# Rounding

Hey guys! Welcome to this video on rounding and estimation!

Rounding is a helpful tool that allows us to simplify numbers so that they are easier for our brains to work with.

## Rounding

When rounding, the first thing you need to decide is your “round-off” digit. For instance, let’s say you are asked to round a number to the nearest hundreds place. The round-off digit is the digit in the hundreds place. The round-off digit is always the **place value** of the number that you are rounding to.

Once you know your round-off number, you then need to look at the very next number to the right of that round-off digit. If that number is less than 5, then the round-off digit stays the same, and you change everything to the right to zeroes. If that number is 5 or greater, add 1 to the round-off digit and change everything to the right of it to zeroes.

Let’s look at an example:

### Example 1

**Round 7,890.45 to the nearest hundreds place.**

So, we need to find our round-off digit, which is the number in the hundreds place, so 8. Now, look at the digit one place to the right, which is 9. 9 is more than 5, so our round-off digit 8 needs to be rounded up. So, we add one to the round-off digit and change everything to the right to zeroes. So that gives us 7,900.00. But since everything to the right is already zeroes, we don’t really need this decimal place so we can just rewrite this as 7,900.

Let’s look at another example.

### Example 2

**Round 37.9824 to the nearest thousandth.**

Remember *thousandth* is not the same as thousand. *Thousandth* lets us know that we are dealing with a decimal number, and *thousand* lets us know we are dealing with a whole number.

So, let’s find our round-off digit, which is 2. Now, look at the number to the right of that round-off digit, which is 4. Since 4 is less than 5, the round-off digit stays the same, and everything to the right of it can be dropped.

So, our answer then would be 37.982, and we drop the last digit.

I hope that this video has been helpful! See you guys next time!

## Frequently Asked Questions

#### Q

### How do you round to the nearest hundred?

#### A

Round a number to the nearest hundred by determining if the number in the tens place is greater than or equal to 5. If the tens place is greater than or equal to 5, increase the hundreds place by 1. If the tens place is less than 5, keep the hundreds place the same. Then, change every number after the hundreds place to a 0.

Ex. Round 6, 852 to the nearest hundred.

Look at the tens place. Since 5 ≥ 5, increase the hundreds place by 1 and replace every number after with a 0. 6,852 rounded to the nearest hundred is 6,900.

#### Q

### How do you round to the nearest tenth?

#### A

Round to the nearest tenth by looking at the hundredth place. If it is greater than or equal to 5, round the tenth place up one digit. If it is less than 5, keep the tenths place the same. Don’t write any numbers after the tenths place.

Ex. Round 16.423 to the nearest tenth.

Find the hundredths place: 2. 2 is less than 5, so round down (tenths place stays the same). Only write up to the tenths place. 16.423 rounds to 16.4

#### Q

### How do you round decimals?

#### A

Round decimals the same way you round non-decimal numbers. Check the number in the place value one below the one you are rounding to. If it is greater than or equal to 5, round up. If it is less than 5, round down. Then, only write the numbers until you reach the place you are rounding to.

Ex. Round 8.715 to the nearest whole number.

Since 7 is greater than 5, round up. 8.715 rounds to 9.

Ex. Round 63.271 to the nearest hundredth.

Since 1 is less than 5, round down. 63.271 rounds to 63.27.

## Practice Questions

**Question #1:**

Which of the following is 1,566.836 rounded to the nearest hundredths place?

1,566.83

1,600

1,566.84

1,566.846

**Answer:**

The correct answer is C: 1,566.84. First of all, we know that the “hundredths place” is the second digit on the right of the decimal; so we know that the 3 is our round-off digit. The digit on the right-side of the 3 is greater than or equal to 5, so we must *round up* that 3 to a 4 and drop the final digit (drop the 6 that’s in the thousandths place).

**Question #2:**

Which of the following is *two hundred seventy-four, and sixty-one hundredths* rounded to the nearest tenths place?

274.7

274.6

300

270

**Answer:**

The correct answer is B: 274.6. The first step is to write “two hundred seventy-four, and sixty-one hundredths” in numeric form: 274.61 . Now, since our rounding-off digit’s place value is the tenths place, we know that we will either round up the 6 or leave it alone (but no matter what, we will be dropping the 1). Because 1 is *less than* 5, we do *not* need to round that 6 up.

**Question #3:**

Consider the number 93.84659 , and you’ve been told to round this to the nearest thousandths place. What is your rounding-off digit?

6

5

7

4

**Answer:**

The digit that is in the thousandths place (three “spaces” to the right of the decimal) is 6. Because the digit to the right of it is 5, we know that we would *round up* the 6, and we’d end up with the number 93.847 .

**Question #4:**

Which of the following is 25.832344 rounded to the nearest thousandths place?

25.83

25.833

25.832

25.84

**Answer:**

The correct answer is C: 25.832. The 2 in the thousandths place is our rounding-off digit, and the digit to the right of it is 3. Since 3 is less than 5, we leave that 2 alone and drop any remaining digits (in other words: we truncate the number to the thousandths place).

**Question #5:**

Jenny pulls up to the nearest gas station, Oval J, to fill up her gas tank. A gallon of Unleaded gasoline costs $2.849, and she wants to fill her car with 11 more gallons of fuel. How much money will she spend on filling up her gas tank? *(Hint: wait to round! Rounding will be the very last step in your calculation.)*

$31.33

$31.24

$31.35

$31.34

**Answer:**

The correct answer is D: $31.34. While it’s tempting to round up the gasoline’s unit price ($2.849 per gallon) and then multiply $2.85 by 11 gal, that is *not* how we’d calculate our final answer! Actually, we first multiply 2.849 by 11 to find that Jenny would pay $31.339 for 11 gallons. This looks strange, though, right? We normally only pay amounts that end in the hundredths place (think: $1.00, $2.50, and so on), so we need to round $31.339 to the nearest hundredths place. Our rounding-off digit is the rightmost 3, and the digit to the right of that is 9. Since 9 is greater than or equal to 5, we *round up* our rounding-off digit to end up with the amount $31.34.