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Arithmetic Place value Significant figures Adding decimalsHere you will learn how to round numbers to the nearest 10, 100, and 1000 as well as how to round decimal numbers to the nearest tenth, hundredth and thousandth.

Students will first learn about rounding numbers as part of their work with place value in the 3rd grade. They build upon this knowledge as they progress through 4th and 5th grade.

**Rounding** a number means to simplify it by scaling it up or down.

Rounding is a type of estimation used to make calculations easier.

To round numbers, you can use a number line or you can apply a rule.

For example, let’s look at several rounding samples with and without a number line.

Rounding \bf{14\underline{7}8} to the nearest \bf{10} with a number line |
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1478 is to the right of the halfway point and closer to 1480 than 1470. It will round to be 1480. |

Rounding \bf{14\underline{7}8} to the nearest \bf{10} with the rule |

7 tens is in the rounding place, and 8 ones is to the right of 7. The rule says that if the number to the right of the rounding digit is greater or equal to 5 \, (5, 6, 7, 8, 9), round up by adding 1 to the rounding digit. 7 tens becomes 8 tens, and the rest of the digits to the right change to be 0’ s. 14\underline{7}8 → Rounded to the nearest ten is 1480 |

Rounding \bf{1\underline{4}78} to the nearest \bf{100} with a number line |
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1478 is to the right of the halfway point and closer to 1500 than 1400. It will round to be 1500. |

Rounding \bf{1\underline{4}78} to the nearest \bf{100} with the rule |

4 hundreds is in the rounding place, and 7 tens is to the right of 4. The rule says that if the number to the right of the rounding digit is greater than or equal to 5 \, (5, 6, 7, 8, 9), round up by adding 1 to the rounding digit. 7 is greater than 5, so 4 hundreds will become a 5 hundreds. 1\underline{4}78 → Rounded to the nearest 100 is 1500 |

Rounding \bf{\underline{1}478} to the nearest \bf{1000} with a number line |
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1478 is to the left of the halfway point and closer to 1000 than 2000. It will round to be 1000. |

Rounding \bf{\underline{1}478} to the nearest \bf{1000} with the rule |

1 thousand is in the rounding place, and 4 hundred is to the right of the rounding digit. The rule says that if the number to the right of the rounding digit is less than 5 \, (5, 6, 7, 8, 9), round down by leaving the rounding digit alone. 4 is less than 5, so the digit 1 will remain as a 1. \underline{1}478 → Rounded to the nearest 1000 is 1000 |

Rounding \bf{147\underline{8}.5} to the nearest whole number with a number line |
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1478 is the halfway point between 1478 and 1479 and the same distance away from either number. When this happens, you will round up 1479. |

Rounding \bf{147\underline{8}.5} to the nearest whole number with the rule |

8 ones is in the rounding place, and 5 tenths is to the right of the rounding digit. The rule says that if the number to the right of the rounding digit is greater than or equal to 5 \, (5, 6, 7, 8, 9), round up by adding one to the rounding digit. 5 is equal to 5, so 8 ones becomes 9 ones. 147\underline{8}.5 → Rounded to the nearest whole number is 1479 |

How does this relate to 4th grade math and 5th grade math?

**Grade 3 – Number and Operations – Base Ten (3.NBT.A.1)**Use place value understanding to round whole numbers to the nearest 10 or 100.

**Grade 4 – Number and Operations – Base Ten (4.NBT.A.3)**

Use place-value understanding to round multi-digit whole numbers to any place.

**Grade 5 – Number and Operations – Base Ten (5.NBT.A.4)**

Use place value understanding to round decimals to any place.

In order to round a whole number:

**Find the rounding place and look at the digit immediately to the right of the rounding place.****When that digit is**5**or greater, add**1**to the rounding digit. When it is less than**5**, leave the rounding digit alone.****Change all the digits to the right or the rounding place to**0**’s.****Write the rounded number.**

In order to round a decimal number:

**Find the rounding place and look at the digit immediately to the right of the rounding place.****When that digit is**5**or greater, add**1**to the rounding digit. When it is less than**5**, leave the rounding digit alone.****Drop all the digits to the right of the rounded digit.****Write the rounded number.**

Assess math progress for the end of grade 4 and grade 5 or prepare for state assessments with these mixed topic, multiple choice questions and extended response questions!

