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### 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:
1. Count the number of decimal places
2. Put the number over a fraction bar
3. Match the number of decimal places to zeros, under the fraction bar, put a 1 in front
4. 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.

### 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 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