Ordering Real Numbers on the Number Line

This video tutorial explains real numbers, including rational and irrational numbers. It covers how to locate and order these numbers on a number line. The tutorial provides examples of rational numbers, such as fractions and integers, and irrational numbers, like non-repeating decimals. It demonstrates how to approximate and truncate decimals to place them accurately on a number line. The video also includes practical examples of ordering real numbers and concludes with a review of the strategies used.

Which of the following is a rational number?

• π (pi)

• √15

• √2

• 4/5

What is the decimal approximation of the square root of 21 to the nearest tenth?

• 4.5

• 4.6

• 4.7

• 4.8

Where would you place 2.87 on the number line?

• Between 2.8 and 2.9

• Between 2.7 and 2.8

• Between 2.9 and 3.0

• Between 2.6 and 2.7

What does it mean to truncate a decimal?

• Round it to the nearest whole number

• Multiply it by 10

• Convert it to a fraction

• Drop all decimal places after a certain place value without rounding

What is the truncated value of the cube root of 31 to two decimal places?

• 3.13

• 3.15

• 3.14

• 3.16

Which number is larger: the square root of 10 truncated to two decimal places or the cube root of 31 truncated to two decimal places?

• They are equal

• Cannot be determined

• Cube root of 31

• Square root of 10

What is the decimal approximation of 4 and 1/3?

• 4.33

• 4.34

• 4.35

• 4.36

Where would you place 1.8 repeating on the number line?

• Between 1.9 and 2.0

• Between 1.8 and 1.9

• Between 1.6 and 1.7

• Between 1.7 and 1.8

What is the correct order of the following numbers: 1.8 repeating, 2.5, 4 and 1/3, and the square root of 19?

• Square root of 19, 4 and 1/3, 2.5, 1.8 repeating

• 4 and 1/3, 1.8 repeating, 2.5, square root of 19

• 2.5, 1.8 repeating, square root of 19, 4 and 1/3

• 1.8 repeating, 2.5, 4 and 1/3, square root of 19

What is the first step in the strategy to order real numbers?

• Place the numbers on a number line

• Enlarge the number line as necessary

• Round or truncate the numbers

• Turn every number into a decimal