What is the correct way to explain the difference between 3 1/4 and 3.25%

2 Answers

durbanville's profile pic

durbanville | High School Teacher | (Level 2) Educator Emeritus

Posted on

The terms used to identify `3 1/4` and `3.25` would be "mixed number" (which is a whole number and a fraction) and "decimal fraction," respectively. The two are equal to each other.

`3 1/4=3.25`

However, whe you add the percentage sign to the `3.25` 

this changes the decimal fraction from 3.25 to

`3.25/100` as the symbol % means "out of 100"

To convert this back to a decimal fraction do the division:

`3.25% = 0.0325`

To compare your new decimal fraction to a standard fraction you would simplify it. It is no longer a mixed number as it is smaller than 1 so there is no whole number:

`0,0325= 13/400` in its simplified form.

So to explain the difference -

A percentage sign means that a number must be divided by 100 as % (percent) means "out of 100" so the difference between `3 1/4 and 3.25%` is that the decimal fraction must be over 100 and `3.25/100`  is not equivalent to `3 1/4`

Wiggin42's profile pic

Wiggin42 | Student, Undergraduate | (Level 2) Valedictorian

Posted on

3 1/4 and 3.25% are two ways of writing numbers. To compare them, we must make both in the same form. 

3.25% can be written as 3.25/100

Now its easy to see that 3 and 1/4 is definitely larger than 3.25/100. The key to this is to remember what a percent means.