which set of numbers is always irrational
non-terminating non-repeating decimals
repeating decimals
Positive decimals
Terminating decimals
non-terminating non-repeating decimals
The diagonal of a square equals √2 times the side length. Using 1.4 for the square root of 2. • Item 5
what is the approximate length in feet from one corner to an opposite corner of a square park
Item 6
that is 70 feet on a side?
To find the length from one corner to an opposite corner of a square park, you can multiply the side length by the square root of 2. Since the side length is given as 70 feet, you can calculate it as follows:
Approximate length = side length × √2
Approximate length = 70 feet × 1.4 (given approximation for √2)
Approximate length = 98 feet
So, the approximate length from one corner to an opposite corner of the square park is 98 feet.
using a number line, what whole number and a rational number to the nearest half is √30 between
√30 is it between __ and __
To determine which whole number and rational number (√30) is between on a number line, let's approximate √30 to the nearest half.
First, we need to find the perfect squares on either side of 30:
5^2 = 25
6^2 = 36
So, √30 is between √25 (which is equal to 5) and √36 (which is equal to 6) on the number line.
To find a rational number that is between √25 and √36 to the nearest half, we can take the average of the two whole numbers:
(5 + 6) / 2 = 5.5
Therefore, √30 is between 5 and 6 on the number line, and it is also between 5.5 and 6 as a rational number to the nearest half.
using a number line, what whole number in national number to the nearest half is √68 between
Between 7.5 and 8
Between 9 and 9.5
Between 8 and 8.5
Between 8.5 and 9
To determine which whole number and rational number (√68) √68 is between on a number line, let's approximate √68 to the nearest half.
First, we need to find the perfect squares on either side of 68:
8^2 = 64
9^2 = 81
So, √68 is between √64 (which is equal to 8) and √81 (which is equal to 9) on the number line.
To find a rational number that is between √64 and √81 to the nearest half, we can take the average of the two whole numbers:
(8 + 9) / 2 = 8.5
Therefore, √68 is between 8 and 9 on the number line, and it is also between 8.5 and 9 as a rational number to the nearest half.
using rational approximation, what is an inequality statement comparing √91 and √98 enter <, >, or =
The inequality is: √91__√98
To compare √91 and √98 using rational approximation, we can round these square roots to the nearest whole number since they are both already close to whole numbers.
√91 is approximately equal to 9 (since the perfect square closest to 91 is 81, and 9 squared is 81).
√98 is approximately equal to 10 (since the perfect square closest to 98 is 100, and 10 squared is 100).
So, we have √91 < √98.
write 2468 in expanded form:
(4 x 100) + (6 x 10) (8 x 1)
(8 x 1,000) + (6 × 100) + (4 x 10) + (2 × 1)
(2 x 1,000) + (4 x 100) + (6 × 10) + (0 × 1)
(2x 1,000) + (4 × 100) + (6 × 10) + (8 × 1)
(2 x 1,000) + (4 x 100) + (6 x 10) + (8 x 1)
Express 7/11 as a repeating decimal. Martha, cycle of repeating digits with a Bar.
To express 7/11 as a repeating decimal, we can perform long division:
7 ÷ 11 = 0.636363...
The decimal representation of 7/11 is 0.63 with the repeating digits 63, which can be represented as 0.63¯¯¯¯¯¯.
convert 0.09 to a rational number in simplest form?
To convert 0.09 to a rational number in simplest form, we can write it as a fraction by placing the decimal value over a denominator consisting of as many decimal places as there are in the number.
Here, 0.09 has two decimal places. So, we can write it as:
0.09 = 9/100
To simplify this fraction further, we can divide both the numerator and denominator by their greatest common divisor, which is 1 in this case.
Therefore, the simplified form of 0.09 as a rational number is 9/100.
convert 0.7 to a fraction.
The fraction equivalent of 0.7 is.
To convert 0.7 to a fraction, we can write it as 7/10.
Therefore, the fraction equivalent of 0.7 is 7/10.
which of the following is an irrational number between 4 and 8
√5
√12
√8
√17
√5
Out of the given options, only √5 is an irrational number between 4 and 8.
which of the following rational numbers is not between √3 and √6
1.8
√4
1.5
2
√4
Out of the given options, √4 is not between √3 and √6.
describe the relationship between integers and whole numbers. Are all integers also whole numbers? Are all whole numbers also integers? Give examples to support your answer.
Integers and whole numbers are closely related, but they are not exactly the same.
All integers are also whole numbers. Integers include both positive and negative whole numbers, as well as zero. For example, -3, 0, and 5 are all integers, and they are also whole numbers.
On the other hand, all whole numbers are not integers. Whole numbers include only the positive whole numbers and zero (0, 1, 2, 3, ...). They do not include negative numbers. For example, 2 and 7 are both whole numbers, but they are not integers because they are not negative.
In summary, every integer is a whole number, but not every whole number is an integer.