PRE-ALGEBRA

PRE-ALGEBRA

Lesson 5-2 Warm-Up

PRE-ALGEBRA

What is a “terminating decimal”?

How do you change a fraction into a decimal?

terminating decimal: a decimal that terminate, or ends, at some point (it doesn’t continue on forever)

To change a fraction into a decimal, divide the numerator (top number) by the denominator (bottom number)

Example: What is the decimal form of ?

or 5 8

2. Move the decimal straight up to answer and then get rid of it in the problem.

3 Go through your division step (Divide, Multiply, Subtract, Bring Down One Number)

4 Add a 0 to the dividend (number in the box), bring it down, and repeat step 3.

5. Repeat step 4 until the decimal terminates or you notice a repeating pattern in the numbers.

5 8 5

8

8 5 . 0 1. Divide bottom into top. Add a decimal and a 0 to the number in the division box.- 4 8

2

.

- 1 6

0 6

4

0

0

2

0

0- 4 0

0

5

terminating decimal

Fractions and Decimals (5-2)

PRE-ALGEBRA

What is a “repeating decimal”

How do you write a repeating decimal?

How do you put rational numbers (fractions, terminating deciamls, and repeating decimals in order).

repeating decimal: a decimal in which the same block of one or more numbers repeats an 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….

To write a repeating decimal, place a bar over the block of digits that repeats.

Example: = 15 11 = 1.363636… = 1.36 (the 36 repeats)

Example: = 2 3 = 06666….… = 0.6 (the 6 repeats)

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].

Example: Write the numbers , - 0.2, - ,1.1 in order from least to greatest.

1 4

3 5

0 . 2 5

__

- 0 . 2 0 1 . 1 0

Line the numbers up by the decimals. Add zeroes to blank spaces to make the same number place values after the decimal.Compare with the left digit. If there is a tie, go to the next digit to the right. Note: Negatives are smaller than positives.

-3 5 = - 0.6

Put the numbers back into their original form.

- 0.6 - 0.2 0.25 1.1

- - 0.2 1.1 3 5

1 4

1 4 = 0.25 Change the fractions to decimals.

15 11

- 0 . 6 0

2 3

_

Fractions and Decimals (5-2)

PRE-ALGEBRA

The fuel tank of Scott’s new lawn mower holds gal

of gasoline. Scott poured 0.4 gal into the tank. Did Scott fill

the tank?12

= 1 ÷ 2 = 0.5

Since = 0.5 and 0.5 > 0.4, Scott did not fill the tank.12

12

Fractions and DecimalsLESSON 5-2

Additional Examples

PRE-ALGEBRA

Write each fraction as a decimal. State the block of

digits that repeats.

a.

b.

56

5 ÷ 6 = 0.83333 … Divide.

Place a bar over the digit that repeats.= 0.8356

= 0.83; the digit that repeats is 3.

711

7 ÷ 11 = 0.636363 … Divide.

= 0.63 Place a bar over the block of digits that repeats.

= 0.63; the block of digits that repeats is 63.7

11

Fractions and DecimalsLESSON 5-2

Additional Examples

PRE-ALGEBRA

Write the numbers in order, from least to greatest.

–0.8, , , 0.125312

54

–

–1.25 < –0.8 < 0.125 < 0.25  Compare the decimals.

3 ÷ 12 = 0.25Change the fractions to decimals.

–5 ÷ 4 = –1.25

From least to greatest, the numbers are , –0.8, 0.125, and .54

– 312

Fractions and DecimalsLESSON 5-2

Additional Examples

PRE-ALGEBRA

How do you write a decimal as a fraction?

How do you write an decimal as a mixed number?

To write a decimal as a fraction, read the decimal and write the fraction so that it will read exactly the same way. Don’t, forget to simplify the fraction if you can.

Example: 0.43 is read “forty-three hundredths. The fraction that is read “forty-three hundredths is .

To write a decimal as a mixed number, change the numbers behind the decimal into a fraction and simplify the fraction if possible. Note: The whole number(s) in front of the decimal do not move.

Example: Write 1.12 as a fraction.

1.12 = 1 1.12 is read “one and twelve hundredths”. Write “twelve hundredths” as a fraction.

1 = 1 Reduce the fraction by dividing the numerator and denominator by the GCF, 4.

1.12 = 1

12 100

43100

12 4 100 4

3 25

3 25

Fractions and Decimals (5-2)

PRE-ALGEBRA

Write 1.72 as a mixed number in simplest form.

Keep the whole number 1.Write seventy-two hundredths as a fraction.

1.72 = 1 72100

Divide the numerator and denominator of the fraction by the GCD, 4.

72 ÷ 4100 ÷ 4= 1

Simplify.1825

1.72 = 1

Fractions and DecimalsLESSON 5-2

Additional Examples

PRE-ALGEBRA

To write a repeating decimal as a fraction, place the numerator over the same number of digits of nines.

Example: 0.6 = 0.33 = = 0.414 =

Example: Write 0.18 as a fraction in simplest form.n Let the variable n equal the decimal.= 0.18

As a fraction in simplest form, 0.18 = .211

100n = 18.18 Because 2 digits repeat, multiply each side by 102, or 100.

1899

99n99

= Divide each side by 99.

n 18 ÷ 999 ÷ 9

= Divide the numerator and denominatorby the GCD, 9.

211

= Simplify.

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.

How do you write a repeating decimal as a fraction? 6

933 3399 33

414999

13

Fractions and Decimals (5-2)

PRE-ALGEBRA

Write 0.18 as a fraction in simplest form.

n Let the variable n equal the decimal.= 0.18

As a fraction in simplest form, 0.18 = .2

11

100n = 18.18 Because 2 digits repeat, multiply each side by 102, or 100.

1899

99n99

= Divide each side by 99.

n 18 ÷ 999 ÷ 9

= Divide the numerator and denominator by theGCD, 9.

211= Simplify.

100n = 18.18n = 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.

Fractions and DecimalsLESSON 5-2

Additional Examples

PRE-ALGEBRA

1. Order , – , 0.625, –0.35 from least to greatest.

2. Write as a decimal.

Write each decimal as a fraction or mixed number in simplest form.

3. 6.04 4. 0.21

65

1720

13

65

13

–0.35, – , 0625,

0.85

61

257

33

Lesson Quiz

Fractions and DecimalsLESSON 5-2