DOWNLOAD FREEAssess math progress for the end of grade 4 and grade 5 or prepare for state assessments with these mixed topic, multiple choice questions and extended response questions!

DOWNLOAD FREERound 382 to the nearest 10.

**Find the rounding place and look at the digit immediately to the right of the rounding place.**

3\underline{8}2 → 8 is in the rounding place (tens place)

3\underline{8}2 → 2 is the digit immediately to the right of 8 which is in the ones place.

2**When that digit is **5** or greater, add **1** to the rounding digit. When it is less than **5**, leave the rounding digit alone.**

2 < 5 \; (2 is less than 5), so keep the digit as an 8.

3**Change all the digits to the right or the rounding place to **0**’s.**

382 → change the 2 to a 0

4**Write the rounded number.**

382 rounded to the nearest 10 is 380.

383 is to the left of the halfway point and closer to 380. It will round to be 380.

Round 573 to the nearest 100.

**Find the rounding place and look at the digit immediately to the right of the rounding place.**

\underline{5}73 → 5 is in the rounding place (hundreds place)

\underline{5}73 → 7 is the digit immediately to the right of 5 which is in the tens place.

**When that digit is **5** or greater, add **1** to the rounding digit. When it is less than **5**, leave the rounding digit alone.**

7 > 5, \; (7 is greater than 5), add 1 to the rounding digit, 5 will become 6.

**Change all the digits to the right or the rounding place to ** 0 **’s.**

\underline{5}73 → 600 – change the 7 and 3 to 0 ’s.

**Write the rounded number.**

573 rounded to the nearest 100 is 600.

Round 29,862 to the nearest 1000.

**Find the rounding place and look at the digit immediately to the right of the rounding place.**

2\underline{9},862 → 9 is the digit in the rounding place

2\underline{9},862 → 8 is the digit immediately to the right of 9 (hundreds place).

**When that digit is **5** or greater, add **1** to the rounding digit. When it is less than **5**, leave the rounding digit alone.**

8 > 5, \; (8 is greater than 5), add 1 to the rounding digit, 9 will become 10.

Place a 0 where the 9 is, add 1 to the digit 2.

**Change all the digits to the right or the rounding place to ** 0 **’s.**

2\underline{9},862 → 30,000

**Write the rounded number.**

29,862 rounded to the nearest 1000 is 30,000.

Round 25.67 to the nearest whole number

**Find the rounding place and look at the digit immediately to the right of the rounding place.**

2\underline{5}.67 → 5 is in the rounded place (ones place)

2\underline{5}.67 → 6 is the digit immediately to the right of 5 (tenths place)

**When that digit is **5** or greater, add **1** to the rounding digit. When it is less than **5**, leave the rounding digit alone.**

6 > 5, \; (6 is greater than 5), add 1 to the rounding digit, 5 will become 6.

**Drop all the digits to the right of the rounded digit.**

2\underline{5}.67 → drop the digits 6 and 7

**Write the rounded number.**

25.67 rounded to the nearest whole number is 26

** **

**Step-by-step guide:** Estimation

Round 7.542 to the nearest tenth.

**Find the rounding place and look at the digit immediately to the right of the rounding place.**

7.\underline{5}42 → 5 is in the rounded place (tenth place)

7.\underline{5}42 → 4 is the digit immediately to the right of 5 (hundredths place)

**When that digit is **5** or greater, add **1** to the rounding digit. When it is less than ** 5**, leave the rounding digit alone.**

4 < 5, \; (4 is less than 5), leave the rounding digit alone.

**Drop all the digits to the right of the rounded digit.**

7.542 → drop the digits 4, 2

**Write the rounded number.**

7.542 rounded to the nearest tenth is 7.5

** **

**Step-by-step-guide:** Rounding decimals

Round 408.095 to the nearest hundredth.

**Find the rounding place and look at the digit immediately to the right of the rounding place.**

408.0\underline{9}5 → 9 is in the rounded place (hundredths place)

408.0\underline{9}5 → 5 is the digit immediately to the right of 9 (thousandths place)

**When that digit is **5** or greater, add **1** to the rounding digit. When it is less than **5**, leave the rounding digit alone.**

5 = 5, so add 1 to the rounded digit, and 9 becomes 10. Replace the 9 with a 0, add 1 to the digit 0.

