Rounding Numbers

Rounding numbers can be very useful when answering questions. For example, would you like to know that the bus is coming in 0.7666666666667 hours or would you rather see that it is coming in ~0.75 hours or 45 minutes? Maybe a better example is on your homework. What if the decimal repeats forever? We obviously can't write a never ending number. By rounding the number, we create a simpler answer that almost anyone can understand.

Where to start with rounding? Typically in a homework situation, you will be told the number of places you will need to round to. This could be listed as the nearest tenth (0.1) or nearest thousandth (0.001). For starters, you will need to know what those places mean.

Let's break down the number 12.5681 into places.

 

Now that you know what the places are, we can begin rounding. Let's look at 12.5681 again and round it to the nearest tenth.

A general rule of rounding is to look at the number just to the left of the place you are rounding to.

12.568

Since this number is equal to or greater than 5, we would round 6 up to 7, leaving us with 12.57.

If the digit is less than 5 (<5), we would leave the proceeding number as is. For example, let's round that same number to the nearest thousandth.

12.5681

 

Since 1 < 5, we can round this to 12.568.

 

 

Keep in mind that you should never round an already rounded number. This time let's look at the number 15.346, let's say we need to round to the nearest tenth. We will still follow the same process. We can't round to the 100th and then round that to the tenth.

 

The answer would be 15.3 (15.34 rounds to 15.3). It would be a mistake to say that since 15.346 rounds to 15.35, that would then round to 15.4. You will always need to look at the original number and round based the digit following your target place.

 

Simple Enough? Try it out on your homework now. Still having problems? Contact us to submit your problem or to set up one-on-one tutoring.