Rounding to the Nearest 10 - Second Grade Mathematics

In everyday life, you often do not need to know the exact number down to the single unit; an estimate or friendly number is faster, easier to communicate, and simpler to calculate in your head. Rounding is the mathematical tool that replaces a complex number with the closest friendly multiple of 10. Multiples of ten (such as 10, 20, 30, 40) are called friendly numbers because their ones digit is zero, making them quick to add and subtract. In this chapter, you will learn how to find bounding tens on a number line, master the halfway rule of 5, and round two-digit and three-digit numbers to the nearest ten with confidence.

What Does Rounding Mean?

Rounding means finding which multiple of ten a number is closest to on a number line.

The Number 37 on a Number Line between 30 and 40:
  30   31   32   33   34   35   36   37   38   39   40
--+----+----+----+----+----+----+----+----+----+----+-->
  <------- 7 steps -------->|<--- 3 steps --->
                           Midpoint
37 is only 3 steps away from 40, but 7 steps away from 30.
Therefore, 37 rounds UP to 40!

The Bounding Tens

Every number sits between two friendly multiples of ten, known as its bounding tens or neighbor tens. For 37, the lower bounding ten is 30, and the upper bounding ten is 40. For 82, the lower bounding ten is 80, and the upper bounding ten is 90. For 164, the lower bounding ten is 160, and the upper bounding ten is 170. Finding your two bounding tens is always the first step in rounding.

Distance Determines the Winner

Look at where the number sits between its bounding tens. If the number is closer to the lower ten, it rounds down. If it is closer to the upper ten, it rounds up. In the diagram above, 37 is much closer to 40 (only 3 steps away) than to 30 (7 steps away), so 37 rounds to 40.

The Halfway Rule: What to Do with 5

What happens when a number lands exactly in the middle, such as 35?

The Roller Coaster Rule at the Midpoint:
          35 (Peak)
         /  \
        /    \
  30   /      \   40
------+--------+------>
Numbers 31, 32, 33, 34 roll back down to 30.
Numbers 35, 36, 37, 38, 39 roll forward to 40!

The Mathematicians' Convention

The number 35 is exactly 5 steps away from 30 and exactly 5 steps away from 40. It is tied! To prevent confusion, mathematicians all over the world agreed on a universal convention: when a number is halfway, always round UP to the larger ten. Think of reaching the top of a roller coaster hill: once you reach the very peak at 5, momentum pushes you forward into the upper decade.

The Ones Digit Decision Rule

This gives us a simple and foolproof rule for rounding to the nearest ten: Look at the ones digit: If the ones digit is 0, 1, 2, 3, or 4 (less than 5), round DOWN to the lower ten. If the ones digit is 5, 6, 7, 8, or 9 (5 or more), round UP to the upper ten.

Rounding 3-Digit Numbers to the Nearest 10

The exact same rounding rule applies to three-digit numbers. When rounding to the nearest ten, you only look at the tens and ones places; the hundreds place usually stays along for the ride.

Rounding 243 to Nearest Ten:
Bounding Tens: 240 and 250
Ones digit is 3 (less than 5).
243 is closer to 240.
243 rounds to 240.

Rounding 586 to Nearest Ten:
Bounding Tens: 580 and 590
Ones digit is 6 (5 or more).
586 is closer to 590.
586 rounds to 590.

When Rounding Crosses a Century

Be careful when rounding a number ending in the nineties, such as 397: The bounding tens for 397 are 390 and 400. The ones digit is 7, which tells you to round up. Rounding up from 39 tens gives 40 tens, which is 400! Therefore, 397 rounded to the nearest ten is 400.

Practice Exercises

Exercise 1: Round the following two-digit numbers to the nearest ten, stating the lower and upper bounding tens for each: 24, 68, 45, and 81.

Exercise 2: Round the number 362 to the nearest ten. Explain your thinking step by step using the ones digit rule.

Exercise 3: Round the number 496 to the nearest ten. Explain what happens to both the tens and hundreds digits.

Exercise 4: A jar contains 73 marbles. If you round the number of marbles to the nearest ten to tell a friend roughly how many are in the jar, what friendly number would you say?

Solutions and Explanations

Solution to Exercise 1: For 24, the bounding tens are 20 and 30; since the ones digit is 4, it rounds down to 20. For 68, the bounding tens are 60 and 70; since the ones digit is 8, it rounds up to 70. For 45, the bounding tens are 40 and 50; since it is at the midpoint 5, it rounds up to 50. For 81, the bounding tens are 80 and 90; since the ones digit is 1, it rounds down to 80.

Solution to Exercise 2: To round 362 to the nearest ten, first identify the bounding tens: 360 and 370. Next, look at the ones digit, which is 2. Because 2 is less than 5, the number is closer to the lower ten. Therefore, 362 rounds down to 360.

Solution to Exercise 3: The bounding tens for 496 are 490 and 500. The ones digit is 6, which is 5 or greater, so we must round up to the next ten. Adding 1 ten to 49 tens results in 50 tens, which equals 500. Both the tens digit and hundreds digit change, yielding 500.

Solution to Exercise 4: To round 73 to the nearest ten, note that the bounding tens are 70 and 80. Because the ones digit is 3 (which is less than 5), 73 is closer to 70 than to 80. You would tell your friend that there are roughly 70 marbles in the jar.