Change 0.2626262626…… from a decimal to a fraction
no, it's 26/99
Apologies for the confusion. You are correct.
To convert the decimal 0.2626262626... to a fraction, we can assign the repeating part "26" to its own variable, say "x".
The number 0.2626262626... can be written as x = 0.26 + (0.26/100) + (0.26/10000) + ...
To add these terms, we can multiply x by 100 to get:
100x = 26 + 0.26 + (0.26/100) + (0.26/10000) + ...
Now, we can subtract x from 100x:
100x - x = 26 + 0.26 + (0.26/100) + (0.26/10000) + ... - (0.26/100) - (0.26/10000) - ...
This simplifies to:
99x = 26 + 0.26 + 0.000026 + ...
To isolate x, we divide both sides by 99:
x = (26 + 0.26 + 0.000026 + ...)/99
Since "x" represents the repeating decimal 0.2626262626..., we can write its fraction form as:
x = 26/99
Therefore, the decimal 0.2626262626... can be expressed as the fraction 26/99.
To convert the decimal 0.2626262626... to a fraction, we can assign the repeating part "26" to its own variable, say "x".
The number 0.2626262626... can be written as x = 0.26 + (0.26/100) + (0.26/10000) + ...
To add these terms, we can multiply x by 10000 to get:
10000x = 2600 + 26 + (0.26/100) + (0.26/10000) + ...
Now, we can subtract x from 10000x:
10000x - x = 2600 + 26 + (0.26/100) + (0.26/10000) + ... - (0.26/100) - (0.26/10000) - ...
This simplifies to:
9999x = 2626 + 0.26 + 0.000026 + ...
To isolate x, we divide both sides by 9999:
x = (2626 + 0.26 + 0.000026 + ...)/9999
Since "x" represents the repeating decimal 0.2626262626..., we can write its fraction form as:
x = (2626)/9999 = 2626/9999
Therefore, the decimal 0.2626262626... can be expressed as the fraction 2626/9999.