6 Part 1: The World of Numbers
DEFINITION
A decimal system is a place value system in which each position in which a digit can
be placed is worth ten times as much as the place to its right.Each move to the left multiplies the value of a digit by another 10. The 4 in 46 represents 4 tens
or forty, the 4 in 9,423 is 4 hundreds, and the 4 in 54,631 represents 4 thousands.
If you understand the value of each place, you should be able to tell the value of any digit as well
as the number as a whole.CHECK POINT
Complete each sentence correctly.- In the number 3,492, the 9 is worth ____.
- In the number 45,923,881, the 5 is worth ____.
- In the number 842,691, the 6 is worth ____.
- In the number 7,835,142, the 3 is worth ____.
- In the number 7,835,142, the 7 is worth ____.
When you read a number aloud, including an indication of place values helps to make sense of
the number. Just reading the string of digits “three, eight, two, nine, four” tells you what the
number looks like, but “thirty-eight thousand, two hundred ninety-four” gives you a better sense
of what it’s worth.
In ordinary language, the ones place doesn’t say its name. If you see 7, you just say “seven,” not
“seven ones.” The tens place has the most idiosyncratic system. If you see 10, you say “ten,” but
11 is not “ten one.” It’s “eleven” and 12 is “twelve,” but after that, you add “teen” to the ones
digit. Sort of. You don’t have “threeteen,” but rather “thirteen.” You do have “fourteen” but then
“fifteen.” The next few, “sixteen,” “seventeen,” “eighteen,” and “nineteen” are predictable.
When the tens digit changes to a 2, you say “twenty” and 3 tens are “thirty,” followed by “forty,”
“fifty,” “sixty,” “seventy,” “eighty,” and “ninety.” Each group of tens has its own family name, but
from twenty on, you’re consistent about just tacking on the ones. So 83 is “eighty-three” and 47 is
“forty-seven.” And the hundreds? They just say their names.
Larger numbers are divided into groups of three digits, called periods. A period is a group of
three digits in a large number. The ones, tens and hundreds form the ones period. The next three
digits are the thousands period, then the millions, the billions, trillions, and on and on.