Maths-
General
Easy
Question
Convert the following repeating decimals to fractions
d) 3.25252525252...............
Hint:
Perform necessary multiplications to make it as a fraction.
The correct answer is: 322/99
Complete step by step solution:
(d) Let x = 0.25252525
Now multiply by 100 on both the sides,
We get, 100x = 25.252525
On subtracting x from both the sides, we have
![table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell 100 x minus x equals 25.252525 minus 0.25252525 end cell row cell not stretchy rightwards double arrow 99 x equals 25 end cell row cell not stretchy rightwards double arrow x equals 25 over 99 end cell end table](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAR8AAABTCAYAAACmugPuAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAva/WvxwAABbJJREFUeNrt3TFoHTcYwHFRggklBEoIHjwUjCmlFC+mQ8kQDKF4MB4CHUKnEOgcirfQKQRMhlBKKJRiOpgQKKGEULqEYELoUDCmlAylUELGLBkyGGMCrj6ko68vp3uS7k5S7v4/+MDv/Fn3LJ3POt07SalmH+j4WscfDTmndXyn43cb39ttsXlDdk7HPR2vdBzZev2iJu+4IVKVXXp5XQk9LsdWz9nabUfHlzMKeKRjY+L1ut0Wmzdkj3Vc0nHKvv5Ix29223RD5i679PK6Enpcjq2es7ebq+DPdXxbs/2bqTfnmzdG7+v4s6eG7Lrs0ssL1dVxObZ6TtpuroKlO/ZZzfZV+73QPHFFx1ZN7nX7va6l3l+dwx4bsuuySy8vRMhxST1najdXwS91zNVsl20vIvIq+zrmJ15f1nG7x4MwdH/HHuHrU9uN7aMhuy679PJChR6X1HOGdnMV/LrhZ44i8iprOm7Zry8kGBtKvb/KSWUGOc/V1LfUiwzy/arjq4lr7lxll15ejNDjknrO0G4xJ5/DiLxJD3WcV2Z0/YzH+2vbEwnZXxfe03Hf0e2vnNCxoswdx790fJip7NLLi23/mONyzPXc5zEbfPJ54ei2npzqtvrmTbpqz6TLiXohIftre7JbtI24FPD+pMEfe+R1XXbp5bURc1yOtZ6ztVvTgPOaY6f3IvIq1WcL5FIoxd2wlPuT/wQ/6Hg34mcPE5ddenlthR6XY63nrO3mOvlctG9q2o9Tf8S+edUZ9oH9ReWaca/ny6CU+5NB7Z9s1zTUxzr+SVh26eV1IeS4HGs9Z2+3psuIXXvJcsJ2Ya85ulo+eWftYNXkH7986Gunp5NB6v394nkN/LMydxTesbFmG/Gi4/Kvj7JLL68rPsflmOs5W7v5jGXIINS27V4dKPPx9FMReXP2F1io+dm7ju5xG6n3N2usaJJ8+O1vZQZEX9r/PJ80lNdn2aWW1xWf43fM9VxquwEAAAAAAAAAAAAAAAAAAAAAAAAAABRJZsh8ov57eFXmClpskZdSqeutAZhBJiZ7qswT3jLVhEzdIauiyBSj8xF5qZW63hqAGfYcvReZguJmRF4Jcq+3BozapvJb7ts1Sb30bvYj8pQa/lpzABrIjIfP1ZtLyEyT2fxWHL2Hg4i8ylDXmgPg+QcrccP2UJTjsumZMoPJ1RSj6/bkcRSRVxniWnMAAmzbP7w7DTlyQtm1lyoSMsXoUk2PxjevMqS15gBE9Hy2Gno+s3oQbfKGstYcgAC+Yz4uq8oMEMfmDWWtOQCBNluOacg40UJk3lDWmgPQIxkIlrWrqmWZ5UQi4yEbkXlv+1pzABKRO1EyiCyf45E7QbIm3HJk3hDWmgMAAAAAAAAAAAAAAAAAAAAAAAAAAEAhWKcLQBas0wWgGKzTBSAb1ukCkBzrdAFIjnW6ACTHOl0AkmOdLgDJsU4XgORYpwtAFqzTBSAL1ukCAAAA8Jba1HHaM/eKjq2a7dft9wDA2zUdz9WbnxR22VfmzlPlso7bDfnHHgFgoI4944Yyd4iayN2jW/brCzoeUb0A2ti2J6A7HrkPdZxXZkKvMwWcNGMDQCE9ny2Pno+4qszDm8sd7RvACIWO+VTTmcql1yWqD0AsudvlO+WEPNT5QJlnq+Rn9nq+7AIAdVaZ+XEmTzbrOnaoGgB9mVPmmamFmu/dVeYOGAAMltxhe6LM9BgHyow9LbbIA4CZZEKwp8o8JCp35GRqDflUtcxSOB+RBwBe9hy9F3mK/WZEHgB4ee3YLr2b/Yg8APAiE4Kt1GyXhQMPIvIAwItcNj1TZjC5mqVw3fZmjiLyAMCbnFB2lbmLJSGzFC7V9Gh88wAgWrV4YFd5AOBlVZnJzLrKAwAvMgfRQod5APA/MmmZLH8zZ1/LiUSWQt6IzAMALzJrogwiy+d4XinzTNlyizynfwHtrI539JWNXAAAAjZ0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bXRhYmxlIGNvbHVtbmFsaWduPSJyaWdodCBsZWZ0IHJpZ2h0IGxlZnQgcmlnaHQgbGVmdCByaWdodCBsZWZ0IHJpZ2h0IGxlZnQgcmlnaHQgbGVmdCIgY29sdW1uc3BhY2luZz0iMGVtIDJlbSAwZW0gMmVtIDBlbSAyZW0gMGVtIDJlbSAwZW0gMmVtIDBlbSI+PG10cj48bXRkPjxtbj4xMDA8L21uPjxtaT54PC9taT48bW8+JiN4MjIxMjs8L21vPjxtaT54PC9taT48bW8+PTwvbW8+PG1uPjI1LjI1MjUyNTwvbW4+PG1vPiYjeDIyMTI7PC9tbz48bW4+MC4yNTI1MjUyNTwvbW4+PC9tdGQ+PC9tdHI+PG10cj48bXRkPjxtbyBzdHJldGNoeT0iZmFsc2UiPiYjeDIxRDI7PC9tbz48bW4+OTk8L21uPjxtaT54PC9taT48bW8+PTwvbW8+PG1uPjI1PC9tbj48L210ZD48L210cj48bXRyPjxtdGQ+PG1vIHN0cmV0Y2h5PSJmYWxzZSI+JiN4MjFEMjs8L21vPjxtaT54PC9taT48bW8+PTwvbW8+PG1mcmFjPjxtbj4yNTwvbW4+PG1uPjk5PC9tbj48L21mcmFjPjwvbXRkPjwvbXRyPjwvbXRhYmxlPjwvbWF0aD5SUxI1AAAAAElFTkSuQmCC)
Now we have a fraction for 0.252525. On adding it with 3, we have
![rightwards double arrow 3 space plus space 25 over 99](data:image/png;base64,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)
as fraction
Hence 3.25252525….= ![322 over 99](data:image/png;base64,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)
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