Rounding

Think of rounding like tidying up a messy number. You're making it neater and easier to handle, usually by changing it to the closest "nice" number. It’s like when you're playing a game and you have 28 points, but you tell your friend you have "about 30 points." You've rounded 28 up to 30!

We round numbers to a specific place value. Remember place value? It's where a digit sits in a number (like the ones place, tens place, hundreds place, or even the tenths place after a decimal point). When you round, you're deciding which number your original number is closest to at that specific place value.

Here’s the golden rule for deciding if you round up or down:

• If the digit to the right of your target place is 5 or more (5, 6, 7, 8, 9), you round up. This means you increase the digit in your target place by one.
• If the digit to the right is less than 5 (0, 1, 2, 3, 4), you round down. This means the digit in your target place stays the same.

After you round, all the digits to the right of your target place become zeros (if they are before a decimal point) or disappear (if they are after a decimal point).

Let's say you're buying snacks for a party. You have $20, and you see a big bag of chips for $4.79, a pack of sodas for $7.15, and some cookies for $5.88. You want to quickly estimate if you have enough money without pulling out a calculator.

Here's how rounding helps:

1. Chips: $4.79. The ones place is 4. The digit to its right (the tenths place) is 7. Since 7 is 5 or more, you round up. So, $4.79 becomes $5.
2. Sodas: $7.15. The ones place is 7. The digit to its right (the tenths place) is 1. Since 1 is less than 5, you round down. So, $7.15 becomes $7.
3. Cookies: $5.88. The ones place is 5. The digit to its right (the tenths place) is 8. Since 8 is 5 or more, you round up. So, $5.88 becomes $6.

Now, add your rounded numbers: $5 + $7 + $6 = $18. Since $18 is less than your $20 budget, you can quickly tell that you probably have enough money! See how much faster that was than adding $4.79 + $7.15 + $5.88?

Let's round the number 3,472.638 to different place values. Follow these steps carefully!

1. Identify the target place value: This is the place you're rounding TO. The question will tell you this (e.g., "round to the nearest tens," "round to the nearest hundredth").
2. Look at the digit immediately to the right: This is the "decider" digit. It tells you whether to round up or down.
3. Apply the rounding rule:
   • If the decider digit is 5 or more (5, 6, 7, 8, 9), round up the digit in your target place. (Increase it by 1).
   • If the decider digit is less than 5 (0, 1, 2, 3, 4), round down the digit in your target place. (Keep it the same).
4. Change digits to the right:
   • Any digits between your target place and the decimal point become zeros.
   • Any digits after the decimal point (to the right of your target place) simply disappear.

Example 1: Round 3,472.638 to the nearest tens place.

1. Target place: Tens place (the digit 7).
2. Decider digit: The digit immediately to the right is 2 (in the ones place).
3. Rule: 2 is less than 5, so we round down. The 7 stays the same.
4. Change digits: The 2 (ones place) becomes 0. The .638 (after the decimal) disappears.
   • Result: 3,470

Example 2: Round 3,472.638 to the nearest hundredths place.

1. Target place: Hundredths place (the digit 3).
2. Decider digit: The digit immediately to the right is 8 (in the thousandths place).
3. Rule: 8 is 5 or more, so we round up. The 3 becomes 4.
4. Change digits: The 8 (thousandths place) disappears.
   • Result: 3,472.64

Example 3: Round 3,472.638 to the nearest whole number (or ones place).

1. Target place: Ones place (the digit 2).
2. Decider digit: The digit immediately to the right is 6 (in the tenths place).
3. Rule: 6 is 5 or more, so we round up. The 2 becomes 3.
4. Change digits: The .638 (after the decimal) disappears.
   • Result: 3,473