COMPARING AND ORDERING REAL NUMBERS



COMPARING AND ORDERING REAL NUMBERS

A) Number Line:

-1.75 -1.25 1.25 1.75

( Smaller Larger (

Numbers Numbers

( ( ( ( ( ( ( ( ( ( (

-3 -2 -1 0 1 2 3

The “trickiest” part of knowing where to place a negative number on the number line is realizing that the placement of negative numbers seem to be written in the

opposite order as the whole numbers.

B) Converting a Fraction to a Decimal:

Remember, a fraction like [pic] means 3 ( 4

1) So if you have a calculator: Press the buttons in this order 3 ( 4 =

The number that appears on your calculator screen is the equivalent decimal version of [pic], which is 0.75.

2) But if you don’t have a calculator: You are stuck converting by using your long division skills. Since we said that [pic] means 3 ( 4 we can set up a division problem [pic]

This will also result in an answer of 0.75 also.

C) Converting a Mixed Fraction to a Mixed Decimal:

If you need to covert a mixed fraction such as 5 [pic] to a mixed decimal,

the procedure is very similar to converting a simple fraction like [pic].

1) Just rewrite the whole number. It never has to be entered in the calculator or be included in your long division problem, because it does not change when you convert to a decimal.

5 [pic] = 5. ?

2) Use your calculator or long division skills to convert only the fractional part of your number to a decimal.

[pic] = .375

2) Your final answer is the whole number combined with the decimal version of

your fraction. SO, the fraction 5 [pic] = 5.375 as a decimal.

D) Comparison Symbols:

( means “less than”

← means “greater than”

← means “equal to”

E) Comparing and Ordering Fractions and Decimals:

This is what you need to know to complete your homework properly.

1) When you are asked to compare fractions and decimals using the symbols , = OR if you are asked to order them from least to greatest, the easiest thing to do is change everything to its decimal form and compare/order the numbers this way.

Why should you change to all decimals? I am glad you asked.

Because, it is easier to compare/order numbers when they are all in a similar form.

ALL DECIMALS or ALL FRACTIONS THAT HAVE COMMON DENOMINATORS.

I am requesting you change all the numbers to decimals, instead of fractions.

2) This is how you should compare/order fractions and decimals.

a) Example 1: Compare 7.008 and 7 [pic] using , or = .

Solution with required work:

7.008 = 7.008 (no need to change this number)

7 [pic] = 7.250 (but this one needs to be changed to a decimal)

Since 7.008 is smaller than 7 [pic] in its new decimal form, the final answer is …

7.008 ( 7 [pic]

b) Example 2: Order 3. 17, -3[pic], and 3[pic] from least to greatest.

Solution with required work:

3.17 = 3.17 (no need to change this number)

-3[pic] = -3.35 (but the other 2 numbers need to become decimals)

3[pic] = 3.20

Final Order: -3.35, 3.17, 3.20 (using the decimal versions)

OR -3[pic], 3.17, 3[pic] (using the original numbers)

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A12

A13

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