Place Value

L. Riddler

6th Grade Mathematics

What is a “digit?”

• A digit is just one number that is a part of a number

• A digit can be one of these numbers: 0 1 2 3 4 5 6 7 8 9

• Sometimes people call their fingers “digits”

• “Digits” is also a slang word that means telephone number.

Let’s count the digits in these numbers:

A) 21

B) 375

C)7

D)6,503,211

E) 50

F) 30.7

G) 7,180

H) 70,123.007

I) 911

J) 23, 004

Let’s add the digits in these numbers:

A) 23

B) 407

C) 1,234

D) 2,200,256

E) 96

F) 67

G) 593

H) 1,000,000

I) 96,301

J) 81

Let’s count the number of whole number digits:

A) 31.5

B) 300.002

C) .344567

D) 1,341

E) 45.000001

F) 54,461.0

G) 67.89

H) 111.111

I) 34.05

J) 45.007

Let’s count the number of decimal digits:

• 31.5• 300.002• .344567• 1,341• 45.000001

F) 54,461.0

G) 67.89

H) 111.111

I) 34.05

J) 45.007

What is “place value?”

• Place value is the amount assigned to a digit.

• Some important place values that we will use are: millions, hundred thousands, ten thousands, thousands, hundreds, tens, ones, tenths, and hundredths.

But there are way, way, way more than that.

Million

Billion

Trillion

Quadrillion

Quintillion

Sextillion

Septillion

Octillion

Nonillion

Decillion

Undecillion

Duodecillion

Tredecillion

Quattuordecillion

Quindecillion

Sexdecillion

Septendecillion

Octodecillion

Novemdecillion Vigintillion And on and on and on…

Googol

Googolplex

And there is even bigger numbers than that!

We will need to memorize the names of the important place values.

Take out a piece of unlined paper.

Fold it in half horizontally.

Use scissors to cut 10 flaps half way through the paper.

Look at the example to label your notes.

Use your foldable notes to help you answer these questions:

What is the place value of the digit that is 5?A) 345.7B) 6612.654C) 85461D) 34.5E) 3457.07F) 500671.43G) 75403462

Now try to answer these WITHOUT your foldable notes:

If you are having trouble (there are two or more you CANNOT do on your own), raise your hand to let your teacher know!

A) 34012.56

B) 10789541

C) 19780.99

D) 103.867

E) 34.08

F) 456.901

G) 10789

H) 4073429

I) 345601854

J) 50

Name the place value of the digit that is a zero (0).

Activity Break

Work on activities that your teacher has selected for you independently or in groups.

If you need help with place value, work with the teacher in small group.

Do not interrupt the teacher unless you have a really, really, really good reason during small group time.

What can I do with place value?

You can use it put numbers in order from least to greatest or greatest to least.

You can use it to put numbers into word form.

You can use it to put numbers into expanded form.

How do I put numbers in order?

Put the following numbers in order from least to greatest: 345.04; 307.04; 511; 307.7; 417.7.

Step One: Find the number with the largest number of digits.

345.04

307.04

511

307.7

417.7

Both of these

numbers have 5 digits!

Step Two: Make a Chart

This chart has 5 columns because the largest

number of digits is 5. It has 5 rows because we

are comparing 5 numbers.

Step Three: Line up the Decimals

3 4 5 0 4

3 0 7 0 4

5 1 1

3 0 7 7

4 1 7 7

Step Four: Compare the Digits, Going from the Biggest (left side) to the Smallest (right side)

You always read the digits on a number in the same order you read words– from left to right.

3 4 5 0 4

3 0 7 0 4

5 1 1

3 0 7 7

4 1 7 7

Biggest

Next to Biggest

Middle

Next to Smallest

Smallest

Step Five: Write your numbers in the order that is asked for in the problem.

• Least to Greatest =

• 307.04

• 307.7

• 345.04

• 417.7

• 511

Here are some practice problems that you can use your notes to help with:

• Put these in order from least to greatest:

• 717• 710• 707• 700.17• 700.07

• Put these in order from greatest to least:

• 1001• 1001.5• 100• 100.5• 5001.5

Here are some problems to do without your notes:

• Put these in order from greatest to least:

• 5601• 5061• 5160• 5161• 5610

• Put these in order least to greatest:

• 60.1• 60.02• 61.02• 60.01• 61

If you are having trouble (there are two or more you CANNOT do on your own), raise your hand to let your teacher know!

Activity Break

Work on activities that your teacher has selected for you independently or in groups.

If you need help with ordering numbers, work with the teacher in small group.

Do not interrupt the teacher unless you have a really, really, really good reason during small group time.

What is “word form?”

It is the way you say the number out loud with all the numbers spelled out.

People write numbers in word form when they write a check.

Practice writing these numbers in word form:

• 561= five hundred sixty one

• 1,342= one thousand three hundred forty two

• 1,789,453= one million seven hundred eighty nine thousand four hundred fifty three

• 56.45= fifty six and forty five hundredths

• 10.6= ten and six tenths

What is “expanded form?”

It looks like an addition problem with each digit represented as its own number.

Expanded form helps explain why you can carry and borrow when you add and subtract large numbers.

Practice writing these numbers in expanded form:

• 617= 600+10+7• 7,846,567=

7000000+800000+40000+6000+500+60+7

• 6001= 6000+1

• 7801= 7000+800+1

• 6.12= 6+0.1+0.02

Now without your notes, write each number in expanded form and in word form:

A) 511

B) 50 613

C) 46.2

D) 7 801 678

E) 3 445.16

If you are having trouble (there is one or more you CANNOT do on your own), raise your hand to let your teacher know!

Activity Break

Work on activities that your teacher has selected for you independently or in groups.

If you need help with ordering numbers, work with the teacher in small group.

Do not interrupt the teacher unless you have a really, really, really good reason during small group time.

Vocabulary Study Guide

DigitPlace value

DecimalLeast

GreatestOrder

IncreasingDecreasing

Expanded formWord form

Standard form