Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Is there a way to estimate the reciprocal of a decimal number? e.g. 1/0.388. Are there any formulas for this sort or thing, or do I just have to calculate it by hand?

share|improve this question
add comment

2 Answers 2

up vote 3 down vote accepted

$ 1/0.388 = 1/(388/1000)=1000/388=250/97$. Now do it by hand, as precise as you need.

share|improve this answer
    
Or say 250/97 is 3% higher than 2.5=2.575, accurate to 1 part in 1000. –  Ross Millikan Feb 19 '11 at 17:02
    
Seconding this way of coming up with 2.575. –  Michael Lugo Feb 19 '11 at 18:08
add comment

It depends what facts you have in your head. Probably you know that 1/2=0.5, 1/3=0.3333, 1/4=0.25, 1/5=0.2. It is less common to know 1/6=0.16666, 1/7=0.142857, 1/8=0.125, 1/9=0.11111. Leading zeros just make a factor of 10. You can just "look down the list" to see 1/.388 is between 2 and 3. Then 0.388 is about 15% bigger than 0.333, so 1/0.388 is about 15% less than 3, or about 2.55. Here we are using that $(1+x)^{-1}\approx 1-x$ for $x$ small compared with 1. This is only 1% off

share|improve this answer
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.