Transcript Fractions and Decimals

PRE-ALGEBRA
Lesson 5-2 Warm-Up
PRE-ALGEBRA
Fractions and Decimals (5-2)
What is a
“terminating
decimal”?
terminating decimal: a decimal that terminate, or ends, at some point (it
doesn’t continue on forever)
How do you
change a fraction
into a decimal?
To change a fraction into a decimal, divide the numerator (top number) by the
denominator (bottom number)
5
Example: What is the decimal form of ?
8
0 625
5
or 5  8  8 5 
. 0 0 0 1. Divide bottom into top. Add a decimal and a 0 to the
8
number in the division box.
-4 8
20
2. Move the decimal straight up to answer and then get rid
-16
of it in the problem.
4 0 3 Go through your division step (Divide, Multiply,
-40
Subtract, Bring Down One Number)
0 4 Add a 0 to the dividend (number in the box), bring it
.
down, and repeat step 3.
terminating decimal 5. Repeat step 4 until the decimal terminates or you notice
a repeating pattern in the numbers.
PRE-ALGEBRA
Fractions and Decimals (5-2)
repeating decimal: a decimal in which the same block of one or more numbers repeats an
What is a
“repeating decimal” infinite number of times (you will never get a remainder of zero if you’re changing a fraction
into a repeating decimal).
Examples: 0.333333
3.62626262….
5.725725725725….
How do you write a
repeating decimal?
To write a repeating decimal, place a bar over__
the block of digits that repeats.
Example: 15 = 15  11 = 1.363636… =_1.36 (the 36 repeats)
11 2
Example: 3 = 2  3 = 06666….… = 0.6 (the 6 repeats)
How do you put
rational numbers
(fractions,
terminating
deciamls, and
repeating decimals
in order).
To order rational numbers: 1. graph them on a number line, or 2. put them all into fraction
or decimal form. If you put the numbers into fraction form, rewrite the fractions so that
they have the same denominator (size of the parts). Then, you can compare the
numerators (number of parts). If you put them into decimal form, line up the numbers
vertically by the decimal points, add zeroes in blank spaces, and comparing the place
values from the left (largest place values) to the right (smallest place values) [In the result
of a tie, go to the next largest place value until there is no longer a tie].
1
3
Example: Write the numbers 4 , - 0.2, -5 ,1.1 in order from least to greatest.
-3  5 = - 0.6 Change the fractions to decimals.
Line the numbers up by the decimals. Add zeroes
to blank spaces to make the same number place
0
.
6
0
values after the decimal.
-0.20
Compare with the left digit. If there is a tie, go to
1.10
the next digit to the right. Note: Negatives are
- 0.6  - 0.2  0.25  1.1
smaller than positives.
1
3
 - 0.2  4  1.1 Put the numbers back into theirPRE-ALGEBRA
original form.
1  4 = 0.25
0.25
5
Fractions and Decimals
LESSON 5-2
Additional Examples
1
The fuel tank of Scott’s new lawn mower holds gal
2
of gasoline. Scott poured 0.4 gal into the tank. Did Scott fill
the tank?
1
= 1 ÷ 2 = 0.5
2
1
Since 2 = 0.5 and 0.5 > 0.4, Scott did not fill the tank.
PRE-ALGEBRA
Fractions and Decimals
LESSON 5-2
Additional Examples
Write each fraction as a decimal. State the block of
digits that repeats.
a.
5
6
5 ÷ 6 = 0.83333 …
= 0.83
Divide.
Place a bar over the digit that repeats.
5
= 0.83; the digit that repeats is 3.
6
7
b. 11
7 ÷ 11 = 0.636363 …
= 0.63
Divide.
Place a bar over the block of digits that repeats.
7
= 0.63; the block of digits that repeats is 63.
11
PRE-ALGEBRA
Fractions and Decimals
LESSON 5-2
Additional Examples
Write the numbers in order, from least to greatest.
–0.8, 3 , – 5 , 0.125
12
4
3 ÷ 12 = 0.25
–5 ÷ 4 = –1.25
Change the fractions to decimals.
–1.25 < –0.8 < 0.125 < 0.25
Compare the decimals.
5
3
From least to greatest, the numbers are – 4 , –0.8, 0.125, and 12 .
PRE-ALGEBRA
Fractions and Decimals (5-2)
How do you write To write a decimal as a fraction, read the decimal and write the fraction so that it
a decimal as a
will read exactly the same way. Don’t, forget to simplify the fraction if you
fraction?
can.
Example: 0.43 is read “forty-three hundredths. The fraction that is read “forty43
three hundredths is 100
.
How do you write To write a decimal as a mixed number, change the numbers behind the decimal
an decimal as a into a fraction and simplify the fraction if possible. Note: The whole number(s)
mixed number? in front of the decimal do not move.
Example: Write 1.12 as a fraction.
12
1.12 = 1 100
1
12  4
100  4
3
= 1 25
1.12 is read “one and twelve hundredths”. Write
“twelve hundredths” as a fraction.
Reduce the fraction by dividing the numerator and
denominator by the GCF, 4.
3
1.12 = 1 25
PRE-ALGEBRA
Fractions and Decimals
LESSON 5-2
Additional Examples
Write 1.72 as a mixed number in simplest form.
1.72 = 1 72
100
72 ÷ 4
= 1 100 ÷ 4
1.72 = 1
18
25
Keep the whole number 1.
Write seventy-two hundredths as a fraction.
Divide the numerator and denominator
of the fraction by the GCD, 4.
Simplify.
PRE-ALGEBRA
Fractions and Decimals (5-2)
How do you write a
repeating decimal
as a fraction?
To write a repeating decimal as a fraction, place the numerator over the
same number of digits of nines.
414
33  33
1
6
Example: 0.6 =
0.33 =
=
0.414 =
999
99  33
3
9
Example: Write 0.18 as a fraction in simplest form.
Let the variable n equal the decimal.
n = 0.18
100n = 18.18
100n = 18.18
– n = 0.18
99n = 18
99n = 18
99
99
n = 18 ÷ 9
99 ÷ 9
2
=
11
Because 2 digits repeat, multiply each
side by 102, or 100.
The Subtraction Property of Equality lets
you subtract the same value from each side
of the equation. So, subtract to eliminate 0.18.
Divide each side by 99.
Divide the numerator and denominator
by the GCD, 9.
Simplify.
As a fraction in simplest form, 0.18 =
2
.
11
PRE-ALGEBRA
Fractions and Decimals
LESSON 5-2
Additional Examples
Write 0.18 as a fraction in simplest form.
n = 0.18
Let the variable n equal the decimal.
100n = 18.18
Because 2 digits repeat, multiply each side by
102, or 100.
100n = 18.18
– n = 0.18
99n = 18
The Subtraction Property of Equality lets you
subtract the same value from each side of the
equation. So, subtract to eliminate 0.18.
99n
18
=
99
99
n = 18 ÷ 9
99 ÷ 9
2
= 11
Divide each side by 99.
Divide the numerator and denominator by the
GCD, 9.
Simplify.
2
As a fraction in simplest form, 0.18 = 11 .
PRE-ALGEBRA
Fractions and Decimals
LESSON 5-2
Lesson Quiz
1. Order 6 , – 1 , 0.625, –0.35 from least to greatest.
5
3
–0.35, – 1 , 0625, 6
3
5
2. Write 17 as a decimal.
20
0.85
Write each decimal as a fraction or mixed number in simplest form.
3. 6.04
1
6 25
4. 0.21
7
33
PRE-ALGEBRA