math

posted by .

how to find the reciprocal??



you flip the reciprocal example (4 over 5 the reciprocal will be 5 over 4.

If it is a fraction, switch the numerator with the deniminator.
Example: reciprocal of 2/7 = 7/2 = 3 1/2

If it is a mixed number, write it as a fraction and turn the fraction and turn upside down.
Example: reciprocal of 2 1/2 = reciprocal of 5/2 = 2/5

If it is a whole number (or any number!) N, the reciprocal is 1/N.

If it is a non-integer in decimal form, such as 1.23, perform the opetation 1 divided by 1.23, and get 0.813...

It looks like you already knew the answer to your own question

If you need to calculate 1/a you can use the following algorithm. You start with a guess x_{0} and you calculate better and better approximations x_{1}, x_{2},...etc recursively using the formula:

x_{n+1} = 2x_{n} - a x_{n}^2


Note that there are no divisions in this equation. This algorithm will double the number of significant digits after each iteration, so it's superior to long division where you only get one more digit per step (which you have to find by trail and error, so the long division algorithm isn't completely division free itself).

Example:
We want to find the decimal expansion of 1/68. 1/50 is 0.02, 1/100 is 0.01, so let's start with an initial guess of x_{0} = 0.015.

The algorithm gives:

x_{1} = 2*x_{0} - 68*x_{0}^2 = 0.0147

x_{2} = 2*x_{1} - 68*x_{1}^2 = 0.01470588

x_{3} = 2*x_{2} - 68*x_{2}^2 =
0.014705882353

The 1/x function of my calculator gives:

1/68 = 0.0147058823529

  • math -

    o

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. math help

    could some one please explain to me reciprocal how to find the reciprocal my math home work says find the reciprocal of (-1/8)(13/2)(4) reciprocal you change over so is the -1/8 -8/1 or would it be 8/1 13/2 would be 2/13 4 would be …
  2. Math

    What is a reciprocal A number's "flip". Like if you have 2/3, it's reciprocal would be 3/2. If you have a whole number like 5, for example, than it is understood that there is a 1 under the 5. (5/1) This means that the reciprocal of …
  3. math

    PLease help! anyy would be appreciated !thx what is an example of a quadratic function that touches its axis and also its reciprocal?
  4. psy

    need some datas to be able to answer those questions. Compare mechanistic and reciprocal interactionism. Give an example of reciprocal interactionism (influences among a person, a situation, and a behavior). Provide an example of mechanistic …
  5. college

    Compare mechanistic and reciprocal interactionism. Give an example of reciprocal interactionism (influences among a person, a situation, and a behavior). Provide an example of mechanistic interactionism (a trait, a situation, and the …
  6. Math

    1. evaluate |-14|=14? 2. add -3/5+8/35=13/35?
  7. Math

    The sum of the reciprocal of 5 and the reciprocal f 7 is the reciprocal of what number?
  8. Math

    For each function, i) determine the corresponding reciprocal function, y =1/f(x) ii) state the non-permissible values of x and the equation(s) of the vertical asymptote(s) of the reciprocal function iii) determine the x-intercepts …
  9. math

    the sum of the reciprocal of two number is 1/2 twice the reciprocal of the sixth less than five times the reciprocal of the 2nd. what are the original #?
  10. Math

    I need help with this problem. It says What is the reciprocal of 0.06?

More Similar Questions