Rounding Numbers

Why Do We Round Numbers

Many times we focus on finding values to a very exact degree of precision, but there are other times where we only need the rough estimate of a value. The process of rounding numbers is where a value is raised or lowered to a less precise number. We might round numbers where we know the precision is higher than we are confident in.

Another common situation is where we want to use a value in a computation and rounding the number to a nearby value makes working with the value much easier. Often rounding numbers makes it easier to perform mental math, especially when working with a longer sequence of numbers.

The rounding worksheets on this page provide plenty of practicing rounding whole numbers and rounding decimal numbers. Each set of rounding worksheets focuses on a different type of rounding, including starting with rounding decimals to only a single digit of precision, progressing through rounding to the tens, hundreds or thousands place. Additional sets of rounding worksheets deal with rounding to the right of the decimal place, rounding decimals to the tenths, hundredths or thousands place.

A common place where 3rd and 4th grade students can get tripped up rounding numbers is when the target place value digit has a nine in it and rounding up requires carrying over into the next place value. There are a special set of rounding worksheets specifically to practice this sometimes confusing extra step.

Rounding Numbers and Common Core

When working within the Common Core standard, rounding numbers is incorporated as part of the Number and Operations in Base 10 domain and is typically introduced in the third grade as part of CCSS.MATH.CONTENT.3.NBT.A.1. The rounding worksheets in this section are appropriate exercises for that domain, and the later worksheets dealing with rounding decimals exceed that area of the standard.

Rounding Numbers in Three Easy Steps

The steps to round numbers are fairly straight forward:

1. Identify the place value to which you are rounding. The problem you are given on one of the rounding worksheets here will specify the precision, for example, 'Round to the nearest ten.' For a number like 127, the number in the tens digit is '2' and that's the digit that we will potentially change by rounding. We'll call that 'the digit to be rounded' to make it easy to remember.
2. Look at the digit to the right of the digit to be rounded (the one we found in the first step.) If this digit is five or greater, then we round up by incrementing the digit to be rounded, otherwise we round down by leaving the digit to be rounded alone. In the example of 127, the digit to the right of the digit to be rounded is the 7 in the ones place. That value is five or greater, so we will round up and the digit to be rounded changes from 2 to 3.
3. Set all of the digits to right of the digit to be rounded equal to zero. In our example, the only digit to the right is the ones digit.

To recap, 127 rounded to the nearest ten is 130. Here are a few more rounding examples...

• 346.15 rounded to the nearest tenths is 345.2 (The value in the hundredths place is five or greater, so we round up the tenths.)
• 346.15 rounded to the nearest whole is 345 (The value in the hundredths place less than five, so we round down the ones.)
• 346.15 rounded to the nearest tens is 350 (The value in the ones place is five or greater, so we round up the tens.)
• 346.15 rounded to the nearest hundreds is 300 (The value in the tens place less than five, so we round down the hundreds.)

Rounding Worksheets for Whole Numbers

The first set of rounding worksheets deals with rounding whole numbers to the most significant digit. This makes selecting the digit to be rounded very obvious (it's always the left-most digit in the value). In the first set of rounding worksheets, the values are always two digit numbers rounded to the nearest ten, which is a super easy introduction to the part of the process where a student mush consider the value of the less significant digit (five or greater, or less than five). Additional rounding worksheets in these sets introduce rounding to the nearest hundred and rounding to the nearest thousand, which gradually introduces the need to identify the correct digit to look at and what to do with the remaining digits in the value.

Once these concepts are down, the other integer rounding worksheets deal with rounding to precisions where they may be digits to the right of the significant digit (so four example rounding a four digit number to the nearest ten). These worksheets will require students to correctly determine the place value for the digit to be rounded and know to leave alone the digits with greater place value to the left of that digit. Some of problems on these rounding worksheets involve longer digit numbers (up to six digits) and are great practice for whole number rounding once all the basics are down.

Rounding Worksheets for Decimals

Once students have mastered rounding whole numbers, moving on to rounding decimals is the next step. Rounding decimal numbers typically involves looking at the fractional place values (tenths, hundredths, thousandths and so on) and then rounding the appropriate place value digit to the left. The process is in many ways similar to rounding whole numbers, and the primary challenge to students is identifying by name the correct place value digit.

Just like the rounding worksheets in the previous section, these start out with less complex decimal rounding problems (problems where the digit to round and the digit to examine are unavoidably obvious) and then gradually work up to problems where students must identify the correct digit.

Rounding Negative Numbers

There's some discussion about the best way to round negative values, and it would seem the exact process depends somewhat on the problem domain. There's an interesting discussion including links to some of the different strategies for dealing with negatives at this link. In part because of the ambiguity, you won't find rounding worksheets for negative numbers here.