Do these numbers have an infinite decimal expansion or a finite decimal expansion?
15/25
2/9
5/16
6/13
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.
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.
Write the infinite decimal expansion as a fraction
0.323232...
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
What is the largest integer with an irrational square root between 3 and 4
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).
What is the largest integer whose square root is an irrational number between 3 and 4?
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.
What integers lie between 3 and 4
The integers between 3 and 4 are 4 and 5.
What irrational integers lie between 3 and 4
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.
What irrational square root integers lie between 3 and 4
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.
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.
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.
Find a rational number with one decimal place that ia between the square root of 17 and the square rot of 18
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.
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