Rounding Numbers Lesson

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

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

It would be much easier to remember the prices as:

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

These numbers represent approximations or estimates. Approximations are values that are close to the actual value, but not exactly the same. It would be just as fair to estimate the used car prices as:

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

To ensure that everyone gets the same value when approximating, we can use a process known as rounding. When we round, we are approximating to a specific round-off place (ones, tens, hundreds,...). The value we obtain when we round depends on how accurate we would like our approximation to be.

Rounding a Whole Number:

1. Locate the digit in the round-off place (e.g., If Rounding to the nearest ten, we identify the digit in the tens' place)
2. 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
3. Replace each digit to the right of the round-off place with a zero

Let's take a look at a few examples:
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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