Which statement is true about the relationships between the number sets?(1 point)
Responses
All rational numbers are also integers.
Some irrational numbers are also integers.
Whole numbers include all natural numbers and 0.
Not all natural numbers are real numbers.
Whole numbers include all natural numbers and 0.
It is both an integer and a whole number.
The price of gas is $3.39 9/10 per gallon. To write this as a decimal, we can ignore the fraction and consider the decimal part. 9/10 is equivalent to 0.9.
So, a gallon costs $3.39 + $0.9 = $<<3.39+0.9=4.29>>4.29.
The length of the diagonal of a square is given by the formula:
diagonal = √2 * side length
Given that √2 is approximately 1.4, we can substitute this value into the formula:
diagonal = 1.4 * 700
diagonal = 980 feet
Therefore, the approximate length from one corner to an opposite corner of the square park that is 700 feet on a side is 980 feet.
Using rational approximations, what is an inequality statement comparing √81 and √88? Enter <, >, or =.(1 point)
Using rational approximations, we can approximate √81 to be 9 and √88 to be approximately 9.38.
So, the inequality statement comparing √81 and √88 would be:
√81 < √88
Express 8/11 as a repeating decimal. Mark the cycle of repeating digits with a bar.(1 point)
To express 8/11 as a repeating decimal, we perform long division:
0. 72
11|8
-77
30
-22
80
-77
30
-22
80
-77
30
-22
80
-77
30
-22
80
-77
30
-22
80
-77
30
-22
The cycle of repeating digits is 72, indicating that 8/11 as a repeating decimal is approximately 0.72 (or 0.7272... with the 72 part repeating).
Convert 0.72¯¯¯¯¯ to a rational number in simplest form.(1 point)
To convert the repeating decimal 0.72¯¯¯¯¯ to a rational number, we can use a variable to represent the repeating decimal. Let's say x = 0.72¯¯¯¯¯.
Multiplying both sides of the equation by 100 (to remove the decimal):
100x = 72.7272¯¯¯¯¯
Subtracting the original equation from the multiplied equation:
100x - x = 72.7272¯¯¯¯¯ - 0.72¯¯¯¯¯
Simplifying:
99x = 72.0072
Dividing both sides by 99:
x = 72.0072/99
To express x as a simplified rational number, we can reduce the fraction 72.0072/99 by dividing both the numerator and denominator by their greatest common divisor:
x = 7200.72/9900
x = 36/50
Therefore, the rational number equivalent to 0.72¯¯¯¯¯ is 36/50, which can be further simplified to 18/25 by dividing both the numerator and denominator by their greatest common divisor of 2.
So, 0.72¯¯¯¯¯ is equivalent to the rational number 18/25 in simplest form.