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Hello!
I read somewhere that remembering the decimal equivalents of reciprocals of first 10 digits will help in solving fractions and percentages problems a bit faster. However, I was really struggling to remember the decimal equivalents and asked someone important - Google!
I found a very useful link that gives good tips on remembering the decimal equivalent of Reciprocals. The link follows - https://testbook.com/blog/remember-reci ... tcuts-pdf/
Here I summarize the tips to remember the reciprocals of 1 to 10. (The Tip of 7 is what I found most useful). I hope it helps you.
Reciprocal of 2
Simplest of the Lot. Reciprocal of \(2 = \frac{1}{2} = 0.5 = 50\)%
Reciprocal of 3
Reciprocal of \(3 = \frac{1}{3} = 0.3333 = 33.33\)%. Reciprocal of 3 contains all 3's.
Reciprocal of 4
Remember 4 parts of a 25 makes a hundred. So, Reciprocal of \(4 = \frac{1}{4} = 0.25 = 25\)%
Reciprocal of 5
If \(\frac{1}{2}\) is 0.5 then \(\frac{1}{5}\) is 0.2 = 20%! Obviously!
Reciprocal of 6
Reciprocal of \(6 = \frac{1}{6} = 0.1666 = 16.66\)%. You can memorize this or, you can half the reciprocal of 3.
Reciprocal of 7 and its multiples
Remember this sequence - 1 4 2 8 5 7
Tip to remember the sequence - 2 times 7 is 14, 2 times 14 is 28, 2 times 28 is 56. But you want to end it with a 7, so lets make it 57. Once you remember 1 4 2 8 5 7 - rest just forms a cycle.
\(\frac{1}{7} = 0.142857 = 14.2857\)% --> starts with the smallest number (1) in the sequence.
\(\frac{2}{7} = 0.285714 = 28.5714\)% --> same cycle but starts with the second smallest number (2) in the sequence
\(\frac{3}{7} = 0.428571 = 48.8571\)% --> same cycle but starts with the third smallest number (4) in the sequence
\(\frac{4}{7} = 0.571428 = 57.1428\)% --> same cycle but starts with the fourth smallest number (5) in the sequence
\(\frac{5}{7} = 0.714285 = 71.4285\)% --> same cycle but starts with the fifth smallest number (7) in the sequence
\(\frac{6}{7} = 0.857142 = 85.7142\)% --> same cycle but starts with the sixth smallest number (8) in the sequence
Reciprocal of 8 and its multiples
\(\frac{1}{8} = 0.125 = 12.5\)% --> Remember this as half of \(\frac{1}{4}\). From this you can easily derive all other multiples
\(\frac{2}{8} = \frac{1}{4} = 0.25 = 25\)%
\(\frac{3}{8} = 3*\frac{1}{8} = 0.375 = 37.5\)%
\(\frac{4}{8} = \frac{1}{2}= 0.5 = 50\)%
\(\frac{5}{8} = \frac{4}{8} + \frac{1}{8} = 0.5 + 0.125 = 0.625 = 62.5\)%
\(\frac{6}{8} = \frac{3}{4} = 0.75 = 75\)%
\(\frac{7}{8} = \frac{6}{8} + \frac{1}{8} = 0.75 + 0.125 = 0.875 = 87.5\)%
Reciprocal of 9 and its multiples
\(\frac{1}{9} = 0.1111 = 11.11%\)
\(\frac{2}{9} = 0.2222 = 22.22%\)
....
....
\(\frac{8}{9} = 0.8888 = 88.88%\)
I bet you will never forget it now!
Reciprocal of 10
Another easy one = 0.1
Reciprocal of 11
\(\frac{1}{11} = 0.0909090\)... (Just something to help you recall : 1/9 has all 1's. 1/11 will have alternating 9)
Post this all the multiples will be multiples of 9 for example
\(\frac{2}{11} = 0.1818181\)... ----> 9*2 = 18
\(\frac{3}{11} = 0.272727\)... ----> 9*3 = 27
\(\frac{4}{11} = 0.363636\)... ----> 9*4 = 36
.... and so on
Though the link shared above has tips for bigger numbers, I am not sure how useful it will be to remember all of those. If interested you can visit the link.
Also, if you know any other trick that will help remember "stuff" please share below and we have everything in one place!
I read somewhere that remembering the decimal equivalents of reciprocals of first 10 digits will help in solving fractions and percentages problems a bit faster. However, I was really struggling to remember the decimal equivalents and asked someone important - Google!