**Drop all the digits to the right of the rounded digit.**

408.0\underline{9}5 → drop the digits 5 and 6

**Write the rounded number.**

408.095 rounded to the nearest hundredth is 408.10

- Reinforce rounding with the number line. It gives students a visual representation of what rounding means.

- You can also utilize math videos for rounding in math centers to help students review concepts.

- Emphasize place value to help students with rounding. Provide a place value chart as a visual aide.

- To help students understand why the rule requires the number to be rounded up when there is a 5 to the right of the rounded digit, give them grouping visuals.

There are ten numbers and these numbers are |

**Rounding errors occur when students do not have a strong understanding of place value.**

For example, rounding 12.34 to the nearest tenth and a student rounds to the nearest whole number.

9**Not rounding up appropriately when****is in the rounding digit.**

For example, rounding 3.4973 to the nearest hundredth would be 3.49 or 3.40 instead of 3.50.

**When rounding decimal numbers be sure to represent the correct place value.**

For example, when rounding the number 5.096 to the nearest hundredth, the rounded decimal number will be 5.10. Be sure to leave 0 as a placeholder.

1. Round 193 to the nearest 100

100

200

1

2

\underline{1}93 → the digit immediately to the right of the rounding digit is 9.

Applying the rule, 9 > 5, add 1 to the rounded digit. 9 will become 10.

Change all digits to the right of the rounded digit to 0 ’s. 3 is to the right of the rounded digit, so it will become 0.

193 rounded to the nearest hundred, is 200.

2. Round 13.782 to the nearest hundredth.

13.79

13.70

13.80

13.78

13.7\underline{8}2 → 8 is in the rounded place and 2 immediately to the right of it.

Following the rule, 2 < 5, leave the rounded digit alone.

Drop all the digits to the right of the rounded digit, drop the 2.

13.782 rounded to the nearest hundredth is 13.78.

3. Round 25,592 to the nearest thousand.

26,000

25,700

25,600

25,690

2\underline{5},592 → 5 is in the rounded place and 5 is immediately to the right of it.

Following the rule, 5 = 5, so add 1 to the rounded digit. 8 will become 9.

Change all the digits to the right of the rounded digit to 0 ’s. 5, 9, 2 will become 0 ‘s.

25,592 rounded to the nearest thousand is 26,000.

4. Round 0.0364 to the nearest thousandth

0.03

0.36

0.036

0.037

0.036 → 6 is the rounded place and 4 is immediately to the right of it.

Following the rule, 4 < 5. Leave the rounded digit alone.

Drop the digits to the right of the rounded digit. Drop the digit 4.

0.0364 rounded to the nearest thousandth is 0.036

5. Round 77.552 to the nearest whole number.

78

77

77.6

78.6

7\underline{7}.552 → 7 is in the rounded place and 5 is immediately to the right of it.

Following the rule, 5 = 5, so add 1 to the rounded digit. 7 will become 8.

Drop the digits to the right of the rounded digit, so drop the digits 5, 5, and 2.

77.552 rounded to the nearest whole number is 78.

6. Round 2,689 to the nearest ten.

2700

2689

2680

2690

26\underline{8}9 → 8 is in the rounded place and 9 is the digit immediately to the right of it.

Following the rule, 9 > 5, so add 1 to the rounded digit. 8 will become 9.

Change the digits to the right of the rounded digit to 0 ’s. Change 9 to a 0.

2689 rounded to the nearest 10 is 2690.

Both rounding and estimating are strategies used to approximate numbers so they are easier to calculate or conceptualize. Estimating is the process of making a guess or calculation, whereas rounding is the process of taking the given number and by scaling it up or down. Rounding can be considered a type of estimation.

Significant figures are the non-zero numbers in a rounded number. You can round a number to a specific number of significant digits.

For example, rounding 1645 to two significant figures would be 1600. This is the same as rounding 1645 to the nearest hundred.

The rules for rounding determine that if the number to the right of the rounding digit is 5 or greater, round up. If the number to the right of the rounding digit is less than 5, round down. However, to help visualize this rule, think of the ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9 ) being divided into two groups.

- Factors and multiples
- Fractions
- Fractions operations

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