Explain 4 key concepts that undergird our base ten number system? Use examples.

Question

Explain four key concepts that undergird our base ten number system? Use examples.

Answer 1

First let me rewrite your statement here so that we may more quickly reference it and the answers which will follow.

Explain the four key concepts that under gird our base ten number system.

Concept One - The two parts of number representation are base and place value.

Concept two - The base ten system is understood in terms of multiples of the power of ten or exponential representation which helps to distinguish one number from another and the value of each number.

Concept three - The numerical quantity of the base ten system is place value which is represented by ten digits beginning at zero and including 1, 2, 3, 4, 5, 6, 7, 8, 9...

Concept four - Positions of the place value number will be decided by the base ten system or exponential value.

I want to approach each concept individually with definitions, explanations, then examples before explaining how the base ten system functions as a whole system with varying "parts".

First, let's examine a variation of your statement as a starting point.

What are the four key concepts which support or undergird and allow the base ten system to function effectively? To UNDER GIRD something means to provide a strong foundation, framework, or BASE beneath or UNDER whatever will be built upon it.

Have you noticed the construction of a bridge or building? They are created, made of a strong framework of enormous metal beams called "girders" or support beams upon which the bridge or building will be constructed and "under girded".

They will give the entire structure the support necessary to function effectively and as intended.

I explain all of this to create imagery in your mind that will enable you to imagine the base ten system as a "construction" created in order to help our mathematical system function effectively.

Now, let's build that bridge to understanding and that building of base ten with four concepts or "girders".

The first key concept or girder is "number representation has two parts, base and place value".

Number representation may be understood in this way; we have an object or many objects and need to "represent" these objects in a different way or "value". For example, I have two quarters. I want to write a numerical value for my two quarters, which would be .50 cents.

I used a numerical expression to represent an object.

"Number representation" may also be understood as to what base numbering system is being implemented. How will I represent that number in that system, what place should I place it and what value will it represent?

Now that we have an understanding of "number representation", let's examine the two parts which are the "base" and "place value"

Think of a bridge with a way to enter and exit or a building with an entrance and exit. Numbers need somewhere to be, a "base" or starting point. Once at that "base" or starting point, a number needs its own "place" just as a car needs its own lane and space to drive safely to its destination on the other side of the bridge or people wanting to enter a building need an entrance designed for entering the building rather than wandering around trying to figure a way in.

Once a number is in its correct place, that place has value.

The value is designated by what type of number or number it is. For example, if you own an inexpensive toy it will have a smaller value then say the latest X-Box or PS system. If you own one outdated PS system and two just released PS systems in their "place" at home, which one has a greater value? Does the one with greater value have a different "place" where you use it? Does the older system of less value have a different place, perhaps below the other system?

The same is true for numbers and how they are represented in the "base ten" system. For example, the

number "one" is represented in the "base tens" as "1" and is PLACED in as a VALUE of "one", giving that one object a numerical representation and that number a value which we designate as "PLACE VALUE".

One more explanation or clarification in hopes it helps with understanding what is meant by "base ten" or what exactly is "base ten" ?

Our numbering system is "based" on counting or grouping in increments of ten or the powers of ten...no not super powers...basically representing how many times ten is multiplied by itself.

The "ones" place value is represented as 10⁰ which means ten to the zero power or ten not multiplied to itself.

Ten to the zero power would be written as 10⁰ which is 10x0 (ten is not multiplied, so the value would be in the ones place value) Wait...how would a ten be placed in the ONES place value? Think of it in this way, 10x0= 0. There are no tens so numbers below would be in this value or think of it as the starting point or "base" on which numbers "10" and higher are placed.

Since we've covered many explanations and examples today, we will complete the remaining three key concepts on Monday. Enjoy your weekend.

Ms. Cheryl