Place Value for Whole Numbers
The earliest number systems likely used only strokes, where each stroke
represented a number. For example, 3 may have looked like ||| and 7 may have
looked like |||||||. While small numbers would have been easy to read, larger
numbers like 40 would have been very difficult:
||||||||||||||||||||||||||||||||||||||||
Even if someone did take the time to count all those lines, he could easily have
made a mistake.
Herein lies the importance of our decimal system, which symbolically
represents the strokes of earlier number systems in a far more user-friendly
way. In the decimal system, the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9, used
in combination, represent all numbers. Because these ten digits represent all
numbers, the decimal system is a base ten numeral system. Under the decimal
system, we assign place value from right to left--ones, tens, hundreds,
thousands, ten thousands, hundred thousands, millions, ten millions, and so on.
For example, the numeral 7,654,321 has a "1" in the ones place, a "2" in the
tens place, a "3" in the hundreds place, etc. We say that "8,702" has 8 thousands,
7 hundreds, 0 tens, and 2 ones. Sometimes, we don't talk about the zeros; we might simply say
"8,702" has 8 thousands, 7 hundreds, and 2 ones. Imagine in the number 8,702 as a
bunch of individual lines. It would be impossible to deal with. Digits and Place values
allow the decimal system to represent large numbers with a minimum of figures.
Because our system is base ten, a value of 10 in one place is equal to a value
of 1 in the place to the left: 10 ones is equivalent to 1 ten, 10 tens is
equivalent to 1 hundred, and so on.
Example 1: In the numeral 7,015,384, what digit is in the...
a) ones place? 4
b) ten thousands place? 1
c) tens place? 8
d) millions place? 7
e) hundreds place? 3
f) hundred thousands place? 0
g) thousands place? 5
Example 2: Write out the following numerals:
a) 8 thousands, 6 hundreds, 4 tens, 7 ones. 8,647
b) 9 ten thousands, 0 thousands, 0 hundreds, 1 ten, 2 ones. 90,012
Example 3: In the following numerals, what place does the "1"
occupy?
a) 6,301,759? thousands place
b) 123? hundreds place
c) 91,000,235? millions place
