Number types

Number Types(and fractions and decimals)

The lesson you just studied is fairly comprehensive.

Rather than repeat the lesson, the purpose of this presentation is to review major

points with the hope of adding clarity in certain areas.

Points to review include:

• types of numbers.

• converting decimals to fractions, and

• converting fractions to decimals,

You may find that other areas were difficult to grasp. If that is the case, don’t

hesitate to talk to Mrs. Kent or to contact me in the evenings.

Types of Numbers

› Natural Numbers: numbers “naturally” used for counting: 1, 2, 3, . . .

› Whole Numbers: the Natural Numbers and zero: 0, 1, 2, 3, . . .

› Integers: the Natural Numbers, their opposites, and zero: . . ., -3, -2, -1, 0, 1, 2, 3, . . .

Types of Numbers

› Irrational Numbers: any number that isn’t rational. An irrational

number can only be approximated as a decimal value because

it never repeats and it never terminates (e.g. the square root of

a prime number).

› Real Numbers: all numbers on the number line.

Types of Numbers

Natural Numbers

(counting numbers)

1, 2, 3, . . .

Whole Numbers

0, 1, 2, 3, . . .

Integers

. . ., -3, -2, -1, 0, 1, 2, 3, . . .

Numbers

A Useful Comparison

San Antonio

The United States

North America

The World

Types of Numbers

Is a person in San Antonio also in Texas?

Yes, always.

Is a person in Texas also in San Antonio?

Maybe, but not necessarily.

Is a Natural Number also a Whole Number?

Yes, always.

Is a Whole Number also a Natural Number?

Types of Numbers

Is a person in North America also in the USA?

If a person in the USA in San Antonio?

Yes, always.

Is a Rational Number also an Integer?

Is an Integer also a Rational Number?

Yes, always.

Types of Numbers

So, as indicated, anyone in one circle is

automatically in all those around/above it.

If a person is in Texas (but not San Antonio),

that person is also in the USA, North America,

and, of course, the world.

So, as indicated, any number that’s one type is

automatically in all those around/above it.

If a number is a Whole Number, that number is

also an Integer, a Rational Number, and, of

course, a Real Number.

Determining Which Number Type

See if you agree:

Natural Number

Whole Number

Integer

Rational Number

Irrational Number

Real Number

Converting Decimals to Fractions

› Steps for non-terminating, non-repeating decimals

› Determine how many places are sufficient and round

› Handle as you would a terminating decimal

Converting Fractions to Decimals0.

*Your teacher will tell you how many places “close enough” is. Often it will be just 2 or 3, but

sometimes, your teacher will want you to continue to see if there’s a pattern.

Do you see the pattern here?

428571

Number types

Technology

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