Download Finite decimal

Equivalent Fractions
Convert fractions to decimals by using long-division
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.
 Student know that when a fraction has a denominator that is the product of 2’s
and/or 5’s, it has a finite decimal expansion because the fraction can then be
written in an equivalent form with a denominator that is a power of 10.
WKSP
HW
Procedure
Media
Student
Outcomes
Standard
Pre Requisite
Fraction  Decimal  Number Line
#25
Spiral #6
Fraction  Decimal  Number Line
Fraction
54
20
7
8
Decimal
Equivalent Fraction
Long Division
Rational Approximation
Number Line
Fraction  Decimal  Number Line
Fraction
Equivalent Fraction
Decimal
Long Division
Rational Approximation
41
6
8
9
When given a fraction, you can look at the denominator to see if it’s decimal form will be finite or infinite.
Finite decimal:
Infinite decimal:
Number Line
Fraction  Decimal  Number Line
Name: __________________________________
Pre-Algebra
1.
Date: ______
Exit Ticket
Convert each rational number into a finite decimal. If the fraction cannot be
written as a finite decimal, then state how you know.
1
200
1
=
12
=
1
2.
Write the decimal expansion of .
3.
Use rational approximation to determine the decimal expansion of 11.
8
35
Fraction  Decimal  Number Line
Name: _______________________________________
Pre-Algebra
Date: _____
HW #25
Lesson Summary

Fractions with denominators that can be expressed as products of only 2’s and/or 5’s have decimal
expansions that are finite.

When the denominator of a fraction cannot be expressed as a product of only 2’s and/or 5’s, then the
decimal expansion of the number will be infinite.

The method of rational approximation can be used to write the decimal expansion of rational numbers.
Example: Use rational approximation to find the decimal expansion of
𝑚
1. tenth’s place value
10
<
𝑚<
2. blast everything by ten
50
3. Break-up numerator
11
5
4. How far off are you?
11
=
−
5
11
50
11
<
11
4
.
𝑚+1
10
<𝑚+1
4 × 11
10
5
11
=
+
6
11
6
110
5. Repeat steps 1-4 replacing tenths with hundredths.
1. Which of the following expressions have a finite decimal? (Circle all that apply)
1
1
1
1
1
1
1
1
1
1
1
2
3
4
5
6
7
8
9
10
11
12
2. Write 3 as a decimal.
250
3. Convert the fraction 3 to a decimal.
8
4. Use rational approximation to determine the decimal expansion of 25.
9
Fraction  Decimal  Number Line
Review:
17
17
3
4. Rodney thinks that √64
is greater than 4 . Sam thinks that 4 is greater. Who is
right and why?
3
5. Which number is smaller, √27
or 2.89? Explain.
6. Place the following numbers at their approximate location on the number line:
√12, √16,
3
20
6
̅̅̅, √27
, 3. ̅53
3
4