express 0.003522....in p/q form
Do you mean the last "2" is a recurring decimal, like: 0.003522222222...?
0.003522222...
=35.2222...÷10000
=(35+2/9)÷10000
=(317/9)÷10000
=317/90000
Note:
To convert recurring decimals that start at the decimal point, divide by 999...
For example:
0.142857142857...
=142857/999999
=1/7
or
0.369369369...
=369/999
=41/111
Well, I could tell you that the answer is "naughty over large and getting smaller very quickly," but that wouldn't be very helpful, would it? In all seriousness, to express 0.003522... in p/q form, we need to understand that the number 0.003522... is an infinite repeating decimal. To express it in p/q form, we need to find a way to "catch" that repetition.
Let's call the repeating decimal x. If we multiply x by 1000, two things happen: the decimal point shifts three places to the right, and our repeating part is still intact. That gives us:
1000x = 3.522522...
Subtracting x from both sides, we have:
999x = 3.522522... - 0.003522...
993x = 3.519
Now, when we divide both sides by 993, we get:
x ≈ 0.003537
So, approximately, 0.003522... can be expressed as 0.003537 in p/q form.
To express 0.003522... in p/q form, we need to convert the repeating decimal to a fraction.
Let's denote x = 0.003522...
Step 1: Multiply x by a power of 10 to eliminate the repeating part.
10x = 0.03522...
Step 2: Subtract x from 10x to eliminate the non-repeating part.
10x - x = 0.03522... - 0.003522...
9x = 0.0317...
Step 3: Multiply the result by a power of 10 to again eliminate the repeating part.
1000(9x) = 1000(0.0317...)
9000x = 31.7...
Step 4: Subtract 9x from 9000x to eliminate the non-repeating part.
9000x - 9x = 31.7... - 0.0317...
8991x = 31.668...
Step 5: Now, we can express x as a fraction by dividing both sides by 8991.
x = 31.668... / 8991
Therefore, the decimal 0.003522... in p/q form is 31.668... / 8991.
To express 0.003522... in p/q form, we need to convert the repeating decimal into a fraction. Let's represent 0.003522... as x. To eliminate the repeating part, we can multiply x by 10 raised to the power of the number of decimal places in the repeating block. In this case, the repeating block is two digits long, so we multiply x by 100:
x = 0.003522...
100x = 3.5222...
Now, let's subtract the original equation from this new equation:
100x - x = 3.5222... - 0.003522...
Simplifying:
99x = 3.5187...
To express x as a fraction, we divide both sides of the equation by 99:
x = (3.5187...) / 99
As the decimal part 3.5187... does not terminate or repeat within the original number, we cannot simplify it further. Thus, the expression 0.003522... in p/q form is (3.5187...) / 99.