Decimals

- sometimes called decimal fractions, because they are related to the special subset of fractions made up of those fractions that powers of 10 as denominator.

Decimal a number that uses place-value and a decimal point to show tenths and hundredths.Example: 3.4 and 3.25

Decimal point a period separating the ones and the tenths places in a decimal. Example: 0.4

Equivalent decimals are decimals that name the same number. Example: 0.9 and 0.90

Explore Decimal Place Value

Materials: 10 by 10 grids Display a 10 by 10 grid. The page is divided into 100 squares, but is it still

1 whole piece of paper? Have students explain a whole number in their own words.

Shade on the grid. Write 2.35 and 2 on the board and say each

form of the number. Have students repeat aloud. Compare a shaded grid to both numbers.

Divide class into pairs or small groups. Distribute paper with 10 by 10 grids and have students shade a block of squares on 1 grid. Use additional grids to represent whole numbers.

Have partners write the number as a decimal and as a fraction and use the grids to present to the class.

Decimal Place Value

Write the number 682.4. Have students point to and identify the number in each place.

Identify the digit in the tenths place. Point to the tenths place, say the value, 4 tenths, and have students repeat aloud.

Have them write 682.47. Repeat for 7 in the hundredths place. Have students write 682473. Repeat for 3 in the thousandths place. Divide class into pairs or small groups. Have partners use price on

catalog pages to practice identifying place values. Have students share their work.

Eg. Show the place value for each of the numbers in the numeral below.

1234.4567

A concept-development activity for decimals

1. Give a decimal to tell how much is shaded. Then write a sentence to tell what you found out using place value ideas.

Eg. Region Decimal Sentence

0.18

1.18

2.187

2. A skill-development activity for decimals

Draw a picture on a square region separated into 100 smaller square region.

Teacher directions:

Use decimals to tell some things about the picture.For example, if you draw a face of a girl.Ask questions such as:

i. How much of the picture shows the girl’s hair?ii. How much shows her lips?

0.13The fraction 0.13 is the same as

+

iii. How much shows her eyes?iv. How much of the pictures show the background?

How can you show 0.4 = 0.40?[Possible answer: Shade 4 parts of a tenths square to show 0.4; shade 40 parts of a hundredths square to show 0.40]

Is 0.54 greater or less than 1? How can you tell?[Less, the 0 means there are no ones, and the 54 hundredths means 54 out of a whole of 100 parts.]

How are 1 and 1.6 related?

[Possible answer: They are equal; they are two different ways of writing the same number]

How would you use hundredths squares to show 1.6?[Show 1 whole square and shade 6 columns of ten on another]

Why can you write 2 as 2.2 0r 2.20?

[Because = 0.2 = 0.20

Activity: Addition

* Provide students with graph paper* Write this decimal on the board and have students colour their graph paper to model it: 0.07. Then have them use a different colour to show 0.43.

* Ask how much of the graph paper is shaded altogether. [ or 0.5]

How is adding decimals like adding whole numbers?[You start with the digits farthest to the right, then add. You regroup if needed]

What are the steps for adding 1.3 and 1.5?

[Start with the tenths, then add each place. Regroup if needed. Place the decimal point between the ones and the tenths.]

Error Intervention If students do not line up the decimal points when adding …..

Then have them use place-value charts to write the addends and the sum.

Where do you place the decimal point when adding decimals?[In the same place as the decimal point in the addends]

How can you tell if you need to regroup when adding decimals?[Possible answer: Check the sum of each place to see if it is greater than 9. If it is, then you will need to regroup.]

Table 1

Strips Read As ValueSix tenths

Seven tenths

Eight tenths

Nine tenths

Ten tenths

Table 2

Strips Read As Decimals0.1 zero point one 0.1

Table 3

Decimals Read As Value0.6 Six tenths or zero point six

0.70.81.0 Ten tenths or

one and zero tenth or one

0.0 Zero tenth or zero point zero

Exercise 1

Decimals Read As Value0.6 Six tenths or zero point six0.7 Seven tenths0.8

1.0

0.0

0.70.81

Decimals Read As Value0.6 zero point six

0.70.81.0 One point zero