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? 4Example 2: Write out the following numerals:
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
a) 8 thousands, 6 hundreds, 4 tens, 7 ones. 8,647Example 3: In the following numerals, what place does the "1" occupy?
b) 9 ten thousands, 0 thousands, 0 hundreds, 1 ten, 2 ones. 90,012
a) 6,301,759? thousands place
b) 123? hundreds place
c) 91,000,235? millions place