The statement "all integers are whole numbers" is true.
The statement "not all natural numbers are rational" is also true. Rational numbers are numbers that can be expressed as a fraction or ratio of two integers, while natural numbers are only positive integers. Therefore, not all natural numbers can be expressed as a rational number (e.g. √2 is a natural number but is irrational).
The statement "some irrational numbers are rational" is false. Irrational numbers are numbers that cannot be expressed as a fraction or ratio of two integers. Therefore, by definition, irrational numbers cannot be rational numbers.
The statement "all natural numbers are integers" is true. Natural numbers include all positive integers, and integers include all positive and negative whole numbers.
Which statement is true about the relationships between the number sets?
all intergers are whole numbers
not all natural numbers are rational
some irrational numbers are rational
all natural numbers are integers
25 answers
Which of the following is true about the number 1/6 ?
it's a rational number but not a real number
it's both an integer and a rational number
It's both an irrational number and a real number
It's a rational number but not a whole number
it's a rational number but not a real number
it's both an integer and a rational number
It's both an irrational number and a real number
It's a rational number but not a whole number
The statement "it's a rational number but not a real number" is false. The number 1/6 is both a rational number and a real number.
The statement "it's both an integer and a rational number" is false. Integers are whole numbers (negative, zero, and positive) and do not include fractions like 1/6. Therefore, 1/6 is not an integer.
The statement "it's both an irrational number and a real number" is also false. Irrational numbers are numbers that cannot be expressed as a fraction or ratio of two integers. Since 1/6 can be expressed as a fraction, it is not an irrational number. However, it is a real number as it can be plotted on the number line.
The statement "it's a rational number but not a whole number" is true. Rational numbers can be expressed as a fraction or ratio of two integers, which 1/6 is. Whole numbers are integers that are greater than or equal to zero. Since 1/6 is a fraction, it is not a whole number.
The statement "it's both an integer and a rational number" is false. Integers are whole numbers (negative, zero, and positive) and do not include fractions like 1/6. Therefore, 1/6 is not an integer.
The statement "it's both an irrational number and a real number" is also false. Irrational numbers are numbers that cannot be expressed as a fraction or ratio of two integers. Since 1/6 can be expressed as a fraction, it is not an irrational number. However, it is a real number as it can be plotted on the number line.
The statement "it's a rational number but not a whole number" is true. Rational numbers can be expressed as a fraction or ratio of two integers, which 1/6 is. Whole numbers are integers that are greater than or equal to zero. Since 1/6 is a fraction, it is not a whole number.
A sign in a gas station advertises gas at the rate listed below. How many dollars does a gallon cost, writing the price strictly as a decimal?
$4.12 9/10
$4.12 9/10
To write the price strictly as a decimal, we need to convert the fraction 9/10 to a decimal. To do this, we divide 9 by 10:
9 ÷ 10 = 0.9
Now we can write the price strictly as a decimal:
$4.12 + 0.9 = $4.129
Therefore, a gallon of gas costs $4.129.
9 ÷ 10 = 0.9
Now we can write the price strictly as a decimal:
$4.12 + 0.9 = $4.129
Therefore, a gallon of gas costs $4.129.
Which set of numbers is always rational
The set of numbers that is always rational is the set of integers. Integers include all whole numbers (positive, negative, and zero) and can be expressed as a ratio of two integers.
The height of an equilateral triangle equals √3/2 times the side length. What is the approximate height in meters of an equilateral triangle with a side length of 16 meters?
To find the height of an equilateral triangle with a side length of 16 meters, we can use the formula given, which states that the height is equal to (√3/2) times the side length.
First, let's calculate (√3/2) times 16:
(√3/2) * 16 = (1.732/2) * 16 = 0.866 * 16 = 13.856
Therefore, the approximate height of the equilateral triangle is approximately 13.856 meters.
First, let's calculate (√3/2) times 16:
(√3/2) * 16 = (1.732/2) * 16 = 0.866 * 16 = 13.856
Therefore, the approximate height of the equilateral triangle is approximately 13.856 meters.
The diagonal of a square equals √2 times the side length. Using 1.4 for √2, what is the approximate length in feet from one corner to an opposite corner of a square park that is 300 feet on a side?
To find the length from one corner to an opposite corner of a square park with a side length of 300 feet, we can use the formula given, which states that the diagonal is equal to √2 times the side length.
First, let's calculate √2 times 300 using 1.4 as an approximation for √2:
1.4 * 300 = 420
Therefore, the approximate length from one corner to an opposite corner of the square park is approximately 420 feet.
