6.1 Introduction to Decimals

Decimal – from the Latin decem meaning ten

Place Value                     43.71625

4	3	.	7	1	6	2	5
Tens	Units	and	Tenths	Hundredths	Thousandths	Ten-thousandths	Hundred-thousandths
10	1		.1	.01	.001	.0001	.00001

Write in Expanded form:

Two Versions – using .1, .01, .001, etc or using powers of ten

Manipulatives   -  could use base ten blocks.

A larger block would be a unit, and the smaller blocks tenths, etc.

Represent 1.32 using base ten blocks

Represent 3.214 using base ten blocks

Activity 1 – page 124

Converting Fractions to Decimals

“Easiest”      The original fraction has a denominator which is a power of ten.

“Moderate”   A terminating decimal, in reduced form, the denominator has only 2 and 5 as factors.

A terminating decimal is a decimal that can be written with only a finite number of places to the right of the decimal point.

Method 1 - rename as a fraction with a denominator of a power of 10

“convert to problem we already know” – tenths, hundredths, …

Multiply by 1 as fraction    

Examples:

Method 2 – Use long division to convert to decimal

Examples:

“Challenging”  (must be converted using long division or calculator!!) 

Fractions which lead to repeating decimal

In reduced form, denominators CANNOT be expressed as power of ten

Theorem  A rational number  in simplest form can be written as a terminating decimal if and only if the prime factorization of the denominator has no primes other than 2 or 5.

Example:  Indicate whether each fraction is terminating or repeating as a decimal

Order Decimals

BE CAREFUL:         .3  versus .15

Arrange in order from smallest to largest:   –1.453, -1.45, -1.4053, -1.493

Arrange in order from smallest to largest:  

Activity 2 – Page 125