Engageny

Lesson 5Objective

Name decimal fractions in expanded, unit, and word

forms by applying place value reasoning.

Forms Activity

5 Stations

Station 1: Written/Word Form

Station 2: Decimal Form/Numerals

Station 3: Expanded Form

Station 4: Fraction Form

Station 5: Unit Form

Make your rounds to the five stations with your group and complete the problems!

Then check your answers using the purple key. You will need your math notebook, pencil, and pen.

What is the purpose of writing numbers in different forms?

Standard form: Shows us digits that we are using to represent that amount

Expanded form: Shows how much each digit is worth and that the number is a total of those values added together

Unit form: Shows how many of each size unit are in the number

Practice

Write “54 tenths” as a decimal.

5.4

Multiply 5.4 by 102

5.4 x 102 = ?

540

three thousand forty-seven

Write in…

a.Standard Form

b.Expanded Form

c.Unit Form

three thousand forty-seven

Answers

a.3,047

b.3 x 1,000 + 4 x 10 + 7 x 1

c.3 thousands 4 tens 7 ones

Unit form Practice

0.54 = 5 tenths 4 hundredths

2.31 = 2 _________ 3 __________ 1 hundredths

16.2 = __ _________ __ _________ __ _________

Unit form Practice

0.54 = 5 tenths 4 hundredths

2.31 = 2 ones 3 tenths 1 hundredths

16.2 = 1 tens 6 tens 2 tenths

1 thousandth

Fraction Form?

Expanded Form? (Fractions and Decimals)

Unit Form?

1 thousandth

1/1,000

1 x 1/1,000 or 1 x 0.001

1 thousandth

3 copies of 1 thousandth

What operation should I use?

3 __ 0.001 = ?

3 thousandths

3 thousandths

Standard Form?

Expanded Form? (Fractions and Decimals)

Unit Form?

3 thousandths

0.003

3 x 1/1,000 or 3 x 0.001

Unit Form?

13 thousandths

Standard Form?

Expanded Form? (Fractions and Decimals)

Unit Form?

13 thousandths

0.013

1 x 1/100 + 3 x 1,000 or 1 x 0.01 + 3 x 0.001

1 hundredth 3 thousandths

25.413

Word Form

Expanded Form

Unit Form

25.413

Twenty-five and four hundred thirteen thousandths

2 x 10 + 5 x 1 + 4 x 1/10 + 1 x 1/100 + 3 x 1/1,000

OR

2 x 10 + 5 x 1 + 4 x 0.1 + 1 x 0.01 + 3 x 0.001

2 tens 5 ones 4 tenths 1 hundredth 3 thousandths

Four hundred four thousandths

Decimal Form?

Four hundred four thousandths

0.404

Four hundred four thousandths

0.404

Expanded form?

Four hundred four thousandths

4 x 1/10 + 4 x 1/1,000

or

4 x 0.1 + 4 x 0.01

Four hundred and four thousandths

Decimal Form?

Four hundred and four thousandths

400.004

Four hundred and four thousandths

400.004

Expanded form?

Four hundred and four thousandths

4 x 100 + 4 x 1 + 4 x 1/1,000

or

4 x 100 + 4 x 1 + 0.001

You can use the rest of the time to...Start on your homework!

* Please complete BOTH sides by tomorrow.

Engageny

Lesson 5

Problem SetAnswer Key