Rounding Decimals for 5th Grade: Nearest Tenth and Hundredth

Rounding decimals helps us estimate, simplify calculations, and communicate approximate values. In Grade 5, students round decimals to a given place value—nearest tenth, hundredth, or thousandth. Rounding is used everywhere: prices (round to nearest cent), distances (round to nearest tenth of a mile), times (round to nearest second), and measurements (round to nearest millimeter). Understanding when and how to round decimals is a practical skill for everyday life and for checking whether answers are reasonable.

Rounding decimals follows the same rules as rounding whole numbers: identify the place you are rounding TO, look at the digit to the RIGHT, and round up (add 1) if that digit is 5 or greater, or round down (keep the same) if it is 4 or less. The only difference is that we do not add zeros to the left of the decimal point when rounding—we simply drop digits to the right or adjust the target digit.

DETAILED EXPLANATION

Rounding rules for decimals:

1. Identify the place value you are rounding TO (the “target” digit).

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2. Look at the digit to the RIGHT of that place.

3. If that digit is 5 or greater, ROUND UP: add 1 to the target digit, and drop all digits to the right.

4. If that digit is 4 or less, ROUND DOWN: keep the target digit the same, and drop all digits to the right.

5. When rounding up and the target digit is 9, we “carry”: 9 + 1 = 10, so we add 1 to the place to the left (e.g., 2.97 rounded to nearest tenth → 3.0).

Examples: Round 2.347 to nearest tenth. The tenths digit is 3. The hundredths digit is 4. Since \(4 < 5\), round down. Answer: 2.3.

Round 5.678 to nearest hundredth. The hundredths digit is 7. The thousandths digit is 8. Since \(8 \geq 5\), round up: 7→8. Answer: 5.68.

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WORKED EXAMPLES WITH STEP BY STEP SOLUTIONS

Example 1

A pencil weighs 2.347 grams. Round to the nearest tenth.

Solutions:

Step 1: Identify the place we are rounding TO: the tenths place. The tenths digit is 3.

Step 2: Look at the digit to the RIGHT of the tenths place: the hundredths digit, which is 4.

Step 3: Apply the rule: Since \(4 < 5\), we ROUND DOWN. The tenths digit 3 stays 3.

Step 4: Drop all digits to the right of the tenths place. The hundredths and thousandths are dropped.

Step 5: Write the rounded number: 2.3 grams.

Answer: 2.3 grams

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Example 2

Round 5.678 to the nearest hundredth.

Solutions:

Step 1: Identify the target place: hundredths. The hundredths digit is 7.

Step 2: Look at the digit to the right: the thousandths digit, which is 8.

Step 3: Since \(8 \geq 5\), we ROUND UP. The hundredths digit 7 becomes 8.

Step 4: Drop the thousandths digit. Write: 5.68.

Answer: 5.68

Example 3

A race time was 12.995 seconds. Round to the nearest tenth for the scoreboard.

Solutions:

Step 1: Target place: tenths. The tenths digit is 9.

Step 2: The digit to the right (hundredths) is 9. Since \(9 \geq 5\), we ROUND UP.

Step 3: 9 + 1 = 10. We cannot write 10 in one digit, so we CARRY. The tenths digit becomes 0, and we add 1 to the ones digit.

Step 4: Ones: 2 + 1 = 3. Tenths: 0. Drop hundredths and thousandths. The result is 13.0.

Step 5: Write with one decimal place: 13.0 seconds (to show we rounded to tenths).

Answer: 13.0 seconds

Example 4

Round 8.456 to the nearest hundredth.

Solutions:

Step 1: Target place: hundredths. The hundredths digit is 5.

Step 2: Digit to the right (thousandths): 6. Since \(6 \geq 5\), ROUND UP.

Step 3: 5 + 1 = 6. Drop thousandths. Result: 8.46.

Answer: 8.46