Sets of Numbers

Number Sets and Hierarchy

Hierarchy (ranking greatest to least)

All integers, whole numbers, and natural numbers are also Rational. Their circles fit inside the Rational set's circle.

​All ________ are also ___________.

Some _______ are also __________.

Not all _______ are ________.


The number _____ is rational and whole.

_____ is a fraction, but it is not a rational number.

Find 2 perfect square numbers the number under the radical is between.

ex. √12 is between _____ and _____

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How to estimate square roots.

​Because 48 is between 36 and 49, its square root will be between √​36 and √49.

It should be between 6 and 7, but closer to 7. Check it in a calculator!

Between what 2 consecutive integers is √48?

Between what 2 consecutive integers is √11 ?

Converting between fractions and repeating decimals.

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Rational Numbers in different forms

Fractions mean division

Top ÷ Bottom
(numerator ÷denominator)

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Fraction to decimal

1. Look at the repeating part. Count the number of digits.

2. Put that many 9s in the denominator.

3. Write the repeating part in the numerator.

4. Simplify.

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Rewrite a repeating decimal as a fraction

1. Look at the repeating part. Count the number of digits.

2. Put that many 9s in the denominator.

3. Write the repeating part in the numerator.

4. Simplify.

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Rewrite 0.121212... as a fraction in simplest form.

Getting between numbers

The space between 1 and 2 is infinite.