subtract the original equation from the multiplied equation:
100x - x = 72.72¯¯¯¯¯ - 0.72¯¯¯¯¯
Simplifying both sides of the equation:
99x = 72
Dividing both sides by 99:
x = 72/99
To further simplify this fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 9:
x = (8 * 9) / (11 * 9)
Simplifying the fraction further:
x = 8/11
Therefore, 0.72¯¯¯¯¯ is equivalent to the rational number 8/11 in simplest form.
Which of the following is a rational number between 5 and 514 ?(1 point)
Responses
517
5 Start Fraction 1 over 7 end fraction
525
5 Start Fraction 2 over 5 end fraction
513
5 Start Fraction 1 over 3 end fraction
26−−√
5 Start Fraction 1 over 7 end fraction
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 that is between 7–√ and 8–√, we can determine the whole number part of each square root:
7–√ is between 2 and 3, since the square root of 7 is approximately 2.65.
8–√ is between 2 and 3, since the square root of 8 is exactly 2.83.
Now, we need to find a rational number with a denominator of 7 that falls between 2 and 3. One such number is 17/7, which simplifies to:
17/7 = 2 and 3/7
Therefore, a rational number with a denominator of 7 that is between 7–√ and 8–√ is 2 and 3/7.
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 as follows:
- Not all rational numbers are whole numbers. Whole numbers include all natural numbers (positive integers) and zero, while rational numbers include numbers that can be expressed as a fraction p/q, where p and q are integers and q is not equal to zero. For example, the rational number 3/2 is not a whole number because it is not an integer or zero.
- However, all whole numbers are rational numbers. This is because every whole number can be expressed as a fraction, where the denominator is 1. For example, the whole number 5 can be expressed as 5/1, which is a rational number.
In conclusion, while all whole numbers are rational numbers, not all rational numbers are whole numbers.