What's the place value of a digit in a negative number?

[Othman]

Hi,
I would like to know what is the place value of a digit in a negative number, for instance 2 in -123 (base 10).
I don't know if it's -20 or 20.

 

[JeffM]

Nice question

[MATH]-123 = (-1)(123) = (-1)(100 + 20 + 3) = -100 - 20 - 3.[/MATH]
The distributive law comes to our rescue again.

 

[Othman]

Nice question

[MATH]-123 = (-1)(123) = (-1)(100 + 20 + 3) = -100 - 20 - 3.[/MATH]
The distributive law comes to our rescue again.

Thanks for your answer
I understand the concept of distributive law howevever I'm not sure of the answer to my question since I can write -123 both ways:
-123 = - (100 + 20 + 3)
-123 = -100 + -20 + -3

 

[Dr.Peterson]

Thanks for your answer
I understand the concept of distributive law however I'm not sure of the answer to my question since I can write -123 both ways:
-123 = - (100 + 20 + 3)
-123 = -100 + -20 + -3

It seems to me that what you've shown here is that the place value of the 2 in 123 is 20, while the place value of the 2 in -123 is -20.

On the other hand, in my experience we don't generally talk about "the place value of a digit" in a negative number; the place value exists in the positive numeral, whose value we then negate. That is, we use place values to read natural numbers, and handle the negative sign separately. In particular, the algorithms we use for operations are applied to unsigned numbers, rather than, for example, adding 43 + -12 by adding 4 + -1 and 3 + -2, or anything like that.

Ultimately, this is just a matter of how one chooses to define "place value", which is not done consistently -- because the term (in this sense) is used not in mathematics proper, where definitions are central, but in pedagogy, talking to children. In fact, I don't think it's generally used after students learn about signed numbers!

The important question is, why do you want to know? What would you do differently based on the answer?

 

[Steven G]

I can write 123 as -(-100 + -20 + -3). Does that mean that the 2 is -20?

If you owed me $123, I would gladly accept 1-$100 bill, 2-$10 bills and 3-$1 bills.

 

[tarry_01]

Place value is just the numerical value that a digit has by virtue of its position. So in your case the position is tens the answer should be 20 irrespective of the sign, the sign in mathematics is basically the direction and place value targets the numerical digits.

 

[Othman]

Thank you for your answers, sorry for the late response.
I guess I didn't know the proper definition of place value (I didn't know this concept before) I wrongly assumed that the place value of a digit in a negative number would be negative as well.
Sorry for the stupid question.

 

[Dr.Peterson]

Thank you for your answers, sorry for the late response.
I guess I didn't know the proper definition of place value (I didn't know this concept before) I wrongly assumed that the place value of a digit in a negative number would be negative as well.
Sorry for the stupid question.

I wouldn't call it stupid; it's actually the kind of question a mathematician would ask when given a definition and trying to extend it to a domain in which no examples have been given! It just doesn't necessarily have an answer.