Question

Which of the following would involve an exact number? The mass of a box of apples, the number of dimes equal to a dollar, the number of grams in a cookie, the number of apples in a box. my guess is the number of dimes equal to a dollar, and the number of apples in a box.

Answer 1

A number is called exact number when we fond that there is no uncertainty in the number i.e a number with complete certainty is called exact number.

Some characteristics features of exact number generally are----------->

1. Exact number is a count number rather than a measured number.

2. It has infinite number of significant figures.

3. Most time it is integer.

4. It can not be expressed in many ways i.e it can not be simplified further.

Now those numbers which follow the above criteria are exact number-----------

(*) ."The mass of a box of apple"-------->First thing first , it is a measured number , as we can find mass of any object by measuring it.The mass value can also be expressed in different unit having different values.

*CONCLUSION---->"The mass of a box of apple" is not an exact number.

(**) . "The number of dimes equal to dollar" -------->

1 $ = 10 dimes. It is a number with the absolute value.It never can be changed.It is a count number.

*CONCLUSION---->"the number of dimes equal to dollar is an exact number.

(***) . "The number of grams in a cookie"----->Again it is a mass of something.Mass never becomes exact number,as it has no absolute value.

*CONCLUSION------>"The number of grams in a cookie is not an exact number.

(****) . "The number of apples in a box"------>It is a count number.It is always single valued.

*CONCLUSION------->"The number of apples in a box" is an exact number.