## What is Rounding?

In math, **rounding** *is replacing a number with a number that has approximately the **same value*. This new number is used for estimation and quicker arithmetic. For example if you were at the store and items cost $3.19, $5.72, $7.45 and you wanted to know how much it will cost to get all of the items you can round.

It is easier to add $3 + $6 + $7 than to add $3.19 + $5.72 + $7.45. When you look at the sums, they are about the same!

$3 + $6 + $7 = **$16** $3.19 + $5.72 + $7.45 = **$16. 36**

This is an example of estimation. Estimation is when you use what you see or know to make a reasonable guess about a total amount. Rounding is often used to help with estimation.

As we use bigger numbers, sometimes there are a lot of digits to keep track of. We want to use numbers that are easier to work with but close to the original value. The more that a number is rounded, the more that an estimation is going to be off.

Here we have unit blocks that represent 212. Those twelve blocks do not look like a lot when comparing them to the hundreds. If we removed them, the value only changes a little, in fact, it changes by twelve.

212 can be rounded to 200

Let’s take a look at another example. Here we have unit blocks that represent the number 389.

Look at all of those tens and ones! We only need to place one tens and one ones block to get another hundred!

389 can be rounded to 400.

## How To Round

When you round, you want to *start with the place value you want to round to*. You can round to any place value. You can even round to a decimal place. In this lesson, we will be rounding to the nearest hundred. This means we want to find the number in the hundreds place. It helps to underline the number in the place value that you are rounding to.

Next, we want to look at the value one place to the right. Since we are rounding to the hundreds place, we want to look at the number in the tens place. Let’s circle that number. This number will determine if we **round up** or **round down**.

## Rules of Rounding

If the number we want to round to, in this case the hundreds place is followed by a **5, 6, 7, 8, or 9 we round up**. This means that the number in the hundreds place will go up by one. All digits to the right will change to zero.

If the number we want to round to is followed by a **0, 1, 2, 3, or 4 we round down**. This means that the number we are rounding to, in this example the hundreds place, will stay the same. All digits to the right will change to zero.

The number to the right of the hundreds place is a one. This means that we will round down to 700.

## Why zero?

The zeros are important to hold the place value of the number. If we were to keep the seven and not place the zeros we would have the number seven, not seven hundred. Seven is not close to the same value as 715!

Round the following numbers to the nearest hundreds.

If the circled number is 0, 1, 2, 3, or 4 we will round down. The digit in the hundreds place will stay the same and the digits to the right will change to zeros. Fantastic!

If the circled number is 5, 6, 7, 8, or 9, we will round up. The digit in the hundreds place will go up by one and the digits to the right will change to zeros.

You have just rounded these numbers to the nearest hundreds. Did you notice that the digits to the left like the thousands place did change when we rounded?

## Try it!

There are about 200 passengers on a plane. Could there be 261 passengers on the plane?

If there are about 200 passengers on a plane, that means that the number of passengers that are on the plane will be around 200. Let’s look at what 261 will round to. The number to the right of the hundred place is six.

That means that the number will round up to the next hundred, 300. 261 is about 300. This means that 261 is too big of a number for the number of passengers on the plane.

How many passengers could be on the plane? We know that if there is a five or more in the tens place, then the number will round up. The largest number that has a two in the hundreds place and a 4 in the tens place is 249. What about numbers that round up to 200?

Now we want a one in the hundreds place so that it can round up to two hundred. The smallest number that will round up will have a five in the tens place. The smallest number can be 150.

There can be between 150 and 249 passengers on the plane.

## Did you know?

The symbol ≈ means “approximately equal to”

Scientific notation can be used to write really large or small rounded numbers.

Truncating a number means dropping all decimal places without rounding.

## Practice questions

Which of the following numbers will round to 600?

- 589
- 645
- 523
- 673

589 and 645 will round to 600.

Solution:

Start by looking at the digits in the tens place. This will determine if the number will round up to the next hundred or not. Numbers that have a five in the hundreds place and five or more in the tens place will round up to six hundred. Numbers that have a six in the hundreds place and four or below in the tens place will round down to six hundred.

5**8**9 rounds to 600

6**4**5 rounds to 600

5**2**3 rounds to 500

6**7**3 rounds to 700

Which of the following are true statements?

- 371 is about 400
- 2,863 is about 2,800
- 531 is about 500

- 371 is about 400
- 531 is about 500

Solution:

The wording “is about” indicates that we want to round the number to find what value the original is close to. All of the options are looking at numbers rounded to the hundreds.

371 is about 400

There is a seven in the tens place. This will round up to the next hundred which is 400.

This statement is **true**.

2,863 is about 2,800

There is a six in the tens place. This means that the number will round up to the next hundred which is a nine. 2,863 is about 2,900. This statement is **not true**.

531 is about 500

There is a three in the tens place. The number will round down to 500. This statement is **true**.

Round the following to the nearest hundred.

100

Solution:

This represents 113. By removing the 13, the value will not change too much. This

means that we will want to round down to **100**.

## Frequently Asked Questions

Rounding numbers provides a number that is about the same value as the original but uses less digits and is easier to work with in terms of arithmetic.

Look at the number to the right of the place value you want to round to. If the number is four or below, you want to round down. If the number is five or more, you would up.

The digits to the right of the place value you want to round to all change to zero.

The numbers to the left of the place value you want to round do not change when rounding.

Rounding is when the numbers are changed to a value that is close to the original value.

Estimation is when you use what you can see or know to make a reasonable guess about an amount. You may use rounding to make an estimation.

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