# Pi(e): A Dessert & A Number!

### This famous irrational number is approximately equal to 3.14159. Although this number is irrational, some of its multiples are almost __rational.__ The fractions below are approximations to the nearest *billionths.*

__According to the TI-84 Plus:__

## 8π ≈ 25 + 553/4166 or 104,703/4166

## 15π ≈ 47 + 823/6643 or 313,044/6643

## 35π ≈ 109 + 907/949 or 104,348/949

## 36π ≈ 113 + 179/1839 or 207,986/1839

## 37π ≈ 116 + 642/2687 or 312,334/2687

#### (To the left of the OR's above are the fractions as mixed numbers; I like to use the plus sign between the integer & the fraction!)

In the image below are the digits of Pi up to 15 digits after the decimal point:

A very close rational number to **Pi** is **22/7** or **3 + 1/7**. If you subtract **Pi** from that number, you get a very small** **number that's approximately...

## 22/7 - π ≈ 6/4,745

Therefore:

## π + 6/4,745 ≈ 22/7 or 3 + 1/7

It's a difference of about **0.00000000033163 or 3.3163 × 10**^{-10} from **Pi** in absolute value.

Note: Be warned, the **TI-84 Plus** sees no significance in adding *non-integers* smaller than a *billionth*(1/1,000,000,000 or 0.000000001) to *integers!* In fact, lots of calculators round up non-integers to the best of their display ability.

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© Derek Cumberbatch