Wednesday, April 29, 2015

Wtriting in Standard Form


Figure A
 A whole number such as 1,083,664,500 is written in what we refer to as STANDARD FORM.

By STANDARD FORM we are referring to how the digits are separated into groups by commas.

Starting from the right each group of three digits are separated into groups of three.  Each group of

three digits is called a PERIOD.  The names of the first four PERIODS are shown in (figure A)

Writing a WHOLE NUMBER in words:  To write a WHOLE NUMBER in words, write the number in each PERIOD  followed by the name of the PERIOD.  "The ONES PERIOD is usually not written".  The same procedure can be used when we read a WHOLE NUMBER.

Example:  245,978

The position occupied by the "2" is the hundred-thousands (see the 6 in the figure A).  Putting a "2" in this position means that there are 2 hundred-thousands or TWO HUNDRED thousand.

Using the same procedure, putting a "4" in the ten-thousands position means that there are "4" ten-thousands for FORTY thousands because 4 tens ( 4x10) is forty.

Finally we put the five in the thousands position and this means that there are 5 thousands or FIVE thousand.

Notice how we read the number.  "2" (using the periods chart above) the "2" is read as TWO (from the position on the chart the "2" is positioned in the period labeled) HUNDRED-THOUSAND so we say TWO HUNDRED THOUSAND  . . . "4" (from the chart we see that the "4" is positioned in the period labeled) TEN THOUSAND -- since 4 x 10 = 40 we SAY forty thousand . . . "5" (from the chart we see that the 5 is positioned in the period labeled) THOUSAND so we say FIVE THOUSAND.



 The "9" is placed in the hundreds position and this means that there are "9" hundreds or NINE hundred.

The "7" is placed in the tens position and this means that there are "7" tens or SEVENTY.

The remaining digit "8" is placed in the ones position indicating that there are EIGHT units or ones.

From the chart we say "9" HUNDRED . . . from the chart we say "7" TENS (since 7 x 10 = 70 we say SEVENTY . . . from the chart we say "8" (since 8 x 1 = 8 we just say "8" - we do not say 8 ones).

Putting it all together we have the following:

------ (two hundred) thousand + (forty) thousand + (six) thousand = (two hundred + forty + six) thousand = (two hundred forty six) thousand = 246 thousand.

++++ (nine) hundred + (fifty) tens + (eight) ones = (nine hundred + fifty + eight) = 958.

***** This number is read as     246 thousand 958.

Things to REMEMBER:
^^^^ COMMAS are used after the name of each PERIOD
^^^^ The ONES PERIOD is usually NOT written or spoken
^^^^ The word "and" is NOT used when reading/writing WHOLE numbers
^^^^ To write a number in STANDARD FORM, write the number in each PERIOD followed by a
         comma.
^^^^ A comma may or MAY NOT be inserted in a four-digit number.  9,456 and 9456 are BOTH
         acceptable ways of writing nine thousand, four hundred fifty six.
^^^^ When you hear the term WHOLE NUMBER this is like a WHOLE PIZZA that has NOT
             been cut into pieces.  If we compare  WHOLE NUMBERS to fractions we
             understand that the whole number is the whole pizza while the fractions represent the
             individual pieces of the pizza.

Examples:
 Write each number in words
1)  85 --------------------------------------------------------------------- eighty-five
2) 126 -------------------------------------------------------------------- one hundred twenty-six
3) 27,034 ---------------------------------------------------------------- twenty-seven thousand, thirty-four
4) 67 --------------------------------------------------------------------- sixty-seven
5) 395 -------------------------------------------------------------------- three hundred ninety-five
6) 12,804 ---------------------------------------------------------------- twelve thousand, eight hundred four

Write each number in STANDARD FORM

7) twenty-nine ---------------------------------------------------------- 29
8) seven hundred ten -------------------------------------------------- 710
9) twenty-six thousand, seventy-one ------------------------------- 26,071
10) six million, five hundred seven --------------------------------- 6,000,507

Testing your KNOWLEDGE - review the questions - the answers are given below.

1) In 687564, the comma is after





2) In 98763245879, the value of the 3 is





3) You can read 5628471





4)You can rewrite 74785202478932 as 74,785,202,478,932



3) Eighty seven million, four hundred fifty thousand, fifty four



WRITING A WHOLE NUMBER IN EXPANDED FORM
The place value of a digit can be used to write a number in expanded form.  The EXPANDED FORM of a number shows each digit of the number with its place value.  5672 written in expanded form is shown below.


Write 2,805,327 in expanded form:

2,000,000 + 800,000 + 5000 + 300 + 20 + 7



Whole numbers are visualized by POINTS on a line (called a NUMBER LINE).  The number line has EQUALLY spaced marks for each whole number.  The arrow shown on the right indicates that the whole numbers CONTINUE indefinitely (they never end).




1) In 687564, the comma is after Correct!




2) In 98763245879, the value of the 3 is Correct!




3) You can read 5628471 Correct!




4)You can rewrite 74785202478932 as 74,785,202,478,932 Correct!


3) Eighty seven million, four hundred fifty thousand, fifty four Correct!







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