Unit 1, Part 2: Place Value and the Number System

Learning objectives:

Define Key Terms
Read and write whole numbers
Identify Place Value
Round whole numbers
Compare whole numbers

Key Terms:

Place-Value System
digits
integers
rounded number

1.2.A Read and Write Whole Numbers

Our system of numbers, the decimal number system uses 10 symbols called digits: 0,1, 2, 3, 4, 5, 6, 7, 8, and 9. Numbers in the decimal system can have one or more digits. Each digit in a number that contains two or more digits that must be arranged in a specific order to have the value we intend for the number to have. In a whole number each digit has a place and a value. To determine the place value of a particular digit in a number, use the following chart:

Trillions			Billions			Millions			Thousands			Ones
Hundred trillions	Ten trillions	Trillions	Hundred billions	Ten billions	Billions	Hundred millions	Ten millions	Millions	Hundred thousands	Ten thousands	Thousands	Hundreds	Tens	Ones
3	1	9	3	0	2	3	7	5	1	2	6	8	8	4
319 trillion, 302 billion 375 Million							126 thousand					884

Beginning with the ones place on the right, the place values are grouped in groups of three places. Each group of three place values is called a period. Each period has a name and a ones place, tens place and a hundreds place. We will always place a comma between periods.

Reading numbers is based on our understanding of the place-value system that is part of our decimal-number system.

Follow these steps to read a whole number:

Example: Read the number 83,893,002

$\longrightarrow$ $\longrightarrow$ Separate the number into periods beginning with the rightmost digit and moving to the left.

$\longrightarrow$ $\longrightarrow$ Identify the period name of the leftmost period: million

$\longrightarrow$ $\longrightarrow$ For each period, beginning with the leftmost period,

Read the three-digit number from left to right and name the period: eighty-three million, eight hundred ninety-three thousand, two

Do not read or name a period that has all zeros and do not name the ones period. Do not use the word "and" unless it is to denote a decimal.

Example: Read the number 380, 000, 200, 010, 199

three hundred eighty trillion, two hundred million, ten thousand, one hundred ninety-nine

Practice 1.2.A

Directions: Using the examples above, Read and write the following numbers. Complete the following practice and submit all practice assignments for this section below.

Write the following numbers using words:

1. 849,870,001

2. 6,009,213,100

3. 30,201,020

Read and write the numbers using digits:

4. thirty-three million one hundred ninety thousand two

5. ninety million twenty thousand two hundred one

6. eighty-eight billion eight hundred eighty-eight million eight hundred eighty-eight thousand twenty-one

1.2.B Identify place Value of Whole numbers

We can use the place value chart above to identify the place value of digits. You will need to memorize that chart.

You need to be able to identify the place of digits.

Example: Identify the place value of the digit 4 in the following number: 243,827,100

The "4" is in the Ten-millions place.

Example: Identify the place value of the digit 7 in the following number: 243,827,100

The "7" is in the thousands place.

Practice 1.2.B

Directions: Using the examples above, identify the place value of the following numbers. Complete the following practice and submit all practice assignments for this section below.

In each of the following numbers identify the place value of the digit 7.

1. 234,714

2. 745,990

3. 234,117

4. 111,172

5. 1,273

6. 795

7. 17,980

8. 709,932

9. 175,000

10. 37,500

1.2.C Round Whole Numbers

When absolute precision is not required, it may be helpful to round whole numbers to the nearest ten, hundred, or thousand. For example, cotton tipped applicators come in boxes of 1,000. You are responsible to keep 3,000 in stock and you find that there are two boxes on the shelf, you would order another box of 1,000. This would be easier then counting each applicator to find out that there are 2,245. By rounding to the nearest thousand, you would find that you had approximately 2,000 depressors on the shelf and you would need to order 1,000 more.

When rounding numbers, you first need to decide what place you will need to round to; the nearest ten, hundred, thousand and so on. Once you determine the place, look at digit immediately to the right of the place being rounded. If the digit is 5-9, round the digit to its immediate left up one. If the digit is 0-4, leave the digit to its immediate left the same. Then change all digits to the right to zeros.

Example: Round 87 to the nearest ten.

By going to the place to the immediate right of the ten's place, we see that the digit is "7", we should round the digit to the immediate left up one. Round the "8" in the ten's place up one, making the number "90".

Example: Round 7,563 to the nearest ten.

By going to the place to the immediate right of the ten's place, we see that the digit is "3", we should leave the digit to the immediate left the same. Change all the digits to the right to zeros, making the number "7,560".

Practice 1.2.C

Directions: Using the examples above, round the numbers to the place specified. Complete the following practice and submit all practice assignments for this section below.

Round to the nearest hundred

1. 1,254

2. 453

3. 989

4. 109

5. 457

Round to the nearest thousand

6. 45,932

7. 43,212

8. 3,454

9. 56,543

10. 191,038

Using the number 343,838,837,120 round to the nearest:

11. ten

12. hundred

13. thousand

14. ten thousand

15. hundred thousand

16. million

17. ten million

18. hundred million

19. billion

20. ten billion

1.2.D Compare Whole Numbers

It is helpful to be able to compare the value of whole numbers. By determining whether a number is greater than, less than or equal to another number, you can compare the values.

We use the following symbols to compare the values.

Symbol	Words	Example Use
=	equals	1 + 1 = 2
≠	not equal to	1 + 1 ≠ 1

>	greater than	5 > 2
<	less than	7 < 9

≥	greater than or equal to	applicators ≥ 1
≤	less than or equal to	cotton balls ≤ 3

We will primarily be using the $<$ , $>$ , and $=$ symbols

If you have trouble remembering which is greater than or less than, use this visual:

To compare the relative value of whole numbers to another number, line the numbers up vertically, in row, according to the place valve.

98,642

99,321

If the number has more digits, it is the larger number ( This is only true of whole numbers, not decimals or fractions; we will discuss in a later unit). Compare the digits starting at the left and work your way to the right, comparing each set of digits.

9	8	4	6	2
9	9	3	2	1
Equal	Not Equal

Since 9 is greater than 8, "99,321" is the larger number. This will be written:

98,462 $<$ 99,321

Practice 1.2.D

Directions: Using the examples above, compare the following whole numbers using (<), (>) or (=) . Complete the following practice and submit all practice assignments for this section below.

1. 1,243 (?) 2,243

2. 98,211 (?) 211,098

3. 78 (?) 178

4. 234 (?) 234

Submit Practice Assignments HERE