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The Real Number Line

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**The Real Number Line On the real number line:**

Every number corresponds to exactly one point Every point corresponds to exactly one number Where is the point 2.5 What number does the following point represent? Where is the origin? -3

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**Comparing Numbers x < y x is less than y x = y x is equal to y**

x is greater than y

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**1 ______ -3 ? = > < Ordering Numbers**

Use a number line to make the following statement true: 1 ______ -3 ? = > <

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**-2 ______ -1.5 ? = > < Ordering Numbers**

Use a number line to make the following statement true: -2 ______ -1.5 ? = > <

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**3 ______ (-9 ÷ -3) ? = > < Ordering Numbers**

Use a number line to make the following statement true: 3 ______ (-9 ÷ -3) ? = > <

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Ordering Numbers Write the following decimals in order from least to greatest. 1.04, -14, -1.4, 0.104 1.04 -14. -1.4 0.104 Write the numbers with the decimal points lined up. Fill in zeros so that each has the same number of decimal places. Order the numbers as if they were integers. 0.104 1.040

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Ordering Numbers Write the following numbers in order from least to greatest. -1.1, , , -1.101 -1.1 -1.01

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**Ordering Decimals & Fractions**

Write the numbers in order from least to greatest: , , , Use a calculator to convert each fraction to a decimal. Top divided by bottom = =0.4583 =0.4 0.4, , , 0.4512

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The Real Number Line

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Absolute Value The distance between zero and a number on the real number line. What is the absolute value of: 4 -4 4 3 3 4 -1.5 1.5

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**Absolute Values = 7 = 7 - - = -7 = -7**

The absolute value of a positive number is itself The absolute value of a negative number is its opposite The negative of the absolute value of a number is negative = 7 = 7 - - = -7 = -7

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**Area = 6 ft Square Roots What is the area of a rug with sides of 6 ft?**

2 Area = 6 ft

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**= 8 x 8 = 64 = 7 x 7 = 49 = -5 x -5 = 25 Square Roots**

When a number is multiplied by itself, the product is the square of the number. 6 x 6 = 36 which is six squared What is: = 8 x 8 = 64 = 7 x 7 = 49 = -5 x -5 = 25

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**Square Roots If = b, then a is called a square root of b**

For example, what is the square root of: = 4 = 9 = 2

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**Estimating Square Roots**

Not all numbers have a perfect square root. Find Find two perfect squares that 14 lies between. = = 4 Refine your estimate Is 14 closer to 9 or 16? → 3.7 or 3.8

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