unit 12 decimals numeration

UNIT 12DECIMALS

NUMERATION4TH GRADE GIFTED

VOCABULARYones tens one hundred number line

1. The number 438,572 has a 7 in the __________ place.

2. Ten tens are equal to ______.

3. A _______ can be used to show numbers in order using a scale.

Comparing Numbers> < =

1,909 1,99943,627 43,167

629,348 629,348455,311 455,331101,101 101,011

95,559 95,555

Order these numbers from greatest to least.

1. 3,687 3,867 3,678 3,768

2. 41,101 41,011 41,110 41,001

3. 4,593 4,395 4,595 4,359

4. 678,912 678,921 687,999 678,291

Order from least to greatest.

15,420 154,200 1,542

543,897 54,380 534,978

Use a decimal model to show

1.6 pounds.

A decimal model can also show 1.6 hundredths.

Write the decimal: 1.64

Standard form:

Expanded form:

Word form:

Write the expanded form and word form.

3.91

6.8

1.09

2.3

Write the decimal for each.

What would the fraction be?

Write the decimal shown.

Write the fraction.

Write the number in word and give the value of each red digit.

2.47 ________________________ 3.19 ________________________ 23.79 ________________________ 0.78 ________________________ 1.8 ________________________ 14.1 ________________________ 9.05 ________________________

Write a number that has a 4 in the tens place and a 5 in the hundredths place.

_________________________________

The capybara can grow to be 1.3

meters long. Write 1.3 in expanded

form and in word form.

___________________

___________________

The Green Darner is one of the

largest dragonflies on Earth.

It weighs about four hundredths

of an ounce. Write the weight in

standard form.

Use the decimal model to explain why 0.08 is less than 0.1

Write the word form and tell the value

of each red digit.

2.300 __________________________

9.027 __________________________

1.982 __________________________

6.17 __________________________

4.983 __________________________

8.46 __________________________

Write each number in standard form.

6 + 0.6 + 0.03 + 0.007

3 + 0.3 + 0.009

9 = 0.2 + 0.04 + 0.008

Write two decimals that are equivalent to the decimal below.

2.200 _________________________

8.1 _________________________

9.50 _________________________

Bella finished a race in 2.6

hours, and Sophia finished the

same race in 2.600 hours.

Which runner finished the

race first?

Alex is buying juice at the

market. He has $9, and each

bottle of juice costs $2.

Does he have enough money to

buy 5 bottles of juice? Explain.

Nikki made 19 pancakes for

breakfast. She took 7 and gave

an equal number to her dad and

mom. How many pancakes did

each of her parents get?

The Borneo stick insect

has a total length, including

its legs, of 21.5 inches.

Name two decimals that are

equivalent to 21.5

Worker leafcutter ants can measure 0.5 inch.

Write three other ways to write 0.5 inch.

Decimal to Whole Number

Connection

thousands hundreds tens ones . tenths hundredths thousandths

1,000 100 10 1 .0.1

1/10

0.01

1/100

0.001

1/1000

5 3 4 2 . 4 3 5

Write the place value for the

red digit.

34.67 _____________________

856.472 _____________________

486.359 _____________________

6,095.375 _____________________

Write the number that is ten times as many.

1. _____________________

0.01 _____________________

100. _____________________

0.001_____________________

A telephone worker used

340.75 feet of cable.

What is the place value of the

5 in 340.75 ?

3 4 0 . 7 5

The grid below shows one hundred equal parts. Each part is equal to one hundredth.

How many hundredths are in

one tenth?

Write the place value for each bold digit.

572.67 2,368.795 1,435.889 9,654.328

601.65 1,754.709 4,597.624 6,332.470

2,867.435 9,555.392 1,843.2 5,642.437

Write the number that is ten times as many.

0.07 40 0.008 0.9

35 0.6 0.03 500

8.0 70.1 250 1.005

There are 100 fiction books in

the classroom library. The

school library has ten times as

many fiction books. What is the

number of fiction books in the

school library?

Ryan and Colin collected aluminum cans

for the school recycling project.

Look at the chart to find out who

collected the most cans. Find the

difference between the number of

cans collected.

