Round whole numbers and decimals: find the missing digit

key notes:

1. Rounding Whole Numbers

  • Definition: Rounding a number means adjusting its value to make it simpler, but keeping it close to the original value.
  • Rules for Rounding Whole Numbers:
    • If the digit in the place value you are rounding to is 5 or more, round up.
    • If the digit is less than 5, round down (or keep the same).
  • Example:
    • Round 3,765 to the nearest hundred: The hundreds digit is 7, and the next digit (tens) is 6, which is 5 or greater. So, round up to 3,800.

2. Rounding Decimals

  • Definition: Rounding decimals is similar to rounding whole numbers but involves decimal places.
  • Rules for Rounding Decimals:
    • If the digit in the place value you are rounding to is 5 or more, round up.
    • If it is less than 5, round down.
  • Example:
    • Round 12.638 to the nearest hundredth: The hundredths digit is 3, and the thousandths digit is 8, so round the hundredths up to 12.64.

3. Find the Missing Digit in a Rounded Number

  • Definition: In problems where a rounded number is given, the goal is to find the missing digit (or digits) based on rounding rules.
  • Steps to Find the Missing Digit:
    • Identify the place value the number is rounded to (e.g., nearest ten, hundred, or decimal place).
    • Use the rules of rounding to determine the missing digit.
  • Example:
    • A number is rounded to the nearest ten, and the result is 230. The missing digit in the ones place could be 0 to 4 (round down) or 5 to 9 (round up).

4. Examples

  • Example 1: The number 4,5_2 rounded to the nearest hundred is 4,500. What is the missing digit?
    • The missing digit is 0 because rounding 4,502 to the nearest hundred gives 4,500.
  • Example 2: The number 5.6_ rounded to the nearest tenth is 5.70. What is the missing digit?
    • The missing digit is 0 because rounding 5.60 to the nearest tenth gives 5.70.

5. Practice Problems

  • Round 1,238 to the nearest ten.
  • Round 8.735 to the nearest hundredth.
  • The rounded number is 540, and it is rounded to the nearest ten. What is the missing digit?
  • The rounded number is 2.70, and it is rounded to the nearest tenth. What is the missing digit?

Learn with an example

🔔 Which digit makes this statement true?

When ? 25 is rounded to the nearest hundred, the result is 700.

6 / 8 / 0 / 7

You want to round to the hundreds place, so look one place to the right:

?25

The digit one place to the right is a 2. As a result, we will be rounding down. So, ?25 rounds down to 700.

Because the missing digit becomes 7 after being rounded down, the missing digit must be 7.

🔔 Which digit makes this statement true?

? 893 rounded to the nearest thousand is 4,000.

6 / 4 / 3 / 5

You want to round to the thousands place, so look one place to the right:

?,893

The digit one place to the right is a 8. As a result, we will be rounding up. So, ?,893 rounds up to 4,000.

Because the missing digit becomes 4 after being rounded up, the missing digit must be 3.

🔔 Which digit makes this statement true?

When? 086 is rounded to the nearest thousand, the result is 8,000.

You want to round to the thousands place, so look one place to the right:

?,086

The digit one place to the right is a 0. As a result, we will be rounding down. So, ?,086 rounds down to 8,000.

Because the missing digit becomes 8 after being rounded down, the missing digit must be 8.

let’s practice: