#### Introduction:

Do you know that we round the number in our day-to-day lives? In the same way, we also round decimal numbers without knowing.

Rounding, which is a way for us to approximate a numerical value, helps us to deal with different situations:

- Money
- Sports statistics
- Height and weight
- Time

**Examples: **

Let’s look at some examples:

- Rather than saying you are 4 feet and 4 and three-quarters inches, we would round up and say you’re 4 feet 5 inches.
- Let’s assume the time is 2:01 pm. Isn’t it just easier to round and say it’s 2 pm?
- Decimal rounding in real life:

Now, let’s apply the comparison rules to decimals stepwise in two different methods:

- Place value
- Number line

#### Round Decimals Using a Number Line:

**Number Line: **

A number line is a tool to compare and order numbers.

Rules for rounding decimals using a number line:

**Step 1:**

Create a number line with a scale that allows you to locate the given decimal.

**Step 2:**

Place a dot on the number line where the given decimal fits.

**Step 3: **

To round the decimal, examine the two numbers, one on either side of the decimal, that end with the appropriate place value. If the decimal is closer to the number on the left, round down to that number. If the decimal is closer to the number on the right, round up to that number. If the decimal is directly in the middle, round up to the number on the right.

Let’s understand this better with the help of the examples:

**Example 1: **

Round 7.69 to the nearest whole number.

**Solution: **

**Example 2: **

Round 5.34 to the nearest tenth.

**Solution: **

#### Round Decimal Numbers Using Place Value:

Rounding can help to find which whole, tenth, or hundredth a decimal is closest to.

Rules for rounding decimal numbers by using place value:

**Step 1:**

Find the rounding place. Look at the digit to the right of the rounding place.

**Step 2:**

If the digit is 5 or greater, add 1 to the rounding digit. If the digit is less than 5, leave the rounding digit alone.

**Step 3:**

Drop the digits to the right of the rounding digit.

Let’s understand this better with the help of the examples:

**Example:**

Round 38.519 to the nearest whole, tenths, and hundredths.

**Solution: **

Round up to the nearest whole number:

**Step 1:** Find the rounding place and look at the digit to the right of the rounding place.

**Step 2: **Since the digit is 5 or greater, add 1 to the rounding digit.

**Step 3:** Drop the digits to the right of the rounding digit.

So, 38.519 rounded to the nearest whole is 39.

Round up to the nearest tenths:

**Step 1:** Find the rounding place and look at the digit to the right of the rounding place.

**Step 2:** Since the digit is less than 5, leave the rounding digit alone.

**Step 3:** Drop the digits to the right of the rounding digit.

So, 38.519 rounded to the nearest tenth is 38.5.

Round up to the nearest hundredths:

**Step 1: **Find the rounding place and look at the digit to the right of the rounding place.

**Step 2:** Since the digit is 5 or greater, add 1 to the rounding digit.

**Step 3:** Drop the digits to the right of the rounding digit.

So, 38.519 rounded to the nearest thousandths is 38.52.

### Try it!

A car rental service charges customers for the number of miles they travel, rounded to the nearest whole mile. Tim travels 45.72 miles. For how many miles will he be charged?

**Solution:**

Round up to the nearest whole number:

**Step 1: **Find the rounding place and look at the digit to the right of the rounding place.

**Step 2: **Since the digit is 5 or greater, add 1 to the rounding digit.

**Step 3:** Drop the digits to the right of the rounding digit.

So, 45.72 rounded to the nearest whole is 46.

So, Tim will be charged for 46 miles.

Exercise:

#### Exercise:

- Round 6.31 to the nearest whole number.
- Round 24.38 to the nearest tenths.
- Round 0.291 to the nearest hundredths.
- Round the number 201.452 to the place of the underlined digit.
- Round the number 9.319 to the place of the underlined digit.
- Round the number 3210.52 to the place of the underlined digit.
- Write three different numbers that round to 1.4 when rounded to the nearest tenths.
- Write two different numbers that round to 32.00 when rounded to the nearest hundredths.
- The height of a horse is 1.625 m. What is the height of the horse rounded to the nearest hundredth?

10. A car-rental service charges customers for the number of miles they travel, rounded to the nearest whole mile. Blake travels 89.54 miles. For how many miles will he be charged?

#### Concept Summary:

#### What We Have Learned:

- Use number lines to round decimal numbers
- Round decimal numbers to the nearest whole numbers, tenths, or hundredths

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