The Real Number Line.

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Real Numbers and The Number Line

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Presentation transcript:

The Real Number Line

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

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

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

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

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

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 -14.000 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. -1.4000 0.104 1.040

Ordering Numbers Write the following numbers in order from least to greatest. -1.1, -1.01, -1.101, -0.1001 -1.101 -1.1 -1.01 -0.1001

Ordering Decimals & Fractions Write the numbers in order from least to greatest: , , , 0.4512 Use a calculator to convert each fraction to a decimal. Top divided by bottom =0.46667 =0.4583 =0.4 0.4, 0.4512, 0.458333, 0.466667 0.4512

The Real Number Line

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

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

Area = 6 ft Square Roots What is the area of a rug with sides of 6 ft? 2 Area = 6 ft

= 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

Square Roots If = b, then a is called a square root of b For example, what is the square root of: = 4 = 9 = 2

Estimating Square Roots Not all numbers have a perfect square root. Find Find two perfect squares that 14 lies between. = 3 = 4 Refine your estimate Is 14 closer to 9 or 16? → 3.7 or 3.8