Reading Numbers That Have Negative Digits
Information for Teachers

The importance of writing numbers in long hand decreases because of the new technology of data processing. But the importance of reading a variety of different representations of numbers increases because of the emphasis on collaboration and communication during the process of solving mathematical problems.

Negative digits in representing numbers in written base-10 have many applications, but this is not generally recognized. Therefore there are no established standards regarding how such numbers should be read. So when you use such notation in your classroom, you have freedom to use any terminology you consider appropriate.

But here we give some very general guidelines about reading numbers based on the way that they can be written as arithmetic expressions, which are often called expanded notation.


The number 2317 can be read either as "twenty three hundred seventeen" or as "two thousand, three hundred seventeen". These two ways of reading correspond to two different arithmetic expressions, 23*100 + 17 and 2*1000 + 3*100 + 17. The operations times, *, and plus, +, are not read, but they can be inserted to explain the meaning of such phrases to students with different linguistic backgrounds.

For example, a student who speaks Polish at home may need an explanation that "twenty three hundred" means "twenty three times one hundred"; and a student who speaks Chinese may need to be told that "seven-teen" means "ten plus seven"; and a German student could say that "twenty seven" means "seven plus twenty".

The same principle can be used in reading numbers that are written with negative digits. For example, the number 28759 = 3 1 3 6 1, can be written as 30*1000 - 13*100 + 6*10 - 1. And it can be read, "thirty thousand minus thirteen hundred plus sixty minus one".

In reading numbers with negative digits. you have two degrees of freedom. One is the choice of an arithmetic formula, and the other is which operations to read and which to omit. And because there are no established standards, in both cases you need to use your own judgment.

Webpage Maintained by Owen Ramsey
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