I found a very useful link that gives good tips on remembering the decimal equivalent of Reciprocals. The link follows - https://testbook.com/blog/remember-reci ... tcuts-pdf/
Here I summarize the tips to remember the reciprocals of 1 to 10. (The Tip of 7 is what I found most useful). I hope it helps you.
Reciprocal of 2
Simplest of the Lot. Reciprocal of \(2 = \frac{1}{2} = 0.5 = 50\)%
Reciprocal of 3
Reciprocal of \(3 = \frac{1}{3} = 0.3333 = 33.33\)%. Reciprocal of 3 contains all 3's.
Reciprocal of 4
Remember 4 parts of a 25 makes a hundred. So, Reciprocal of \(4 = \frac{1}{4} = 0.25 = 25\)%
Reciprocal of 5
If \(\frac{1}{2}\) is 0.5 then \(\frac{1}{5}\) is 0.2 = 20%! Obviously!
Reciprocal of 6
Reciprocal of \(6 = \frac{1}{6} = 0.1666 = 16.66\)%. You can memorize this or, you can half the reciprocal of 3.
Reciprocal of 7 and its multiples
Remember this sequence - 1 4 2 8 5 7
Tip to remember the sequence - 2 times 7 is 14, 2 times 14 is 28, 2 times 28 is 56. But you want to end it with a 7, so lets make it 57. Once you remember 1 4 2 8 5 7 - rest just forms a cycle.
\(\frac{1}{7} = 0.142857 = 14.2857\)% --> starts with the smallest number (1) in the sequence.
\(\frac{2}{7} = 0.285714 = 28.5714\)% --> same cycle but starts with the second smallest number (2) in the sequence
\(\frac{3}{7} = 0.428571 = 48.8571\)% --> same cycle but starts with the third smallest number (4) in the sequence
\(\frac{4}{7} = 0.571428 = 57.1428\)% --> same cycle but starts with the fourth smallest number (5) in the sequence
\(\frac{5}{7} = 0.714285 = 71.4285\)% --> same cycle but starts with the fifth smallest number (7) in the sequence
\(\frac{6}{7} = 0.857142 = 85.7142\)% --> same cycle but starts with the sixth smallest number (8) in the sequence
Reciprocal of 8 and its multiples
\(\frac{1}{8} = 0.125 = 12.5\)% --> Remember this as half of \(\frac{1}{4}\). From this you can easily derive all other multiples
\(\frac{2}{8} = \frac{1}{4} = 0.25 = 25\)%
\(\frac{3}{8} = 3*\frac{1}{8} = 0.375 = 37.5\)%
\(\frac{4}{8} = \frac{1}{2}= 0.5 = 50\)%
\(\frac{5}{8} = \frac{4}{8} + \frac{1}{8} = 0.5 + 0.125 = 0.625 = 62.5\)%
\(\frac{6}{8} = \frac{3}{4} = 0.75 = 75\)%
\(\frac{7}{8} = \frac{6}{8} + \frac{1}{8} = 0.75 + 0.125 = 0.875 = 87.5\)%
Reciprocal of 9 and its multiples
\(\frac{1}{9} = 0.1111 = 11.11%\)
\(\frac{2}{9} = 0.2222 = 22.22%\)
....
....
\(\frac{8}{9} = 0.8888 = 88.88%\)
I bet you will never forget it now!
Reciprocal of 10
Another easy one = 0.1
Reciprocal of 11
\(\frac{1}{11} = 0.0909090\)... (Just something to help you recall : 1/9 has all 1's. 1/11 will have alternating 9)
Post this all the multiples will be multiples of 9 for example
\(\frac{2}{11} = 0.1818181\)... ----> 9*2 = 18
\(\frac{3}{11} = 0.272727\)... ----> 9*3 = 27
\(\frac{4}{11} = 0.363636\)... ----> 9*4 = 36
.... and so on
Though the link shared above has tips for bigger numbers, I am not sure how useful it will be to remember all of those. If interested you can visit the link.
Also, if you know any other trick that will help remember "stuff" please share below and we have everything in one place!
Other helpful resources on same topic
- 1. https://gmatclub.com/forum/common-fdps- ... 44945.html
2. https://gmatclub.com/forum/calculate-fa ... fl=similar
09 Jun 2017, 23:50
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Thanks naorba for the letting me know this is helpful! One Kudos to you for the appreciation!
naorba
