Converting, Comparing and Ordering Rational Numbers

Foundations of Algebra

Rational Numbers: Fractions and Decimals

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What is a rational number?• Definition: Any number that can be made by

dividing one integer by another. The word comes from "ratio”.

• Examples: 1/2 is a rational number (1 divided by 2) 0.75 is a rational number (3/4) 2 is a rational number (2/1) 2.12 is a rational number (212/100) -6.6 is a rational number (-66/10)

What is NOT a rational number?• If a number is not rational, then it is

irrational. • An irrational number CANNOT be written

as a fraction - the decimal goes on forever without repeating.

• Examples: π = 3.141592654…..

Comparing Fractions and Decimals

You cannot compare fractions and decimals. In order to compare fractions and decimals, you have to use all of the skills you have learned to convert them all to decimals.

Converting Fractions to Decimals

6 10

8 100

Think about how you say the fraction.

How many TENTHS are there? The 6 goes in the TENTHS place.

.6=

= .08How many HUNDREDTHS are there? The 8 goes in the HUNDREDTHS place.

Converting Decimals to Fractions

• Converting decimals to fractions is the opposite of converting fractions to decimals.

• Once again, read the fraction.

• What do you hear? Tenths or hundredths?

Converting Decimals to Fractions

6 10

8 100

Think about how you say the decimal.

Read the decimal. The 6 is in the TENTHS place, so the denominator is 10.

.6 =

=.08What place is the 8 in? The HUNDREDTHS place. The denominator is 100.

Converting Decimals to fractions

60 100

or=

16 100

40 100

=

= or

.60

.16

.40

6 10

4 10

Comparing Decimals

• When comparing decimals, you have to look at the whole numbers.

• If the whole numbers are the same, then look at the decimal in the tenths place.

• Keep looking at the digits until you can identify which is the greatest or least.

Comparing Fractions and Decimals

Not all fractions are over 10 or 100, some may have different denominators. In order to change them to decimals, we will have to use our calculators.

Example #1 ~ Compare these fractions.

Next, compare the decimals.

4 5÷ 3 7÷= =

Comparing DecimalsStep 1. Line up the decimal points. Use zeros to make an equal number of decimal places.

0.800 0.428

Step 2. Start by comparing the greatest place. Find the first place where the digits are different.

0.800 0.428

Comparing DecimalsStep 3. Compare the values of the digits.

0.8 is greater than 0.4So,

0.8 > 0.428