Reading Decimals

Say what you see before the decimal

Say “and” for the decimal

Say what you see after the decimal

Say the place value of the final digit

To write in words, you write what you say

five hundred eighty

and

5 8 0 . 3 2 4

three hundred twenty-four thousandths

Ten thousands

tenths

hundredthsone

s

hundreds

thousands

tensthousandt

hs

tenthousandt

hs

Hundred thousandt

hs

One and

forty-six hundredths

sixty seven and

four thousand eighteen ten thousandths

Twelve thousand three hundred four

and two thousandths

three and forty seven hundredths

Three and forty seven thousandths

three and forty seven

tenths

Three and forty seven

hundred

seventeen thousand eighty two

seventeenand

eighty-two hundredths

seventeenand

eighty-two tenths

seventeenand

eighty-two thousandths

three thousand

two

three thousand two ten

thousandths

Zero and three

thousand two

three thousand

two thousandths

Sixty-four thousand

twenty one

Six hundred forty

thousand twenty one millionths

Sixty four hundredths twenty one

Six hundred forty

thousand twenty one thousandths

Base Ten Blocks

One and

four tenths

One and four tenths

Representsone whole

bar

Represents one tenthof a bar

(meaning youneed ten to make a bar)

Represents one hundredth

of a bar(meaning you

need one hundred to make a bar)

Represents one thousandth

of a bar (meaning you

need one thousand to make a bar)

One and

seven hundredths

One and seven hundredths

Fifty-threehundredths

Fifty-threehundredths or

0.53

One and two hundred forty-five

thousandths

One and two hundred forty-

five thousandths or 1.245

Six thousandths

Six thousandths or 0.006

One and thirteen thousandths

One and thirteen thousandths or

1.013

Two and one hundred

seventy-three thousandths or

2.173

four hundred twenty-five

thousandths or 0.425

One and two hundred eighty-

three thousandths or

1.283

Which is the larger value?

0.129 or 0.31

Prove your choice!

0.129 is less than

0.31, so 0.31 is the largest value

0.129

0.31

Which is the larger value?

0.2 or 0.05

Prove your choice!

0.2 is greater than

0.05

0.2

0.05

Understanding Decimal Values

45.076 45.0076

1098.41098.44

673.09 673.1

1. Understanding Decimal Values

67.7600 67.76

15.9815.099

0.515 0.551

nine out of ten

0.9

910

nine tenths

four out of ten

0.4four tenths

410

2.7

two and seven tenths

two wholes and seven out

of ten

2 7 10

thirty-two hundredths

0.32

Thirty-two out of one hundred

32100

eighty out of one

hundred

0.80

eighty hundredths

80100

six out of one

hundred

0.06

six hundredths

6100

                   

                   

                   

                   

                   

                   

                   

                   

                   

                   

                   

                   

                   

                   

                   

                   

                   

                   

                   

                   

 

                   

                   

                   

                   

                   

                   

                   

                   

                   

                   

                   

                   

                   

                   

                   

                   

                   

                   

                   

                   

Three and two

hundredths

Three and two

hundredths

3 2 100

3 2 100

3.023.02

Three wholes and

two parts out of a hundred

Three wholes and

two parts out of a hundred

                   

                   

                   

                   

                   

                   

                   

                   

                   

                   

 

                   

                   

                   

                   

                   

                   

                   

                   

                   

                   

Two and fourteen

hundredths

Two and fourteen

hundredths

2.142.14

                   

                   

                   

                   

                   

                   

                   

                   

                   

                   

                   

                   

                   

                   

                   

                   

                   

                   

                   

                   

Two wholes and fourteen out of one hundred

Two wholes and fourteen out of one hundred

2 14 100

2 14 100

Decimals in Expanded Form

Writing decimals in expanded form is an extension of whole numbers in expanded form.To do this you represent each individual place value

EXAMPLE 4.305 is 4 + 0.3 + 0.0054 x 1 + 3 x 0.1 + 5 x 0.0014 x 100 + 3 x 10-1 + 5 x 10-3

Decimals in Expanded Form34.308

30 + 4 + 0.3 + 0.008

3 x 10 + 4 x 1 + 3 x 0.1 + 8 x 0.001

3 x 101 + 4 x 100 + 3 x 10-1 + 8 x 10 -3

5.28

5 + 0.2 + 0.08

5 x 1 + 2 x 0.1 + 8 x .01

5 x 100 + 2 x 10-1 + 8 x 10-2

Decimals in Expanded Form3 + 0.4 + 0.09 =

9 x 101 + 3 x 10-1 + 5 x 10-2 =

40 + 0.8 + 0.003 =

0.7 + 0.03 + 0.0002 =

0.06 + 0.4 + 3 + 20 + 0.001 =

800 + 3 + 60 000 + 0.02 + 0.007 =

3.493.49

40.80340.803

23.46123.461

60 803.o27

60 803.o27

0.73020.7302

90.3590.35

Decimals in Expanded Form4 x 1000 + 5 x 0.1 + 3 x 0.01 =

7 x 100 + 2 x 0.1 + 5 x 1 + 8 x 0.001 =

4 x 0.0001 + 3 x 0.1 + 2 x 0.01 =

0.006 + 0.01 + 700 + 20 + 0.0004 =

3 x 1 + 4 x 0.01 =

8 x 100 + 5 x 10-2 + 3 x 10-3 =

4000.534000.53

705.208705.208

720.0164720.0164

3.043.04

0.32040.3204

8.0538.053

Rounding DecimalsWhen rounding decimals it is first necessary to identify the place value you are rounding to. The digit that follows will tell you whether you should round up or leave the digit the same.If the digit is: 5 or higher – round up by one

If the digit is: 4 or lower – leave the same

Digits past the rounded digit are not recorded in the rounded number.

When rounding it is helpful if you . . .

Circle the place value you are rounding to. Underline the digit that follows; it is this digit that tells you to round up or leave the same.

Example

34.561 rounded to the nearest tenth

is . . .

3 4 . 5 6 1

34.6

Example

4.6341 rounded to the nearest hundredth is . . .

4 . 6 3 4 1

4.63

Example

67.1125 rounded to the nearest thousandths is

6 7 . 1 1 2 5

67.113

Example

.6971 rounded to the nearest hundredth is . . .

0 . 6 9 7 1

.70

Example

5.96 rounded to the nearest tenth is . . .

5 . 9 6

6

Example

587.469 rounded to the nearest whole number is . . .

5 8 7 . 4 6 9

587

Example

7535.9 rounded to the nearest whole number is . . .

7 5 3 5 . 9

7536

Example

619.844 rounded to the nearest whole number is . . .

6 1 9 . 8 4 4

620

Example

6198 rounded to the nearest hundred is . . .

6 1 9 8

6200

Example

463 228 rounded to the nearest hundred thousand is . . .

463 228

500 000

8 x 0.3 =

Eight groups with three tenths in each group

2.4

2 x 1.6 =

Two groups with one and six tenths in each group

3.2

4 x 0.9 =

Four groups with nine tenths in each group

3.6

9 x 0.5 =

Nine groups with five tenths in each group

4.5

2 x 1.2 =

Two groups with one and two tenths in each group

2.4

Question # 9 Example

To share 1.7 of a bar I would need two bars. I would give away one whole bar and break the second bar into ten equal pieces and give away seven pieces of the ten or one and seven tenths.

One and seven tenth as a fraction is 1 7

10