Real Numbers Reteach

The Real Number System & Scientific Notation

Essential Question

How can we compare, order, sort, and convert real numbers?

Learning Intention

We will categorize real number into set and subsets, order on and off a number line and convert between scientific notation and standard form.

Language Objective

Success Criteria

I can identify rational vs. irrational numbers

I can take a square root of a given number

I can place rational numbers on a number line

I can convert standard from into scientific notation

I can convert scientific notation into standard form

Let's review categorizing real numbers.

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Lets Recap

Natural Numbers- Numbers you can count on your hands and feet.

Whole Numbers- Starts with 0, positive values

Integers- Positive and negative whole numbers including 0.

Rational- Any number that can be written as a fraction and all terminating decimals.

Irrational- Non perfect square roots, non-terminating decimals, and numbers that cannot be written as a fraction.

Real Numbers

Multiple Choice

The number is a/an...

• Rational Number

• Irrational Number

• Integer

• Whole Number

Multiple Select

The number is a/an...

• Rational Number

• Irrational Number

• Integer

• Whole Number

Multiple Select

The number is a/an...

• Rational Number

• Irrational Number

• Integer

• Whole Number

Multiple Select

The number is a/an...

• Rational Number

• Irrational Number

• Integer

• Whole Number

Let's review perfect squares vs. Non-perfect squares.

Lets Recap

Perfect squares are the result of multiplying the side length times itself.

Non-Perfect Squares result in irrational values.​

If given an area take the square root to get the exact side length

Perfect Squares & Square Roots

Multiple Choice

Evaluate
√36

• 6

• -9

• 18

• -18

Multiple Choice

If I know the area of a square, how do I find the side length?

• I square the area.

• I divide the area by 2.

• I take the square root of the area.

• I divide the area by 4.

Multiple Choice

Which of the following in NOT a perfect square?

• 49

• 81

• 111

• 144

Multiple Choice

Between which two whole numbers is this located?
√55

• 2 and 3

• 7 and 8

• 8 and 9

• 4 and 5

Let's review comparing and ordering real numbers.

Lets Recap

Ascending - Going up, increasing, smallest to largest, coldest to hottest, etc.

Descending - Going Down, decresding, largest to smallest, hottest to coldest, etc.

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Comparing & Ordering

Multiple Choice

Which is ordered from least to greatest?

• $$4\frac{1}{3},\ \frac{26}{4},\ 4\frac{1}{2},\ \frac{12}{5}$$

• $$\frac{12}{5},\ 4\frac{1}{2},\ \frac{26}{4},\ 4\frac{1}{3}$$

• $$\frac{26}{4},\ 4\frac{1}{2},\ 4\frac{1}{3},\ \frac{12}{5}$$

• $$\frac{12}{5},\ 4\frac{1}{3},\ 4\frac{1}{2},\ \frac{26}{4}$$

Multiple Choice

Order the fractions from least to greatest.

  $$\frac{1}{3,}\ \frac{1}{4},\ \frac{5}{8},\ \frac{1}{2}$$  

• $$\frac{1}{4},\ \frac{1}{2},\ \frac{8}{8},\ \frac{1}{3}$$  

• $$\frac{1}{4},\ \frac{1}{3},\ \frac{1}{2},\ \frac{5}{8}$$   

• $$\frac{5}{8},\ \frac{1}{2},\ \frac{1}{3},\ \frac{1}{4}$$  

• $$\frac{1}{2},\ \frac{1}{3},\ \frac{1}{4},\frac{5}{8}$$  

Multiple Choice

Which set is in descending order?

• 15%  .45  9/10

• .45  15%  9/10

• 9/10  15%  .45

• 9/10  .45  15%

Multiple Choice

Which list shows the numbers  $$4\pi,\ \sqrt{115},\ \frac{13\pi}{5}$$  in order from least to greatest? 

• $$4\pi,\ \sqrt{115},\ \frac{13\pi}{5}$$  

• $$\frac{13\pi}{5},\ \sqrt{115},\ 4\pi$$  

• $$\sqrt{115},\ 4\pi,\ \frac{13\pi}{5}$$  

• $$\sqrt{115},\ \frac{13\pi}{5},\ 4\pi$$  

Let's review Scientific Notation

Lets Recap

1. Place a decimal between the first 2 non-zero digits

2. Multiply by 10

3. Exponent (number of times decimal moves)

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Scientific Notation

Fill in the Blanks

How would you write 4.3756 x 10⁴ in standard form?

Multiple Choice

Which of the following numbers is written in scientific notation?

• 20.35 x 10⁴

• .2035 x 10⁴

• 2035 ⁴

• 2.035 x10⁴

Multiple Choice

Convert to scientific notation:

520,000,000

• 52 x 10⁷

• 5.2 x 10^-7

• 5.2 x 10⁸

• 0.52 x 10⁹

Multiple Choice

If the exponent is a positive number the original number was...

• a really big number.

• a really small number.

Multiple Choice

If the exponent is a negative number the original number was...

• a really large number.

• a really small number.

Open Ended

How are you feeling about the first part of the unit now? Reflect in 10-20 words.