First, let's calculate √2 times 300 using 1.4 as an approximation for √2:
1.4 * 300 = 420
Therefore, the approximate length from one corner to an opposite corner of the square park is approximately 420 feet.
What whole number and rational number to the nearest half is √128 between?
To find the whole number and rational number to the nearest half that √128 falls between, we can calculate the square root of 128 and identify the two numbers it lies between.
√128 ≈ 11.3137
To the nearest half, √128 falls between:
11 and 11.5,
or
11.5 and 12.
Therefore, the whole number to the nearest half is 11 and the rational number to the nearest half is 11.5.
√128 ≈ 11.3137
To the nearest half, √128 falls between:
11 and 11.5,
or
11.5 and 12.
Therefore, the whole number to the nearest half is 11 and the rational number to the nearest half is 11.5.
hat whole number and rational number to the nearest half is √8 between?
To find the whole number and rational number to the nearest half that √8 falls between, we can calculate the square root of 8 and identify the two numbers it lies between.
√8 ≈ 2.8284
To the nearest half, √8 falls between:
2 and 2.5,
or
2.5 and 3.
Therefore, the whole number to the nearest half is 2 and the rational number to the nearest half is 2.5.
√8 ≈ 2.8284
To the nearest half, √8 falls between:
2 and 2.5,
or
2.5 and 3.
Therefore, the whole number to the nearest half is 2 and the rational number to the nearest half is 2.5.
Using rational approximations, what is an inequality statement comparing √72 and √76?
To compare √72 and √76 using rational approximations, we can calculate the square roots and compare the results:
√72 ≈ 8.4853
√76 ≈ 8.7178
Since 8.4853 is less than 8.7178, we can write the inequality statement as:
√72 < √76
√72 ≈ 8.4853
√76 ≈ 8.7178
Since 8.4853 is less than 8.7178, we can write the inequality statement as:
√72 < √76
Write 5,143 in expanded form
5,143 in expanded form is:
5,000 + 100 + 40 + 3.
5,000 + 100 + 40 + 3.
Express 8/27 as a repeating decimal.
To express 8/27 as a repeating decimal, we need to perform long division. Here's the process:
0.296296...
----------------
27 | 8.0000000000000
- 7.56
0.440
- 0.405
0.350
- 0.324
0.260
- 0.243
0.170
- 0.162
0.080
- 0.081
-0.001
The division keeps repeating from where the remainder becomes zero. Therefore, 8/27 as a repeating decimal is approximately 0.296296...
0.296296...
----------------
27 | 8.0000000000000
- 7.56
0.440
- 0.405
0.350
- 0.324
0.260
- 0.243
0.170
- 0.162
0.080
- 0.081
-0.001
The division keeps repeating from where the remainder becomes zero. Therefore, 8/27 as a repeating decimal is approximately 0.296296...
Which of the following is a rational number between 3 and 3 1/6
To find a rational number between 3 and 3 1/6, we can determine the average of these two numbers.
The average is calculated as follows:
(3 + 3 1/6) ÷ 2
Converting 3 1/6 to an improper fraction:
3 1/6 = (3 * 6 + 1) / 6 = 19/6
Now, calculating the average:
(3 + 19/6) ÷ 2 = (18/6 + 19/6) ÷ 2 = 37/6 ÷ 2 = 37/12
Therefore, a rational number between 3 and 3 1/6 is 37/12.
The average is calculated as follows:
(3 + 3 1/6) ÷ 2
Converting 3 1/6 to an improper fraction:
3 1/6 = (3 * 6 + 1) / 6 = 19/6
Now, calculating the average:
(3 + 19/6) ÷ 2 = (18/6 + 19/6) ÷ 2 = 37/6 ÷ 2 = 37/12
Therefore, a rational number between 3 and 3 1/6 is 37/12.
What is a rational number with a denominator of 7 that is between √11 and √12. Write your answer as an improper fraction
To find a rational number with a denominator of 7 that is between √11 and √12, we can find a common denominator and choose a numerator that falls between the square roots.
√11 is between 3 and 4, while √12 is between 3 and 4.5.
For a denominator of 7, we can choose a numerator such as 17 to ensure it falls between √11 and √12.
Therefore, a rational number with a denominator of 7 that is between √11 and √12 is 17/7 as an improper fraction.
√11 is between 3 and 4, while √12 is between 3 and 4.5.
For a denominator of 7, we can choose a numerator such as 17 to ensure it falls between √11 and √12.
Therefore, a rational number with a denominator of 7 that is between √11 and √12 is 17/7 as an improper fraction.
1 answer