Expert: Josh - 9/13/2006

Question
what is the difference beetween place value and the the value of a digit in a number? the number 123456 ,is the place value of digit 4 is hundreds and value of digit 4 is 400 ?please clarify?

Answer
Hello,

The term "place value" has to do with how numbers are represented in the metric system. The metric system is essentially a base-10 representation. If we consider a number string "dcba" for instance, each digit "a","b","c" or "d" can take one of ten integer values from the set {0,1,2,3,4,5,6,7,8,9}. That's why it's called the base-10 system. Now, if d=1, c0, b=0 and a=0, we have "1000". Here, "d" is simply a multiplier, which gives some units of "thousand". The fourth digit from the right, viz. "d", is said to have a place value of a "thousand". By a similar token, "c" is said to have a place value of a "hundred", because "c00" represents c times a hundred. If "c" has a value of 3, then, "300" is three hundred (3 times 100).

In general, observe that the number string "dcba" actually represents d*1000+c*100+b*10+a*1. e.g., 8246=8*1000+2*100+4*10+6*1.

The place value denoted by a digit depends on its position (how far it is from the right hand side of the number string). All digits, in this example, I am referring to "d","c","b" and "a", each can take one of ten values from {0,1,2,3,4,5,6,7,8,9}.

In your question, the digit 4 in "123456" has a place value of "hundred" and the multiplier is 4. It represents 4*100=400.