For more information, please see full course syllabus of Pre Algebra

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For more information, please see full course syllabus of Pre Algebra

For more information, please see full course syllabus of Pre Algebra

### Equivalent Forms of Rational Numbers

- A rational number is a number that can be written as a/b where b is a nonzero number. Rational numbers are integers, fractions, and terminating and repeating decimals.
- To convert a decimal to a fraction:
- Count the number of decimal places
- Put the number over a fraction bar
- Match the number of decimal places to zeros, under the fraction bar, put a 1 in front
- Simplify if possible!
- To convert a fraction to a decimal, divide the numerator by the denominator. Round the quotient to the requested decimal place if necessary.

### Equivalent Forms of Rational Numbers

Write - 0.54 as a simplified fraction.

- − 0.54 =
- − [54/100] =
- − [(54 ÷2)/(100 ÷2)] =

− [27/50]

Write 0.0125 as a simplified fraction.

- 0.0125 =
- [125/10,000] =
- [(125 ÷25)/(10,000 ÷25)] =
- [(5 ÷5)/(400 ÷5)] =

[1/80]

Write 0.0088 as a simplified fraction.

- 0.0088 =
- [88/10,000] =
- [(88 ÷4)/(10,000 ÷4)] =
- [(22 ÷2)/(2500 ÷2)] =

[11/1250]

Write [1/8] as a decimal.

- 8| ― 1.000 =

0.125

Write [12/33] as a decimal.

- 33| ― 12.0000 =
- 0.3636... =

0.―36

Write − [13/8] as a decimal.

- − 8| ― 13.000 =

= − 1.625

Is [1/9] equal to a repeating decimal?

- 9| ― 1.000 =
- 0.111... =
- 0.―1

Yes

Is [3/8] equal to a repeating decimal?

- 8| ― 3.000 =
- 0.375

No

Jason and Christian are playing darts. Jason hits the bulls - eye 9 out of 28 times, and Christian hits the bulls - eye 11 out of 36 times. Which player has the higher accuracy?

- Jason: [9/28] =
- 28| ― 9.000 ≈ 0.321
- Christian: [11/36] =
- 36| ― 11.000 ≈ 0.306

Christian

Which of the following numbers is not a rational number? 2.5, - 0.788, 0.999..., √2

- 2.5 and - 0.788 are terminating numbers, so they are rational.
- 0.999... is a repeating number, so it is rational.
- √2 ≈ 1.41421356237, and it is not terminating nor repeating.

√2 is not a rational number.

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Answer

### Equivalent Forms of Rational Numbers

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

- Intro
- What You'll Learn and Why
- Vocabulary
- Converting Decimals to Fractions
- Converting Decimals to Fractions
- Converting Fractions to Decimals
- Converting Fractions to Decimals in Word Problems
- Converting Fractions to Decimals in Word Problems
- Extra Example 1: Write 0.038 as a Fraction
- Extra Example 2: Write -13/7 as a Decimal
- Extra Example 3: Batting Average
- Extra Example 4: Rational Number

- Intro 0:00
- What You'll Learn and Why 0:06
- Topics Overview
- Vocabulary 0:30
- Rational Number
- Terminating Decimal
- Repeating Decimal
- Converting Decimals to Fractions 1:22
- Write 0.47 as a Fraction
- Write 0.48 as a Fraction
- Write 0.245 as a Fraction
- Converting Decimals to Fractions 4:20
- Write 0.08 as a Fraction
- Write 0.8 as a Fraction
- Converting Fractions to Decimals 5:26
- Write 1/2 as a Decimal
- Write 6/33 as a Decimal
- Write -9/5 as a Decimal
- Converting Fractions to Decimals in Word Problems 8:19
- Batting Average
- Converting Fractions to Decimals in Word Problems 11:22
- Cooking Festival
- Extra Example 1: Write 0.038 as a Fraction 14:45
- Extra Example 2: Write -13/7 as a Decimal 15:35
- Extra Example 3: Batting Average 16:38
- Extra Example 4: Rational Number 19:55

0 answers

Post by dzung tran on April 12, 2014

On Extra Example III, Batter A would have a batting average of .259 with the repeating decimal sign on top since you started off with 7 and ended with 7.

1 answer

Last reply by: Professor Fung

Wed Jun 5, 2013 4:40 AM

Post by Rishabh Kasarla on January 12, 2013

Can you please make a video about converting repeating decimals into fractions?

0 answers

Post by Arpana Duggal on August 1, 2012

Ms.Fung

Finding the GCD every time you need to simplify isn't a good idea. You should tell everyone to use simplifying rules because if you are taking a test, people will use the whole method of GCD and they will loose valuable time.

1 answer

Last reply by: jeffrey breci

Fri Dec 23, 2011 10:05 PM

Post by James Browning on January 17, 2011

The answer for -13/7 is incorrect. I came up with -1.857

0 answers

Post by ALI MAHDAWI on January 4, 2011

wrong answer they are both the same .5714285