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The ideas in this place value lesson are taken from the Place Value 3 ebook that I sell at MathMammoth.com. Only a few examples of each problem type are shown; you should make more problems of each kind for the student.


Rounding to nearest hundred or thousand
Free lesson plan from HomeschoolMath.net

[NUMBER LINE available in the ebook]

What numbers between 400 and 500 are closer to 400 than to 500?
What numbers are closer to 500?

[NUMBER LINE available in the ebook]

What numbers between 2400 and 2500 are closer to 2400 than to 2500?
What numbers are closer to 2500?

Numbers closer to 2400 are rounded down to 2400 when rounding to nearest hundred.  And those closer to 2500 are rounded up to 2500.  For example, 2412 ≈ 2400;  2429 ≈ 2400;  2478 ≈ 2500;  2490 ≈ 2500.  

 
Practice

1.  Mark the following numbers as little dots on the number line (approximately) and round them to either 800 or 900.

[NUMBER LINE available in the ebook]

804 ≈ ____

859 ≈ ____

808 ≈ ____

892 ≈ ____

 
2.  Round these numbers to the nearest hundred.

416 ≈ ____

437 ≈ ____

254 ≈ ____

247 ≈ ____



When you are rounding to the nearest hundred, look at the TENS DIGIT of the number. 
  • If the tens digit is 0, 1, 2, 3, or 4, then the hundreds digit does not change. You are rounding down.

  • If the tens digit is 5, 6, 7, 8, or 9, then the hundreds digit increases by one. You are rounding up.

  • All the other digits after the hundreds digit (tens digit and ones digit) go to zero in both cases.

  • All the other digits before the hundreds digit (thousands digit) stay the same in both cases.

Does the hundreds digit 
(7) change or not? We need
to look at the tens digit.
Tens digit is 2,  so the
hundreds digit does not
change.
The thousands digit (6) stays
the same, and the tens and
ones digits go to zero.

6728

6728

6728 ≈ 6700

 
Does the hundreds digit (9)
change or not? We need to
look at the tens digit.
Tens digit is 5, so the
hundreds digit (9)
would change to ten
But chancing nine by
one makes it to be ten,
so actually the '49' goes to 50.

4952

4952

4952 ≈ 5000

671 ≈ 700 (up),  because the tens digit in 671 is 7.
726 ≈ 700 (down), because the tens digit in 726 is 2
5409 ≈ 5400  (down) because the tens digit in 5409 is 0.
9790 ≈ 9800  (up) because the tens digit in 9790 is 9.

It doesn't matter what the ones digit is when we round to the next hundred.  Just look at the TENS digit.


3.    Round these numbers to the nearest hundred.

578 ≈ ____

2264 ≈ ____

1816 ≈ ____

5567 ≈ ____

2088 ≈ ____

4197 ≈ ____

9008 ≈ ____

2347 ≈ ____



Rounding to the nearest thousand

[NUMBER LINE available in the ebook]

What numbers between 0 and 1000 are closer to 0 than to 1000?
What numbers are closer to 1000?

[NUMBER LINE available in the ebook]

What numbers between 8000 and 9000 are closer to 8000 than to 9000?

Numbers closer to 8000 are rounded down to 8000 when rounding to nearest thousand. And those closer to 9000 are rounded up to 9000.

For example, 8134 ≈ 8000;  8478 ≈ 8000;  8513 ≈ 9000;  8802 ≈ 9000.  Mark these numbers approximately on the number line above.

When you are rounding to the nearest thousand, look at the HUNDREDS DIGIT of the number. 
  • If the hundreds digit is 0, 1, 2, 3, or 4, then round down.

  • If the hundreds digit is 5, 6, 7, 8, or 9, then round up.

When you round down, the thousands digit doesn't change, and the hundreds and tens and ones digits go to zero.
When you round up, then thousands digit increases by one, and the hundreds and tens and ones digits go to zero.  Examples:

5471 ≈ 5000 (down).  
4726 ≈ 5000 (up)
          2099 ≈ 2000 (down).
7901 ≈ 8000  (up).

