# Introduction to decimals

### Introduction to decimals

In this lesson, we will learn:

• Decimals are numbers with place values even smaller than the ones place
• How to use base ten (block) models to represent a decimal's place values (ones place, tenths place, hundredths place) using hundred blocks, tens sticks, and single blocks
• How to write decimals in standard, expanded, and written forms.

Notes:

• Decimals are numbers with place values even smaller than the ones place.
• You can write a decimal point (.) at the end of any whole number
• Writing digits to the right of the decimal point gives decimal place values

• Ex. 1.5 shows decimal place of tenths; 2.64 shows decimal place of hundredths
• The names of decimal place values mirror the names of whole number place values, but you need to add the "-ths" suffix to the end.
• Each place value is 10 times MORE than the place on its right
• Each place value is 10 times LESS than the place on its left

• Ex. 111.11

 hundreds tens one . tenths hundredths 1 1 1 . 1 1 =100 =10 =1 =0.1 =0.01

• Decimals can be represented with base ten (block) models
• "One whole" or hundred block = ones place value
• Column or stick = tenths place value
• Single square = hundredths place value

• Ex. 1.25

• Decimals can be written in standard, expanded, and written forms:
• Standard form: the decimal is written with number digits and a decimal point
• Expanded form: the decimal is written as a sum of values for all place values
• Written form: the decimal is written with words naming digits and place values from left to right

• Ex. 12.34 (read aloud as "twelve point three four")

 Standard form: 12.34 Expanded form: 10 + 2 + 0.3 + 0.04 Written form: twelve and three tenths four hundredths OR twelve and thirty-four hundredths

• Trailing zeroes (at the end/right of the number) are NOT important in decimals
• Ex. 0.5 and 0.50 are equal (5 tenths = 50 hundredths)

#### Lessons

• Introduction
a)
What are decimals?

b)
How to use base ten (block) models to represent decimals

c)
Standard, expanded, and written forms for decimals

• 1.
Naming decimal place values
Write the place value of the underlined digit in the decimal number.
a)
14.9

b)
357.2

c)
0.68

d)
4.21

• 2.
Decimal digit values
Fill out the value of each digit in the boxes. Then, write the expanded and written forms for the decimal.
a)

b)

c)

d)

• 3.
Decimals represented by base ten (block) models
What is the decimal represented by the base ten (block) model?
a)

b)

c)

d)

• 4.
Equivalent decimal tenths and hundredths
Using the list of decimals shown below:

0.60 $\enspace$ 0.04$\enspace$ 0.20$\enspace$ 0.5$\enspace$ 0.02$\enspace$ 0.40$\enspace$ 0.2$\enspace$ 0.8$\enspace$ 0.4$\enspace$ 0.31$\enspace$ 0.97$\enspace$ 0.06$\enspace$
a)
Circle all equivalent pairs of decimals and write out number sentences using the equal (=) sign

b)
Colour in a hundredths model block to represent each equivalent pair.

c)
Describe each pair of equivalent decimals from parts a and b using words (written as number of tenths vs. number of hundredths)