RYAN 1,352

COLIN 1,329

Kiley baked 3 times as many

muffins as Kayla for the

school bake sale. If Kayla

baked 36 muffins, how many

did Kiley bake?

Kayla

Kiley

36

Mrs. B has 6 gallons of gas in her car.

Her tank can hold 15 gallons.

Will Mrs. B need more or less than 10 gallons of gas to fill her tank?

_______

If gas is $3.49 per gallon, how much will it cost to fill up the tank?

Ethan found two shells that are the same

shape but are different sizes.

One weighs 0.01 pound and the other

weighs ten times as much.

How much does the heavier shell weigh?

Charlie and Kohle are discussing

the value of the first 1 and the

second 1 in the number 4.115

Charlie thinks the first 1 has

greater value than the second.

Is he correct?

Decimals on the number line.

0 1 2 3 4

Locate 1.90 on the number line.


0 1 2 3 4



Name the points on the number line.

A B C D

0 1 2 3 4

A B

C D

Mark each point on the number line.

0 1 2 3 4

2.6 1.3

0.4 3.9


A B C D E F

7 8 9

A B C

D E F


A B C D E F

2 3 4

A B C

D E F


7.00 7.30 7.60


10 11 12 13 14




0 1 2 3 4

How many tenths between 1 and 2?

How many hundredths between 1 and 2?


7 8 9

Name two decimals between

8.4 and 8.6

Sea level at Key West is rising

about 1.8 millimeters per year.

What is the place value of the

digit 8 in this number?

How do you round to the nearest tenth?

What is 211.98 rounded to the nearest tenth?

Look at the tenths place 211.98

Look at the digit to the right. 211.98

211.98 rounds to 212.0Since the digit is 8, the digit in the

tenths place increases by 1.

Round 68.142 to the nearest hundredth.

Look at the hundredths place 68.142

Look at the digit to the right 68.142

Since 2 < 5, the hundredths

digit stays the same.

68.142 rounds to 68.14

Round each to the place of the underlined digit.

17.23 19.805

49.562 67.591

Round each to the place of the underlined digit.

60.82 88.3 2.283 0.695 72.564

41.483 0.819 147.61 857.95 591.95

312.12 4.108 1009.1 64.93 7.452

99.99 78.61 38.8 230.9 12.55

Name 3 decimals that when

rounded to the nearest tenth,

round to 7.8

Which of these decimals does NOT round to 6?

5.71

5.91

6.82

6.249

6.001

Megan wanted to know the total mass of two

pieces of volcanic rock. The first piece had a

mass of 4.99 grams and the second had a

mass of 2.85 grams.

Megan wants to record the combined masses

of the two pieces of volcanic rock to the

nearest gram. Is 4.0 + 2.9 a reasonable

estimate of the masses to the nearest gram?

Lauren was asked to round 89.367

to the nearest hundredth. She answered 89.40

Is she correct?

Explain

According to Jimmy’s rain gauge, it had rained 2.28

inches in 24 hours.

What is 2.28 rounded to the nearest tenth?

What is 2.28 rounded to the nearest whole number?

Landon filled the car with 8.53

gallons of gasoline. To the

nearest tenth of a gallon, how

much gasoline did Landon

put in the car?

Maggie’s dog weighs

5.521 pounds.

To the nearest whole number,

how much does Maggie’s

dog weigh?

Autumn jogs 12 miles each

week. How many miles does

Autumn jog in 1 year?

Which ones don’t belong?

3.6 4.2 4.1 3.9

4.4 3.8 4.6 3.5

4.8 3.7 4.3 3.2

Ari bought 10 bagels.

Three-tenths of the bagels are

plain and the rest are cinnamon. How many cinnamon bagels

are there?

According to MapQuest,

Bella and her family need to

travel 53.19 miles to get to her

grandmother’s house. What is

this distance rounded to the

nearest mile?

Venn diagrams are very useful to show how different data belong to groups. Remember, if the data

overlaps, the data belongs in more than one group.

2 3

2 4 8 10

14

20 16

6

12

18

3

9

15

Which numbers in the Venn are multiples or 2?

Which are multiples of 3?

Which are multiples of both 2 and 3?

Add the numbers 21, 22, and 24 to the Venn.

