Rounding to any place

What is this skill?

Rounding replaces a number with a nearby friendlier one. In third grade children round to the nearest ten or hundred. In fourth grade they round whole numbers up to a million to any place: the nearest ten, hundred, thousand or ten thousand. 8,187 rounded to the nearest hundred is 8,200, and 28,864 rounded to the nearest thousand is 29,000.

The method is always the same two steps. Find the place you are rounding to and look at the digit just to its right. If that digit is 5 or more, round up, which means the digit in the target place goes up by one. If it is 4 or less, round down, which means it stays the same. Every digit to the right of the target place becomes zero. Number lines help children see why: 28,864 sits between 28,000 and 29,000, and it is closer to 29,000.

Why it matters

Rounding is the tool behind estimating, and estimating is how people decide whether an answer is reasonable. Rounding 4,812 + 3,096 to about 5,000 + 3,000 gives a quick check on a longer calculation. It is also how large numbers appear in everyday life, in news stories, distance signs and prices.

It also reinforces place value. A child cannot round 28,864 to the thousands without knowing which digit is in the thousands place and what sits to its right. Rounding exercises are a quick way to find out whether place value is secure.

Common mistakes

• Looking at the wrong digit. The deciding digit is the one right after the place being rounded, not the digit in the place itself.
• Forgetting to replace the digits on the right with zeros, writing 28,900 when rounding to the nearest thousand.
• Rounding up a 9 incorrectly. Rounding 698 to the nearest ten gives 700, because 69 tens becomes 70 tens, so the change carries into the hundreds.
• Rounding in stages, such as turning 8,187 into 8,190, then 8,200, then 8,000. Only the first digit to the right of the target place decides, so 8,187 to the nearest thousand is 8,000 because the digit is 1, not because of a chain.
• Treating 5 as “round down.” By the usual rule a 5 rounds up.

How to help at home

• Draw a number line from one thousand to the next and mark the midpoint. Place the number and see which end it is closer to.
• Round prices and counts you see: a 6,478-step walk is about 6,500 steps to the nearest hundred.
• Ask “nearest what?” every time. The same number rounds differently to the ten, hundred or thousand.
• Use rounding to check answers. Before your child adds two big numbers, ask for a rounded estimate and compare it afterwards.
• Practice the 4 versus 5 line with a quick game: say a number and a place, and your child answers up or down.

Worked examples

These are real questions from the Tutorsaurus rounding to any place practice, with the answers worked out.

1. Example 1

   Round 698 to the nearest ten.

   Answer: 700. Look at the digit to the right of the tens place. It is 5 or more, so round up: 700.

2. Example 2

   Round 8,187 to the nearest hundred.

   Answer: 8200. Look at the digit to the right of the hundreds place. It is 5 or more, so round up: 8,200.

3. Example 3

   Round 28,864 to the nearest thousand.

   Answer: 29000. Look at the digit to the right of the thousands place. It is 5 or more, so round up: 29,000.