It doesn't matter what the ones digit or the tens digit is when we round to the next hundred.
Just look at the HUNDREDS digit.


4.   Round these numbers to the nearest thousand.

1678 ≈ ____

2064 ≈ ____

1916 ≈ ____

2088 ≈ ____

2119 ≈ ____

1645 ≈ ____

9830 ≈ ____

9437 ≈ ____

 

5.  In the following number line the | marks appear at every whole ten.  Underlined and illustrated in yellow is the range of numbers that is rounded to 3800, when rounding to nearest hundred. 

[NUMBER LINE available in the ebook]

Look and think:  What numbers (exactly) are rounded to 3800?
What numbers would be rounded to 3900?

Draw a similar number line from 7400 till 7700 in your notebook.  
What numbers would be rounded to 7600?

 

6.  Below is a number line from 4400 till 5800.  Underlined and illustrated in yellow is the range of numbers that is rounded to 5000, when rounding to nearest thousand. 

[NUMBER LINE available in the ebook]

Draw a similar number line from 6300 till 7900 in your notebook.  What numbers on your number line would be rounded to 7000?

 

Note that there are several solutions to this problem.  What all numbers can fulfill the  conditions?

"If rounded to nearest hundred, I would go to 8500, and if rounded to nearest thousand, I would go to 8000.  If you add ten to me and round me to the nearest thousand, I'll go to 9000."  

 

 

What numbers between 0 and 1000 are closer to 0 than to 1000?
What numbers are closer to 1000?

What numbers between 8000 and 9000 are closer to 8000 than to 9000?

Numbers closer to 8000 are rounded down to 8000 when rounding to nearest thousand.
And those closer to 9000 are rounded up to 9000.

For example, 8134 ≈ 8000;  8478 ≈ 8000;  8513 ≈ 9000;  8802 ≈ 9000.  Mark these numbers approximately on the number line above.

When you are rounding to the nearest thousand, look at the HUNDREDS DIGIT of the number. 
  • If the hundreds digit is 0, 1, 2, 3, or 4, then round down.

  • If the hundreds digit is 5, 6, 7, 8, or 9, then round up.

When you round down, the thousands digit doesn't change, and the hundreds and tens and ones digits go to zero.
When you round up, then thousands digit increases by one, and the hundreds and tens and ones digits go to zero.  Examples:

5471 ≈ 5000 (down).  
4726 ≈ 5000 (up)
          2099 ≈ 2000 (down).
7901 ≈ 8000  (up).

It doesn't matter what the ones digit or the tens digit is when we round to the next hundred.  
Just look at the HUNDREDS digit.

4.    Round these numbers to the nearest thousand.

1678 ≈ ____

2064 ≈ ____

1916 ≈ ____

2088 ≈ ____

5098 ≈ ____

8405 ____

6223 ≈ ____

4197 ≈ ____

5094 ≈ ____

2583 ≈ ____

4603 ≈ ____

9508 ≈ ____

9567 ≈ ____

8966 ≈ ____

3700 ≈ ____

3786 ≈ ____

 

.  

2.  Above is a number line from 4400 till 5800.  Underlined and illustrated in yellow is the range of numbers that is rounded to 5000, when rounding to nearest thousand. 

Draw a similar number line from 6300 till 7900 in your notebook.  What numbers on your number line would be rounded to 7000?

 

Note that there are several solutions to this problem.  What all numbers can fulfill the  conditions?

"If rounded to nearest hundred, I would go to 8500, and if rounded to nearest thousand, I would go to 8000.  If you add ten to me and round me to the nearest thousand, I'll go to 9000."  

Next lesson


The ideas in this place value lesson are taken from the Place Value 3 ebook that I sell at MathMammoth.com. Only a few examples of each problem type are shown; you should make more problems of each kind for the student.

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