Which statement is true about the relationships between the number sets?
Not all natural numbers are real numbers.
All rational numbers are also integers.
Some irrational numbers are also integers.
Whole numbers include all natural numbers and 0.
Whole numbers include all natural numbers and 0.
Which of the following is true about −9?
It is both an integer and a whole number.
It is a whole number but not an integer.
It is an integer but not a whole number.
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 $3.39 9/10 (nine tenths or nine over ten in fraction) per gallon. How many dollars does a gallon cost, writing the price strictly as a decimal?
To convert the fraction 9/10 to a decimal, divide the numerator (9) by the denominator (10):
9 ÷ 10 = 0.9
Therefore, a gallon of gas costs $3.39 + $0.9 = $3.39 + $0.90 = $4.29 as a decimal.
Which set of numbers is always rational?
positive numbers
integers
decimals
fractions
The set of numbers that is always rational is fractions.
The height of an equilateral triangle equals √3/2 (3 square rooted over 2 in fraction) times the side length. Using 7/4 (seven over four in fraction) for the square root of 3, what is the approximate height in meters of an equilateral triangle with a side length of 8 meters?
To find the approximate height of an equilateral triangle with a side length of 8 meters, we need to multiply the side length by the value of √3/2.
Given that √3 is approximately 7/4, we can substitute this value into the formula:
Height = (√3/2) * Side Length
Approximating √3 as 7/4:
Height = (7/4) * 8
= 56/4
= 14 meters
Therefore, the approximate height of an equilateral triangle with a side length of 8 meters is 14 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?
To find the approximate length from one corner to an opposite corner of a square park with a side length of 700 feet, we need to multiply the side length by the value of √2.
Given that √2 is approximately 1.4, we can substitute this value into the formula:
Diagonal = √2 * Side Length
Approximating √2 as 1.4:
Diagonal = 1.4 * 700
= 980 feet
Therefore, the approximate length from one corner to an opposite corner of the square park is 980 feet.
Using a number line, what whole number and rational number to the nearest half is √40 between?
To determine the whole number and rational number that √40 is between, we can utilize a number line.
First, we need to find which whole number √40 is closest to. The square root of 40 is approximately 6.32, so it is closer to 6 than it is to 7 on the number line.
Next, we can find the closest rational number to √40 to the nearest half. The nearest half value to √40 would be √36, which is equal to 6.
Therefore, on the number line, √40 is between the whole number 6 and the rational number 6.5 (6 1/2).
Using a number line, what whole number and rational number to the nearest half is √58 between?
between 7.5 and 8
between 8 and 8.5
between 7 and 7.5
between 8.5 and 9
To determine the whole number and rational number that √58 is between, let's use a number line.
First, let's find the closest whole number to √58. The square root of 58 is approximately 7.62, so it is closer to 8 on the number line.
Next, let's find the closest rational number to √58 to the nearest half. √58 is closer to √56, which is approximately 7.48, and √59, which is approximately 7.68.
Therefore, on the number line, √58 is between the whole number 8 and the rational number 7.5 (7 and a half).
Using rational approximations, what is an inequality statement comparing 81−−√ and 8–√8? Enter <, >, or =.
To compare 81−−√ and 8–√8 using rational approximations, we can approximate the square roots to rational numbers.
Approximating √81 as 9 and √8 as 2.83 (or 2 5/6), we can compare:
9 > 2.83
Therefore, the inequality statement comparing 81−−√ and 8–√8 is:
81−−√ > 8–√8
Express 8/11 (8 over 11 in fraction) as a repeating decimal. Mark the cycle of repeating digits with a bar.
To express 8/11 as a repeating decimal, we can use long division.
When we divide 8 by 11, the decimal part starts repeating after the decimal point. The remainder 8 continues to reappear in a cyclic pattern.
0.7272...
_________
11 | 8.000
-7 7
-----
30
-22
----
80
-77
----
30
-22
----
80
-77
----
The decimal representation of 8/11 is 0.7272..., with the digits 72 repeating infinitely. Therefore, the cycle of repeating digits is marked with a bar, and the number can be written as 0.72¯.
Convert 0.72¯¯ to a rational number in simplest form.
To convert the repeating decimal 0.72¯¯ to a rational number in simplest form, we need to express it as a fraction.
Let x = 0.72¯¯.
We can multiply both sides of this equation by 100, since there are 2 digits repeating after the decimal point:
100x = 72.72¯¯
Next, we can subtract the original equation from this new equation to eliminate the repeating part:
100x - x = 72.72¯¯ - 0.72¯¯
99x = 72
Dividing both sides of this equation by 99:
x = 72/99
To simplify this fraction, we can divide 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 representation of the repeating decimal 0.72¯¯ is 8/11 in simplest form.
Which of the following is a rational number between 5 and 5 1/4 (5 and 1 over 4 in mixed number)?
5 1/7 (5 and 1 over 7 in mixed number)
5 2/5 (5 and 2 over 5 in mixed number)
√26
5 1/3 (5 and 1 over 3 in mixed number)
To find a rational number between 5 and 5 1/4, we can convert both numbers to improper fractions and look for a fraction that lies between them.
5 can be written as 5/1 and 5 1/4 can be written as 21/4.
Now, let's look at the given options:
- 5 1/7 can be written as 36/7.
- 5 2/5 can be written as 27/5.
- √26 is not a rational number since it involves taking the square root of a non-perfect square.
- 5 1/3 can be written as 16/3.
Among these options, the rational number 16/3 lies between 5 and 5 1/4.
What is a rational number with a denominator of 7 that is between √7 and √8? Write your answer as an improper fraction.
To find a rational number with a denominator of 7 that is between √7 and √8, we can convert both square roots to fractions with a denominator of 7.
√7 ≈ 2.65/7
√8 ≈ 2.83/7
To find a rational number between these two fractions, we can add them together and divide by 2:
(2.65/7 + 2.83/7) / 2 = (2.65 + 2.83) / (7 * 2) = 5.48 / 14
Simplifying the numerator and denominator:
5.48 / 14 = 548/1001
Therefore, a rational number with a denominator of 7 that is between √7 and √8 is 548/1001.