# 4th Grade - Decimals And Fractions Equivalents

 Grade Level: 4th Skill: Fractions and Probability Topic: Decimals and Fractions Equivalents Goal: Write tenths and hundredths in decimal and fraction notations and know the fraction and decimal equivalents for halves and fourths (i.e. 1 - 2 = 0.5 or 0.50; 7 - 4 = 1 andfrac34; = 1.75 Skill Description: Change fractions to decimals and decimals to fractions.

## Building Blocks/Prerequisites

### Sample Problems

(1)

Choose the fraction that represents the model on the base-ten grid:

1. 3/10

2. 3/7

3. 7/10

Change the fraction you chose to a decimal.

(a; 0.3)

(2)

Choose the fraction that represents the model on the base-ten grid:

1. 15/100

2. 36/64

3. 36/100

Change the fraction you chose to a decimal.

(c; 0.36)

(3)

Change 7/10 to a decimal and categorize the numbers in standard form, expanded form, and word form:

 Standard Form Expanded Form Word Form

(Standard form: 0.7; Expanded form: 0 + 0.5; Word form: seven tenths)

(4)

Write the fraction below as a decimal:

2/4

Tip: Change the fraction to simplest form, and then convert to a decimal.

(1/2 – 0.5)

(5)

Add the decimals below, then covert to a fraction:

1.2 + 0.38 =

(1.58 = 1 58/100)

### Learning Tips

(1)

Model forms for decimals:

 Standard Form Expanded Form Word Form 0.4 0 + 0.5 Zero and five tenths or five tenths 0.45 0 + 0.4 + 0.05 Forty five hundredths

(2)

Explain base ten grids (tenths & hundredths)

Tenths grid: 10 parts

Hundredth Grid: 100 parts

(3)

Converting the denominator for the fractions to 10 or 100 in order to convert to a decimal.

i.e.) 3 x 2 = 6

5 x 2 = 10 the decimal would become 0.6

(4)

The difference of:

Ten & tenths-

tens place value is the second column before the decimal

tenths place value is the first column after the decimal (there is no oneths column).

Hundred & hundredths

Hundred place value is the third column before the decimal

Hundredths place value is the second column after the decimal

 ones • Tenths Hundredths Word Form 0 • 4 5 Forty five hundredths 3 • 0 6 Three and six hundredths

(5)

Math Vocabulary

Standard form- write numbers ( 1,349)

Word form- write with words (one thousand, three hundred forty-nine)

Expanded form- add place values (1,000 + 300 + 40 + 9)

### Extra Help Problems

(1)

Write each fraction as a decimal:

8

10

(0.8)

(2)

Write each fraction as a decimal:

32

100

(0.32)

(3)

Write each fraction as a decimal:

4

5

(0.8)

(4)

Write each fraction as a decimal:

1

4

(0.25)

(5)

Write each fraction as a decimal:

9

100

(0.09)

(6)

Find the missing numerator:

??

100 = 0.47

(47)

(7)

Find the missing decimal:

6

10 = _____

(0.6)

(8)

Find the missing denominator:

6

? = 0.06

(100)

(9)

Find the missing decimal:

1

1. = ____

(0.25)

(10)

Find the missing numerator:

?

4 = 0.75

(3)

(11)

Fill in the missing fraction and decimal on the number line:

------------------------------------------------------------------------------------

2/10 3/10 5/10 6/10

------------------------------------------------------------------------------------

0.1 0.2 0.3 0.5

(0.6)

(12)

Fill in the missing decimals on the number line:

------------------------------------------------------------------------------------

1/4 2/4 3/4

---------------------------------------------- ---- --------- -------------------------

(0.25; 0.5; 0.75; 1)

(13)

Write equivalent decimal for:

½

(0.5)

(14)

Write equivalent decimal for:

¼

(0.75)

(15)

Write fraction and decimal for the model:

(0.5; ½)

(16)

Write fraction and decimal for the model:

(0.9; 9/10)

(17)

Write fraction and decimal for the model:

(0.57; 57/100)

(18)

Write fraction and decimal for the model:

(0.10; 10/100= 1/10)

(19)

Write a decimal for the mixed number:

15 3/100

(15.03)

(20)

Write a decimal for the mixed number:

6 7/10

(6.7)

(21)

Write a mixed number for the decimal:

1.25

Simplify the fraction.

(1 ¼ )

(22)

Write a mixed number for the decimal:

6.90

Simplify the fraction.

(6 9/10)

(23)

Fill in the chart:

 Standard Form Expanded Form Word Form 0.43

(Expanded form: 0 + 0.40 + 0.03; Word form: Forty-three hundredths)

(24)

Fill in the chart:

 Standard Form Expanded Form Word Form One and three tenths

(Standard form: 1.3; Expanded form: 1 + 0.3)

(25)

Fill in the chart:

 Standard Form Expanded Form Word Form 10 +8+ 0.2 +0.05

(Standard form: 18.25; Word form: Eighteen and twenty five hundredths)