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