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Place Valuewhole number counting with decimals Digit by Digit Decimal Place ValueFirst ExampleDecimal place value says
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
So the right to left direction in which place value is found
is opposite to the left to right direction in which the number is read aloud in word form. Second ExampleThe 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
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 ValueSecond Example Revisited
We may also read 23,456,778 backward as
and forward as
Third ExampleFor longer numbers, we find place value from right to left 96 456 899
138 443 704 789 123
Hence from left to right, 96 456 899 138 443 704 789 123 is 96 sextillions, 456 quintillions, 899 quadrillions, 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 to three significant digits is
To more significant digits
Now 1021 = one septillion. So Avogradros numbers is 602.21415 sextrillions or
to the nearest 10 quadrillion. The foregoing discussion may help. A Slightly Different Viewpoint
A compound number like 345325 may be expressed at length in words as three hundred thousand, four ten thousands, five thousands, three hundreds, two tens and five ones. It may be expanded numerically as
where 100 = one, 101 = ten, 102 = one hundred, 103 = one thousand, 104 = ten thousand and 105 = one hundred thousand. Now 325 and 345 may be read aloud as 3-2-5 and 3-4-5 respectively. With that convention, we express 345325 as 345 thousands and 325 ones. More generally, a large number like
may read aloud backward as
and so save the decimal places to last.
Likewise,
may be read forward direction as
It is simple an exercise to express the numbers and fractions decillions =1030 to decillionths = 10-30 in power of ten. Metric Development
Now 325 and 345 may be read aloud as 3-2-5 and 3-4-5 respectively. With that convention, we express 345325 as 345 thousands and 325 ones. More generally, a large number like
may read aloud backward as
and so save the decimal places to last.
Likewise,
may be read forward direction as
It is simple an exercise to express the numbers and fractions decillions = 1030 to decillionths = 10-30 in power of ten. In
college and senior high school courses in science
Avogadro's number = 6.0221415 × 1023 may be introduced as the number of Carbon-12 atoms in 12 grams of the
substance.
to the nearest 10 peta-units.
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