5-2

Rational Numbers

Converting Decimals to Fractions

• To convert a decimal to a fraction:1)Determine where the

decimal ends2)Place the numerals after the

decimal over the appropriate denominator If there is a whole number, it

stays whole, just add it on at the end.

3)Simplify Let’s try one….

Converting Decimals to Fractions

Convert 0.3 to a fraction using the steps in the previous slide.

Step 1: determine where the decimal ends

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0 3Our decimal ends in the tenths place.

Converting Decimals to Fractions

Convert 0.3 to a fraction using the steps in the previous slide.

Step 2: place the numerals after the decimal point over the appropriate denominator.

Only 3

We discovered that our decimal ends in the tenths place. So our appropriate denominator is 10.

3

10

Converting Decimals to Fractions

Convert 0.3 to a fraction using the steps in the previous slide.

Step 3: Simplify

Can we simplify this fraction?

No! is already in simplest form!

Converting Decimals to Fractions

Let’s try with 1.46. How do we convert it to a fraction?

Step 1: determine where the decimal ends

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Converting Decimals to Fractions

Let’s try with 1.46. How do we convert it to a fraction?

Step 2: place the numerals after the decimal point over the appropriate denominator.

We discovered that our decimal ends in the _________ place. So our appropriate denominator is _____.

Converting Decimals to Fractions

Let’s try with 1.46. How do we convert it to a fraction?

Step 3: Simplify

Can we simplify this fraction?

1 46100

Converting Decimals to Fractions

• When you have a repeating decimal, your appropriate denominator is a multiple of 9 .1)If the numerals after the

decimal begin to repeat in the tenths place, our denominator is 9, if they begin to repeat in the hundredths place, our denominator is 99.

Let’s try one….

Converting Decimals to Fractions

Convert 0.8 to a fraction.

Step 1: determine where the decimal ends

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0 8Our decimal repeats after the tenths place. 88

Converting Decimals to Fractions

Convert 0.8 to a fraction.

Step 2: place the numerals that repeat

over the appropriate denominator.

Only 8

We discovered that our decimal ends in the tenths place. So our appropriate denominator is 9.

8

9

Converting Decimals to Fractions

Convert 0.8 to a fraction.

Step 3: Simplify

Can we simplify this fraction?

No! is already in simplest form!

89 8

9

Converting Decimals to Fractions

Let’s try with 0.64 .

Step 1: determine where the decimal repeats

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Converting Decimals to Fractions

Let’s try with 0.64 .

Step 2: place the numerals that repeat

over the appropriate denominator.

We discovered that our decimal ends in the _________ place. So our appropriate denominator is _____.

Converting Decimals to Fractions

Let’s try with 0.64 .

Step 3: Simplify

Can we simplify this fraction?

64100

The Number System

Natural Numbers

• Natural numbers are all positive whole numbers that are not zero. These are also called counting numbers.

14

9

1,187859

68

Whole Numbers

• Whole numbers are all the natural numbers, plus zero.

14

9

1,187859

68

0

Integers

• Integers are all whole and natural numbers, plus the negatives.

14

9

1,187859

68 -14

-9

-859

-68

-1,187

0

Rational Numbers

• A rational number is any number that can be written as a simple fraction. This includes all the integers as well as fractions, terminating decimals, and repeating decimals, 1.1 ½

0.333333…- 8

Irrational Numbers

• A number that cannot be written as a simple fraction, or a number containing a decimal that goes on forever but does not repeat is called irrational.

0.02858294462…

= 3.141592654

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The Number System

Natural

Whole

Rational

Integers

Irrational

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