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Using a number line, what whole number and rational number to the nearest half is 40−−√ between?(1 point)
40−−√ is between __ and __.
40−−√ is between 6 and 7.
Using a number line, what whole number and rational number to the nearest half is 58−−√ between?(1 point)
between 8 and 8.5
between 8.5 and 9
between 7.5 and 8
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.
The inequality statement is: 81−−√ > 8 – √8.
Write 6,739 in expanded form.(1 point)
(7×100)+(3×10)+(9×1)
(6×1,000)+(7×100)+(3×10)+(0×1)
(9×1,000)+(3×100)+(7×10)+(6×1)
(6×1,000)+(7×100)+(3×10)+(9×1)
(6×1,000)+(7×100)+(3×10)+(9×1)
Express 811 as a repeating decimal. Mark the cycle of repeating digits with a bar.(1 point)
The number 811 as a repeating decimal is 811.000000...
Convert 0.72¯¯¯¯¯ to a rational number in simplest form.(1 point)
Let x = 0.7272...
Multiplying both sides of the equation by 100, we get:
100x = 72.7272...
Subtracting the original equation from the new equation, we get:
100x - x = 72.7272... - 0.7272...
Simplifying, we have:
99x = 72
Dividing both sides of the equation by 99, we get:
x = 72/99
Thus, 0.7272... is equal to 72/99 in simplest form.
Which of the following is a rational number between 5 and 514?(1 point)
Responses
513
5 Start Fraction 1 over 3 end fraction
525
5 Start Fraction 2 over 5 end fraction
517
5 Start Fraction 1 over 7 end fraction
26−−√
One of the rational numbers between 5 and 514 is 5 + 1/3.
What is a rational number with a denominator of 7 that is between 7–√ and 8–√. Write your answer as an improper fraction.(1 point)
To find a rational number with a denominator of 7 between 7–√ and 8–√, we can convert these expressions into irrational fractions:
7–√ = 7 - √7
8–√ = 8 - √8
To simplify further, let's express √7 and √8 as decimals:
√7 ≈ 2.65
√8 ≈ 2.83
So, the range we have now is between 7 - 2.65 and 8 - 2.83.
To get a rational number with a denominator of 7, we can choose the closest rational number to √7 and √8. In this case, the closest rational number to both is 2.6.
Therefore, a rational number with a denominator of 7 between 7–√ and 8–√ is:
7 - 2.6 = 4.4/7
Describe the relationship between rational numbers and whole numbers. Are all rational numbers also whole numbers? Are all whole numbers also rational numbers? Give examples to support your answer.(4 points)
Rational numbers and whole numbers are related but are not the same.
Not all rational numbers are whole numbers. Rational numbers include fractions and decimals that can be written as a ratio of two integers. Whole numbers, on the other hand, consist of positive integers and zero.
For example, 0.5 is a rational number since it can be written as 1/2, but it is not a whole number.
However, all whole numbers are rational numbers. This is because whole numbers can be expressed as a fraction with a denominator of 1. For instance, the whole number 5 can be written as 5/1, which is a rational number.
Therefore, while all whole numbers are rational, not all rational numbers are whole numbers.