Which set of numbers is always rational?(1 point)
Responses
integers
integers
positive numbers
positive numbers
decimals
decimals
negative numbers
negative numbers
integers
Using a number line, what whole number and rational number to the nearest half is 20−−√
between?(1 point)
20−−√ is between
and
20−−√ is between 4 and 5.
Write 1,357 in expanded form.
1,000 + 300 + 50 + 7
Write 1,357 in expanded form.(1 point)
Responses
(7 x 1,000) + (5 x 100) + (3 x 10) + (1 x 1)
(7 x 1,000) + (5 x 100) + (3 x 10) + (1 x 1)
(3 x 100) + (5 x 10) + (7 x 1)
(3 x 100) + (5 x 10) + (7 x 1)
(1 x 1,000) + (3 x 100) + (5 x 10) + (7 x 1)
(1 x 1,000) + (3 x 100) + (5 x 10) + (7 x 1)
(1 x 1,000) + (3 x 100) + (5 x 10) + (7 x 1)
(1 x 1,000) + (3 x 100) + (5 x 10) + (7 x 1)
(1 x 1,000) + (3 x 100) + (5 x 10) + (7 x 1)
Which of the following is an irrational number between 8 and 10?(1 point)
Responses
62−−√
square root of 62
120−−−√
square root of 120
50−−√
square root of 50
84−−√
square root of 62
Convert 0.18¯¯¯¯¯
to a rational number in simplest form.
To convert the repeating decimal 0.18¯¯¯¯¯ to a rational number, let's assign a variable to the repeating part.
Let x = 0.18¯¯¯¯¯
Multiply both sides of the equation by 100 to move the decimal point two places to the right:
100x = 18.18¯¯¯¯¯
Subtract the original equation from the new equation to eliminate the repeating part:
100x - x = 18.18¯¯¯¯¯ - 0.18¯¯¯¯¯
99x = 18
Divide both sides by 99 to solve for x:
x = 18/99
Simplifying the fraction, we get:
x = 2/11
Therefore, 0.18¯¯¯¯¯ = 2/11.
Using a number line, what whole number and rational number to the nearest half is 32−−√
between?(1 point)
Responses
between 5 and 5.5
between 5 and 5.5
between 6 and 6.5
between 6 and 6.5
between 5.5 and 6
between 5.5 and 6
between 6.5 and 7
32−−√ is between 5 and 5.5.
Convert 0.5¯¯¯
to a fraction.(1 point)
The fraction equivalent of 0.5¯¯¯ is
To convert the repeating decimal 0.5¯¯¯ to a fraction, let's assign a variable to the repeating part.
Let x = 0.5¯¯¯
Multiply both sides of the equation by 10 to move the decimal point to the right:
10x = 5.5¯¯¯
Subtract the original equation from the new equation to eliminate the repeating part:
10x - x = 5.5¯¯¯ - 0.5¯¯¯
9x = 5
Divide both sides by 9 to solve for x:
x = 5/9
Therefore, 0.5¯¯¯ = 5/9.
Determine for each number whether it is a rational or irrational number.(2 points)
Rational Irrational
1.3¯¯¯
Rational – 1 point repeating 3
Irrational – 1 point repeating 3
π2
Rational – pi over 2
Irrational – pi over 2
3–√
Rational – square root of 3
Irrational – square root of 3
5117
Rational – 5 and 1 over 17
Irrational – 5 and 1 over 17
−25−−√
1.3¯¯¯ is a rational number.
π^2 is an irrational number.
√3 is an irrational number.
5117 is a rational number.
-25−−√ is an irrational number.
Karissa says the number 17 is an irrational number. Which statement best explains whether Karissa is correct?(1 point)
Responses
Karissa is correct because 17 only has 2 factors.
Karissa is correct because 17 only has 2 factors.
Karissa is incorrect because 17 can be written as a fraction.
Karissa is incorrect because 17 can be written as a fraction.
Karissa is correct because 17 is not written as a fraction.
Karissa is correct because 17 is not written as a fraction.
Karissa is incorrect because 17 only has 2 factors.
Karissa is incorrect because 17 can be written as a fraction.
Which of the following rational numbers is between 5–√ and 10−−√
?
To find a rational number between 5−√ and 10−−√, we need to find a number that is greater than 5−√ but less than 10−−√.
One possible rational number between these two values is 7−√.
Which of the following rational numbers is between 5–√ and 10−−√
?(1 point)
Responses
2.5
2 point 5
3
3
16−−√
square root of 16
4–√
To find a rational number between 5−√ and 10−−√, we can simplify them as follows:
5−√ ≈ 5−2.236 ≈ 2.764
10−−√ ≈ 10−3.162 ≈ 6.838
Therefore, a rational number between 5−√ and 10−−√ is 3.