Monday, November 21, 2011

!±8± EatSmart Digital Nutrition Scale - Professional Food and Nutrient Calculator

Brand : EatSmart | Rate :

| Price : $89.95
Post Date : Nov 22, 2011 04:04:15 | Usually ships in 24 hours

EatSmart Digital Nutrition Scale - Professional Food and Nutrient Calculator

Calculate calories, carbs, fiber, sodium, fats, vitamin k and six other nutrients from thousands of packaged and 999 whole foods
White backlight with on/off button for conserving battery life
Memory Mode - save up to 99 entries for daily or weekly tracking
Weighs in grams (to nearest whole gram) and ounces (to nearest .1 ounce); Max weight 11 pounds
Tare feature, auto power off, runs on 4AAA batteries (included); 2 Year Warranty & Guarantee

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EatSmart Digital Nutrition Scale - Professional Food and Nutrient Calculator

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Monday, November 14, 2011

A Neat Trick About Multiples of 3

!±8± A Neat Trick About Multiples of 3

Did you know that any natural number is a multiple of 3 if and only if the sum of its digits is also a multiple of 3? For example 411 must be a multiple of 3 since 4+1+1=6 is a multiple of 3. Pretty neat!

This is a great little tool for figuring out whether or not some large number is a multiple of 3 or not. Let's try to prove this result just to be sure. The proof is simple once you get your head around the notation.

Let a number with the digits xj to x0 be divisible by 3. Then we have to show that xj + ... + x0 is also divisible by 3. The large number can be represented by ( xj* 10^j ) + ... + ( x1* 10) + x0.

This is equal to xj + ... + x0 + xj* (10^j - 1) + ... + x1* ( 10 - 1) . The terms on the right of the x0 are terms of the form 99999, 9999, 999, etc. These are all clearly divisible by 3. Hence the remaining sum xj + ... + x0 must also be divisible by 3. So we're done.

The same argument can be used in reverse to show that if the sum of the digits of a number is divisible by 3, then so is the whole number. This concludes the proof.

This is pretty useful for determining if extremely large numbers are divisible by 3 since adding is much easier than dividing! Similar tricks can be used for other multiples but more proofs are required for that; can you find them?