CHAPTER 1                            LESSON 1

 

 

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“PLACE VALUE AND ROUNDING NUMBERS”

 

 

Problem:  Show the places and values of the digits of a number.

Answer:  see chart below

PLACES

 Millions

Hundred-

thousands

Ten-

Thousands

Thousands

Hundreds

Tens

Units or

Ones

.

tenths

hundredths

thousandths

DIGITS

4,

1

5

2,

9

0

7

.

8

6

3

VALUES

4,000,000

100,000

50,000

2000

900

NO

TENS

7

.

8

10

or

0.8

6

100

or

0.06

3

1000

or

0.003

 

Examples:               

                  30.47

Digit

Place

Value

1.   3

    ??

   ??

2.   0

    ??

   ??

3.  ??

    tenths

   ??

4.   ??

     ??

   7

 100

 

Answer: 

                             30.47

Digit

Place

Value

1.   3

    tens

   30

2.   0

    units or

    ones

     0

3.   4

    tenths

   0.4 or 4

             10

4.   7

hundredths

   7

 100

 

 

ROUNDING WHOLE NUMBERS AND DECIMALS

 

The most common method for rounding WHOLE NUMBERS consists of the following steps:

Example:

Round 8467 to nearest hundred. 

Let’s follow the rules above—

1.  The digit in the hundreds place in the number 8467 is 4

2.  Check the digit to the right of the 4.  What number is to the right of the 4??  Answer: 6.    6 is more than 5 so we will round up.

3.  We need to add a 1 to the 4 which was in the hundreds place—so the answer becomes 8500 since we are rounding off.

 

 

 

To round off decimals:

Find the place value you want (the "rounding digit") and look at the digit just to the right of it.

If that digit is less than 5, do not change the rounding digit but drop all digits to the right of it.

If that digit is greater than or equal to five, add one to the rounding digit and drop all digits to the right of it.

 

 

Example:

Round 0.628 to nearest tenth.

1.  Find the digit that is in the tenths place.  In the problem 0.628—the 6 is in the tenths place.

2.  Look at the digit that is to the right of the 6—that would be 2.  Since 2 is less than 5, we would not change the number in the tenths place—just drop the numbers after the 6, since we are rounding off to the nearest tenth.

Answer:  0.6

 

 

Final Example: 

Round 326,735 to the nearest thousand. 

 

Follow the rules above for rounding whole numbers.

1.  Determine what digit is in the thousands place??  In the number 326,735--the number in the thousands place is 6.  Look to the number to the right of the 6.  That number is 7.  7 is more than 5, so we will add a 1 to the number 6, which changes the number to 327,000 since the final numbers are changed to zeros since we are rounding off.  The answer is 327,000

 

 

 

 

Work on the problems below.  You will see boxes below.  After working on your problems, you are to type the correct answer into the selected boxes and then submit only those answers. Your other answers can be checked by clicking onto “CHECK ANSWERS.”

 

 

 

Round each number to the place shown.

To the nearest hundred:

1.  6324

2.  8761

3.  71,583

4.  69, 208

 

To the nearest thousand:

5.  4294

6.  5026

7.  39,057

8.  79,637

 

To the nearest tenth:

9.  0.12

10.  0.46

11.  6.021

12.  4.903

13.  2.695

 

To the nearest hundredth:

14.  0.392

15.  0.018

16.  35.613

17.  98.765

18.  3.166

19.  48.019

 

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