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  Decimal Place Value  Home ] Next ]    

Place Value

whole number counting with decimals

Digit by Digit Decimal Place Value

First Example

 Decimal place value says

3452  = 2 ones + 5 tens + 4 hundreds + 3 thousands

where the plus sign + may be read as the word and.  The recognition of place value from right to left means the place value of the leading digit is found last rather than first. We might read

3452 aloud as   3 thousands, 4 hundreds, 5 tens and 2 ones

 So the right to left direction in which place value is found

 <<<<<<<<<<<<<<<<
3452 
>>>>>>>>>>>>>>>>

is opposite to the left to right direction in which the number is read aloud in word form.

Second Example

The significance or value of the the digits in the larger whole number represented by the decimal

23,456,778
<<<<<<<<<

is given from right to left by   8 ones, 7 tens, 7 hundreds, 6 thousands, 5 ten thousands, 4 one hundred thousands, 3 millions, 2 ten millions, and read from left to right as 

2 ten millions,  3 millions, 4 one hundred thousands, 5 ten thousands, 6 hundred thousands, 7 hundreds, 7 tens and 8 ones

Each column in a decimal representation of a whole number, except for the last,  has a place value ten times greater than the following column

Groups of Three Place Value

Second Example Revisited

Reading Aloud in Groups of Three

We may also read 23,456,778 backward as

778 ones, 456 thousands and 23 millions, 

and forward as

23 millions,  456 thousands and 778 ones

Third Example

For longer numbers, we find place value from right to left

         96 456 899 138 443 704 789 123
 <<<<<

123 ones
789 thousands
704 millions
443 billions  (a US billion is a thousand million)
138 trillions 
899 quadrillions
456 quintillions
96 sextillions

Hence from left to right,    96 456 899 138 443 704 789 123 is

96 sextillions,  456 quintillions, 899 quadrillions,
138 trillions, 443 billions,
704 millions, 789 thousands and 123 ones

Each group of three (or less) in a decimal representation of a whole number, except for the last group of three,  has a place value a thousand  times greater than the following column

Reading numbers aloud from right to left and then left to right in groups of three could provide two to four  hilarious exercises in primary or secondary school mathematics class. 

Fourth Example: 

Avogrado's Number  

N = 6.02 * 1023 = 602 000  000 000  000 000 000 000

= 602 sextrillions or 0.602 septrillions.

sextrillions quintillions quadrillions trillions billions millions thousands ones
 000 000  000  000  000  000  000  000
21 18 15 12 9   6 3

To come:  UK version of above exercise

 

       

 

Number Theory

A. Start of Number Theory

Origins of Counting or Tallying
Adding Wholes
Multipling Wholes
Distributive Law  Preamble
Distributive Law for Wholes
Consequences
More Consequences
What is a Fraction
Compound Fractions

B. Number Theory
Continued


Decimal Place Value
Place Value Reinforcement
Addition Method
Comparison Method
Subtraction Methods
Multiplication Methods
Division Methods
Long Division Continued
Remainder Arithmetic I
Primes & Composites
Primes Factorization Theorem
Primes & Composites
Prime Factorization Examples
Counting  Whole No.  Factors
Prime Factorization Aids
Square Roots  & Primes
Fractions & Decimals
Fractions as Decimals
1 = 0.999 Recurring
Infinite Decimals Expansion Arithmetic
Ratio of Simple Fractions
Ratio of Decimal Fractions
Unsigned Reals Numbers
Signed Coordinates
Plane Vectors
Horizontal Vectors
Adding Vector Multiplies
Adding Signed Numbers
Multiplying Signed Numbers
Distributive Law for Reals
Real Numbers Axioms
Remainder Arithmetic II

Related Site Folders

Euclidean-Geometry/Complex No.s
Complex Numbers More 2

 


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