Express the repeating decimal as a ratio of two integers.
1.23535353535...
here is one way...
let x = 1.23535353...
1000x= 1235.35353... (#1)
10x = 12.353535.. (#2)
subtract #1 - #2 :
990x = 1223
x = 1123/990 , the answer that Bosnian gave you
1223 / 990
can you explain how you got that?
1 / 5 = 0.2
1 / 198 = 0.0050505050
7 * 1 / 198 = 7 / 198 = 0. 0353535
1.23535353535 = 1 + 1 / 5 + 7 / 198
198 * 5 = 990
1 = 990 / 990
1 / 5 = 1 * 198 / 990 = 198 / 990
7 / 198 = 5 * 7 / 990 = 35 / 990
1 + 1 / 5 + 7 / 198 =
990 / 990 + 198 / 990 + 35 / 990 =
1223 / 990
Sure! Let's take a closer look at the repeating decimal 1.23535353535...
If we let x = 1.23535353535..., we can multiply both sides of the equation by 100 to eliminate the decimal point:
100x = 123.53535353535...
Now, if we subtract the original equation x from the new equation 100x, the repeating parts will cancel out:
100x - x = 123.53535353535... - 1.23535353535...
This simplifies to:
99x = 122.3
To express this repeating decimal as a ratio of two integers, we can simplify the equation further:
99x = 122.3
x = 122.3/99
Thus, the repeating decimal 1.23535353535... can be expressed as a ratio of two integers: 122.3/99.
To express the repeating decimal 1.23535353535... as a ratio of two integers, we first need to understand the pattern of the repeating decimal.
Let's denote x as the repeating decimal 0.35353535...
To find the value of x, we can multiply it by 100 to move the decimal point two places to the right:
100x = 35.35353535...
Next, we subtract x from 100x to eliminate the repeating part:
100x - x = 35.35353535... - 0.35353535...
Simplifying the equation, we get:
99x = 35
Now we can solve for x by dividing both sides of the equation by 99:
x = 35/99
Therefore, the repeating decimal 1.23535353535... can be expressed as a ratio of two integers: 35/99.