Fundamental Mathematics from an Advanced Standpoint

Math 4303 - Fall 2009

Helmut Knaust, Department of Mathematical Sciences, UTEP, El Paso TX 79968
hknaust@utep.edu

Last Edits: 9/10/09

Calculating the Decimal Representation of Fractions on a Cheap Calculator

We want to compute the decimal representation of 1/19. The fraction 1/19 has a simple-periodic decimal representation with period 18.

N[1/19,25]

We first build a calculator that will only display 7 digits :

Calc[x_]:=PaddedForm[x,7]

We will extract 5 digits of the decimal representation of 1/19 at a time.

Calc[10^5 1/19.]

This means that the first five digits of the decimal representation of 1/19 are "05263".

Calc[10^5-5263 19]

Calc[ 3 10^5/19.]

The next five digits are "15789".

Calc[3 10^5-15789*19]

Calc[ 9 10^5/19.]

Digits 11 - 15 are "47368".

Calc[9 10^5-47368*19]

Calc[ 8 10^5/19.]

Digits 16 - 20 are "42105".

Calc[8 10^5-42105*19]

Calc[ 5 10^5/19.]

Digits 21 - 25 are "26315". Note that the digits are starting to repeat.