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?

A Neat Trick About Multiples of 3

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Best 5 Electronic-Based Kitchen Scales

!±8± Best 5 Electronic-Based Kitchen Scales

If you love cooking and you are planning to use electric run kitchen scales, then there can be five best choices you can choose from. These scales can really help you a lot with the weighing tasks and feel great for you can already balance the nutrition intake of your family by simply determining the nutritional value of the food you prepare. So if you are still using the traditional device in weighing, it is already the right time for you to shift into digital. It will never be become unnecessary for you because you cook food everyday of your life and it is just wise to be healthy, right? Below are the top 5 best choices of scales:

Salter Housewares 1038 Electronic Kitchen Scales - This Salter Housewares 1038 comes along with amazing features and the best of which is the install timer having an alarm signal, room temperature determinant display, and nice display screen. This would be perfect for any type of kitchen. Moreover, aside form those features stated, the Salter Housewares 1038 can weigh food items accurately and with its clear glass surface, food stains and food carry over can be easily wiped out.

Salter 1004 Electronic Kitchen Scales - This type of device is just small in size, thus it is easier and more convenient for one to store or display them on kitchen countertops. They can't really take huge spaces. These scales have the ability to subtract the empty bowl's weight from one bowl which is full. The material is completely made out stainless steel so cleaning and maintenance is just simple.

EatSmart Precision Pro Digital Kitchen Scales - This type come in a modern sleek appearance and only include two control buttons, making it simpler and very easy to operate. The EatSmart Precision Pro Digital Kitchen Scale comes with a huge LCD screen use for displaying information and it can measure food weighing 1 gram to 5 kilograms. Its size completely makes it unique among the others.

KINTREX SCL0625 Digital Kitchen Scales - The KINTREX SCL0625 weighing device has a good set of features which include its touch-based controls. It has a big LCD backlit display screen which is very easy to read whenever you are close or far. The SCL0625 can weigh 1 gram up to 5 kilograms also. It comes in a black glass platform.

Salter Housewares 1041B Glass Digital Kitchen Scales- The Salter Housewares 1041B is very thin and sleek. It is totally touch-based and cleaning can be easy.

Best 5 Electronic-Based Kitchen Scales

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EatSmart Precision GetFit Digital Body Fat Scale w/ 400 lb. Capacity & Auto Recognition Technology

!±8±EatSmart Precision GetFit Digital Body Fat Scale w/ 400 lb. Capacity & Auto Recognition Technology

Brand : EatSmart
Rate :
Price : $79.95
Post Date : Oct 17, 2011 08:14:10
Usually ships in 24 hours

The EatSmart Precision GetFit is not your ordinary bathroom scale as it can quickly and easily measure weight, body fat, body water, body muscle and bone mass using our new ITO BIA technology. This scale is perfect for individuals who are serious about taking control of their health.

BIA (Bio-Electrical Impedance Analysis) technology allows you to easily calculate your body fitness by imputing information of gender, height, age, activity level and your weight. In bare feet, this technology sends a low-level electrical signal though your body fat and then measures the resistance the signal encounters. This signal is perfectly safe and will not be felt.

The Precision GetFit Scale stores up to 8 different users' personal profiles and will be able to recognize these users as soon as they step onto the scale. This auto recognition software makes it simple to operate, since all you have to do is stand on the platform barefoot and it identifies who you are based on past weight. Not having to select a user gives it the same functionality as a basic bathroom scale with added benefit of % body fat, % body muscle, % body water and bone mass.

Let's not forget about its universal EatSmart features! The Precision GetFit uses "Step-On" technology which means no more tapping to turn on your scale. It measures up to 400lbs and will display an accurate readout to the nearest .2 lbs on the oversized 3.5" LCD display. Its sleek design and slim profile fits perfectly into any surrounding. The touch screen interface makes it one of the most user friendly bathroom scales on the market today.

Along with your Precision GetFit, you receive our easy to follow Instruction Manual (which also defines body fat, body water, body muscle and bone mass) and 4 AAA batteries.

100% EatSmart Guaranteed Product Satisfaction. Customer satisfaction is our highest priority. Contact us via phone or email anytime for support.

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