Asked by Dllhwvs

Do these numbers have an infinite decimal expansion or a finite decimal expansion?

15/25
2/9
5/16
6/13
Answered by GPT 3.5
The numbers 15/25 and 5/16 have a finite decimal expansion because their denominators are powers of 10.

15/25 simplifies to 3/5, which has a finite decimal expansion of 0.6.

5/16 also has a finite decimal expansion that is approximately 0.3125.

On the other hand, the numbers 2/9 and 6/13 have an infinite decimal expansion.

2/9 can be written as 0.2222..., where the digit '2' repeats infinitely.

Similarly, 6/13 can be expressed as 0.461538..., where the sequence of digits repeats infinitely.
Answered by Dllhwvs
Write the infinite decimal expansion as a fraction

0.323232...
Answered by GPT 3.5
Let's denote the infinite decimal expansion 0.323232... as x. To convert this infinite decimal expansion into a fraction, we can create an equation by multiplying x by a power of 10 to align the decimal point with the repeating pattern.

Let's multiply x by 100, written as 10^2, to move the repeating pattern two places to the left:

100x = 32.323232...

Now, subtract x from 100x to eliminate the repeating part:

100x - x = 32.323232... - 0.323232...
99x = 32

Divide both sides by 99:

x = 32/99

Therefore, the infinite decimal expansion 0.323232... can be written as the fraction 32/99.
Answered by Dllhwvs
Which of the following is an irrational number between 5 and 7

square root of 6
Square root of 12
Square root of 27
Square root of 36
Answered by GPT 3.5
The square root of 6 is an irrational number between 5 and 7.
Answered by Dllhwvs
What is the largest integer with an irrational square root between 3 and 4
Answered by GPT 3.5
The largest integer with an irrational square root between 3 and 4 is 3. The square root of 3 is an irrational number, and it lies between the square roots of 4 (which is 2) and 9 (which is 3).
Answered by Dllhwvs
What is the largest integer whose square root is an irrational number between 3 and 4?
Answered by GPT 3.5
The largest integer whose square root is an irrational number between 3 and 4 is 3. The square root of 3 is an irrational number, and it lies between the integers 2 and 3.
Answered by Dllhwvs
What integers lie between 3 and 4
Answered by GPT 3.5
The integers between 3 and 4 are 4 and 5.
Answered by Dllhwvs
What irrational integers lie between 3 and 4
Answered by GPT 3.5
There are no irrational integers lying between 3 and 4. Integers are by definition rational numbers, meaning they can be expressed as fractions or whole numbers. Irrational numbers cannot be expressed as fractions or whole numbers, and therefore cannot be integers.
Answered by Dllhwvs
What irrational square root integers lie between 3 and 4
Answered by GPT 3.5
There are no integers with irrational square roots between 3 and 4.

The integers between 3 and 4 are 4 and 5. The square root of 4 is 2, which is a rational number. The square root of 5 is approximately 2.236, which is also irrational. However, 2.236 is not an integer, so there are no integers with irrational square roots between 3 and 4.
Answered by Dllhwvs
Find a rational number between 2 and 2 1/4 using the method of adding the numbers together and dividing by 2. Write the answer as a mixed number.
Answered by GPT 3.5
To find a rational number between 2 and 2 1/4 using the method of adding the numbers together and dividing by 2, we follow these steps:

Step 1: Convert 2 1/4 to an improper fraction.
2 1/4 = 9/4

Step 2: Add the two numbers together.
2 + 9/4 = 8/4 + 9/4 = 17/4

Step 3: Divide the sum by 2.
(17/4) ÷ 2 = 17/4 × 1/2 = 17/8

Step 4: Simplify the fraction.
17 ÷ 8 = 2 remainder 1
17/8 can be rewritten as 2 1/8.

Therefore, a rational number between 2 and 2 1/4 using the method of adding the numbers together and dividing by 2 is 2 1/8.
Answered by Dllhwvs
Find a rational number with one decimal place that ia between the square root of 17 and the square rot of 18
Answered by GPT 3.5
To find a rational number with one decimal place between the square root of 17 and the square root of 18, we can approximate the square roots and then round to one decimal place.

The square root of 17 is approximately 4.123105625617661, and the square root of 18 is approximately 4.242640687119285.

To find a rational number between these two values, we can use the average of the two square roots:

(4.123105625617661 + 4.242640687119285) / 2 ≈ 4.18287315637

Rounding this value to one decimal place, we get 4.2.

Therefore, a rational number with one decimal place between the square root of 17 and the square root of 18 is 4.2.
Answered by Dllhwvs
Which of the following is between pi and square root of 11

Square root of 10
Square root of 12
Square root of 8
Square root of 7
Answered by GPT 3.5
The square root of 10 is between pi and the square root of 11.