Lesson Objectives

- Learn why we sometimes approximate values using the rounding procedure
- Learn the rule for rounding a whole number down
- Learn the rule for rounding a whole number up

## How to Round Whole Numbers

In many real world situations, an exact value is not needed. Let's suppose you were comparing the price of three used cars:

Example 1: Round 67 to the nearest ten

Step 1: Find the digit in the round-off place:

In this case, we are looking for the digit in the tens' place. In the number 67, the 6 is in the tens' place.

67

Step 2: We look at the digit to the right. In this case, our digit is a 7. This tells us we will be rounding up, since this falls in the category of 5 or more. We will increase the digit in the round-off place (6) by 1. This will give us a 7 in the tens' place.

77

Step 3: Replace the digit to the right of the round-off place with a zero

The 7 in the ones' place is changed to a 0. This will give us our final answer of 70.

67 rounded to the nearest ten is 70

Example 2: Round 2043 to the nearest thousand

Step 1: Find the digit in the round-off place:

In this case, we are looking for the digit in the thousands' place. In the number 2043, the 2 is in the thousands' place.

2043

Step 2: We look at the digit to the right. In this case, our digit is a 0. This tells us we will be rounding down, since this falls in the category of 4 or less. We will leave the digit in the round-off place (2) unchanged.

2043

Step 3: Replace each digit to the right of the round-off place with a zero

The 0 in the hundreds' place doesn't need to be changed, but we will change the 4 in the tens' place, along with the 3 in the ones' place each into a zero. This will give us our final answer of 2000.

2043 rounded to the nearest thousand is 2000

Example 3: Round 914,307 to the nearest ten thousand

Step 1: Find the digit in the round-off place:

In this case, we are looking for the digit in the ten thousands' place. In the number 914,307 the 1 is in the ten thousands' place.

914,307

Step 2: We look at the digit to the right. In this case, our digit is a 4. This tells us we will be rounding down, since this falls in the category of 4 or less. We will leave the digit in the round-off place (1) unchanged.

914,307

Step 3: Replace each digit to the right of the round-off place with a zero

The 0 in the tens' place doesn't need to be changed, but we will change the 4 in the thousands' place, the 3 in the hundreds' place, and the 7 in the ones' place each into a zero. This will give us our final answer of 910,000.

914,307 rounded to the nearest ten thousand is 910,000

- Ford: $15,195
- Mazda: $17,889
- Chevy: $28,135

- Ford: $15,000
- Mazda: $18,000
- Chevy: $28,000

- Ford: $15,200
- Mazda: $17,900
- Chevy: $28,100

### Rounding a Whole Number:

- Locate the digit in the round-off place (e.g., If Rounding to the nearest ten, we identify the digit in the tens' place)
- If the digit to the right of the round off place is:
- less than 5 (0,1,2,3, or 4) - leave the digit in the round-off place unchanged
- 5 or larger (5,6,7,8, or 9) - increase the round-off place digit by 1

- Replace each digit to the right of the round-off place with a zero

Example 1: Round 67 to the nearest ten

Step 1: Find the digit in the round-off place:

In this case, we are looking for the digit in the tens' place. In the number 67, the 6 is in the tens' place.

67

Step 2: We look at the digit to the right. In this case, our digit is a 7. This tells us we will be rounding up, since this falls in the category of 5 or more. We will increase the digit in the round-off place (6) by 1. This will give us a 7 in the tens' place.

77

Step 3: Replace the digit to the right of the round-off place with a zero

The 7 in the ones' place is changed to a 0. This will give us our final answer of 70.

67 rounded to the nearest ten is 70

Example 2: Round 2043 to the nearest thousand

Step 1: Find the digit in the round-off place:

In this case, we are looking for the digit in the thousands' place. In the number 2043, the 2 is in the thousands' place.

2043

Step 2: We look at the digit to the right. In this case, our digit is a 0. This tells us we will be rounding down, since this falls in the category of 4 or less. We will leave the digit in the round-off place (2) unchanged.

2043

Step 3: Replace each digit to the right of the round-off place with a zero

The 0 in the hundreds' place doesn't need to be changed, but we will change the 4 in the tens' place, along with the 3 in the ones' place each into a zero. This will give us our final answer of 2000.

2043 rounded to the nearest thousand is 2000

Example 3: Round 914,307 to the nearest ten thousand

Step 1: Find the digit in the round-off place:

In this case, we are looking for the digit in the ten thousands' place. In the number 914,307 the 1 is in the ten thousands' place.

914,307

Step 2: We look at the digit to the right. In this case, our digit is a 4. This tells us we will be rounding down, since this falls in the category of 4 or less. We will leave the digit in the round-off place (1) unchanged.

914,307

Step 3: Replace each digit to the right of the round-off place with a zero

The 0 in the tens' place doesn't need to be changed, but we will change the 4 in the thousands' place, the 3 in the hundreds' place, and the 7 in the ones' place each into a zero. This will give us our final answer of 910,000.

914,307 rounded to the nearest ten thousand is 910,000

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