audio read-through Deciding if Numbers are Equal or Approximately Equal

Many real-life problems involve numbers that are not convenient to work with without calculator assistance. Many calculator-solved problems give an approximate solution, not an exact solution, and the purpose of this section is to increase your awareness of the difference between the two.

When two numbers $\,x\,$ and $\,y\,$ live at the same place on the number line, we say ‘$\,x\,$ equals $\,y\,$’ and write ‘$\,x = y\,$’. However, when two numbers $\,x\,$ and $\,y\,$ are just close to each other, but not equal, we say that ‘$\,x\,$ is approximately equal to $\,y\,$’.

Here, you will compare two numbers, and decide if they are equal, or approximately equal.

Examples

Question: Compare $\,\frac13\,$ and $\,0.333333\,$.
Answer: approximately equal
Question: Compare $\,\frac4{10}\,$ and $\,0.4\,$.
Answer: equal

Practice

Do not use your calculator for these problems.

Compare  
  and  
 :
EQUAL
APPROXIMATELY EQUAL