Download Infinite decimal

Convert Decimals to Fractions
8.NS.1 Know that numbers that are not rational are called irrational. Understand
informally that every number has a decimal expansion; for rational numbers
show that the decimal expansion repeats eventually, and convert a decimal
expansion which repeats eventually into a rational number.
8.NS.2 Use rational approximations of irrational numbers to compare the size of
irrational number, locate them approximately on a number line diagram, and
estimate the value of expressions.
 Students know that every number has a decimal expansion.
WKSP
HW
Procedure
Media
Student
Outcomes
Standard
Pre Requisite
Decimal  Fraction  Number Line
&
Square Root  Number Line
#24
Spiral #6
Decimal  Fraction  Number Line
&
Square Root  Number Line
Decimal
Expanded Form
0.3
0.376
0. 3̅
Finite decimal:
Infinite decimal:
Number Line
Decimal  Fraction  Number Line
&
Square Root  Number Line
Square Root (approximate) Decimal
√2
√28
Number Line
Decimal  Fraction  Number Line
&
Square Root  Number Line
Name: __________________________________
Pre-Algebra
1.
Show on the number line the representation of the decimal 0.829.
2.
Is the decimal 0.829 finite or infinite?
3.
̅̅.
Find the fraction equal to 0. ̅̅
81
Date: ______
Exit Ticket
Decimal  Fraction  Number Line
&
Square Root  Number Line
Name: _______________________________________
Pre-Algebra
Date: _____
HW #24

Lesson Summary

An infinite decimal is a decimal whose expanded form and number line representation are infinite.

The number 0.83̅ is represented on the number line shown below. Each new line is a magnification of
the interval shown above it.

To get the decimal expansion of a square root of a non-perfect square, you must use the method of
rational approximation.

Any number that cannot be expressed as a rational number is called an irrational number. Irrational
numbers are those numbers with decimal expansions that are infinite and do not have a repeating
block of digits.
1. Show on the number line the representation of the decimal 0.125
Is the decimal finite or infinite?
2. Determine the 3 decimal digit approximation of the number √17.
3. Classify the following numbers as rational or irrational, and explain how you know.
3
5
0.737373 …
√31
Decimal  Fraction  Number Line
&
Square Root  Number Line
Review:
4. Represent each of the following as a base with a positive exponent.
a. (43)-5
b.
43
4−5
c. 43 x 4-5
5. What is the smallest power of 10 that would exceed 123,456?
6. Simplify: −1 4 + 0.4
5