Which statement is true about the relationships between the number sets?(1 point)
Responses
All rational numbers are also integers.
All rational numbers are also integers.
Some irrational numbers are also integers.
Some irrational numbers are also integers.
Not all natural numbers are real numbers.
Not all natural numbers are real numbers.
Whole numbers include all natural numbers and 0.
The price of a gallon of gas is $3.39910.
To determine the whole number and rational number to the nearest half that 58−−√ is between, we need to find the integers closest to it on a number line.
Approximating 58−−√ to the nearest whole number, we have:
To the left: 7
To the right: 8
Next, let's find the rational numbers to the nearest half:
To the left: 7.5
To the right: 8.0
Therefore, 58−−√ is between 7 and 8 on the number line and between 7.5 and 8.0 as rational numbers to the nearest half.
(6×1,000)+(7×100)+(3×10)+(9×1)
Whole numbers include all natural numbers and 0.
Which of the following is true about −9?(1 point)
Responses
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 an integer but not a rational number.
It is an integer but not a whole number.
It is an integer but not a whole 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)
$
what is 3.39910 shortened
Which set of numbers is always rational?(1 point)
Responses
integers
integers
fractions
fractions
decimals
decimals
positive numbers
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)
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
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
(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
(9×1,000)+(3×100)+(7×10)+(6×1)
It is both an integer and a whole number.
3.39910 can be shortened to 3.40.
fractions
The height of an equilateral triangle equals 3√2 times the side length.
Given that √3 is approximately 1.732, we can substitute the value into the equation.
Approximate height = 3(1.732) * 8 = 24.768 meters.
The diagonal of a square equals 2–√ times the side length.
Given that √2 is approximately 1.4, we can substitute the value into the equation.
Approximate length = 2(1.4) * 700 = 1960 feet.
To determine the whole number and rational number to the nearest half that 40−−√ is between, we need to find the integers closest to it on a number line.
Approximating 40−−√, which is roughly 6.325, we can identify the whole number to the left and right of it:
To the left: 6
To the right: 7
Next, let's find the rational numbers to the nearest half:
To the left: 6.5
To the right: 7.0
Therefore, 40−−√ is between 6 and 7 on the number line and between 6.5 and 7.0 as rational numbers to the nearest half.
To compare 81−−√ and 8–√8 using rational approximations, we can simplify and compare the decimal values.
Approximating the square roots:
√81 is exactly 9.
√8 is approximately 2.828.
Comparing the approximate values:
9 > 2.828
Therefore, the inequality statement is:
81−−√ > 8–√8.