2 4 8 10

14

20 16

6

12

18

3

9

15

Comparing Decimals

> = <

48.64 48.68 9.27 9.2

3.692 3.697 7.21 7.203

Use the number line to help you compare

2.453 and 2.458

2 3

COMPARE

0.890 0.89 5.733 5.693 9.70 9.71

4.953 4.951 1.403 1.4 3.074 3.740

0.7 0.57 0.23 0.32 6.562 6.559

1.1 1.10 3.406 3.4 6.57 6.571

The most important thing you

must remember is to

LINE UP THE

DECIMAL POINTS

before you do ANYTHING!

4.601 34.8 2.79 1.02

+3.280 - 12.4 x .35 : .10

Sophia earns $4 per week doing

chores. If one flower costs

$2, how many flowers can

Sophia buy if she saves for

three weeks?

Which number is less than

0.125?

0.5 0.13 0.119

0.2 0.124 0.126

Alex said the numbers

3.04, 0.43, and 2.4

are in order from greatest to

least. Is he correct or do the

numbers need to be rearranged?

Nikki has a bag of 500

nickels which weigh 5.5 pounds.

A bag of 200 half dollars

weighs 5 pounds.

Which weighs more?

Ryan said the numbers 7.37,

7.36, 2.59, and 2.95 were in

order from greatest to least.

Is he correct. Explain.

Help Kiley put these

numbers in order from least

to greatest.

0.352 0.15 0.79

0.04 0.096 0.12

0.28 0.09 0.186

Look at the line below.

If you start at 0.4 and walk 0.8

mile, where will you end up on

the line?

0 0.4

Look at the drawing below.

How can you use the mark on

the line to find where 1.0

should be located?

0 0.2

Kayla needs to redesign a

banner for field day. She wanted

her banner to be 2 feet long.

Kayla marked 0.5 foot on her

drawing. How can she use this

distance to find 2 feet?

0 0.5

Jimmy jogged 1.7 miles one

morning. Ethan jogged

1.75 miles that same day.

Who jogged the farthest?

Explain.

Colin wrote a four-digit

number. He used the digits 2,

4, 6, and 8. How many different

four-digit numbers could

Colin have written?

Kohle has half as many

brothers as Charlie. If Kohle

has “K” brothers, how many

brothers does Charlie have?

Write an algebraic expression.

Maggie has 3 coin purses with

58 coins in each. How many coins

does Maggie have?

Lauren and Bekah sold

45 boxes of Girl Scout cookies.

They deliver “C” boxes each

day for 5 days.

Solve.

Maggie wants to find which number is equal to three and

twenty-two thousandths?

Which should she pick?

3.2200 3,22

3.022 3.0022

Megan is cooking 4.619 pounds of spaghetti.

To the nearest hundredth, how many pounds of spaghetti is

Megan cooking?4.60 pounds 4.62 pounds

5 pounds 4.7 pounds

Landon is trying to find which number has a 5 in the

thousandths place.

9,562,791.1 825.858

385.59 176.245

Ari is making a banner for Girl Scouts. She marked 0.5 on a piece of banner paper. What should she do to find

1.0?

Find the distance halfway to 1

Find the 0.5 and move right 0.5 more

Double the distance from 0.5

Move 0.5 to the left of 0.5

Autumn is mailing a present that weighs 15.683 pounds. To the nearest tenth, how

many pounds does the package weigh?

What is the place value of the 9 in 4,602.791?

Ones

Tenths

Hundredths

Thousands

Put these numbers in a

Place Value chart.

Now put them in order from least to greatest.

90.49 90.4 9.149

Which of these statements is true?

5.352 < 5.350 5.350 = 5.360

5.353 < 5.360 5.358 > 5.360

Which of the following are

less than 8.007

8.002 8.200

8.020 8.022

Put each set of numbers in order from greatest to least.

9.8 9.78 9.87

9.87 9.8 9.78

9.78 9.87 9.9

9.9 9.8 9.98

What is ten times as many as the number 0.04?

0.004 0.04

4.0 0.4

Which decimal is shown in the model below?

2.0

2.96

2.40

2.04

unit 12 decimals numeration

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