Test on Numbers Thursday 7 th October Surds Index laws Cubes and Squares Scientific Notation

Quick Revisit- Surds 12 10

Quick check Index Laws

Order each set of numbers from least to greatest ( ascending order)

Order each set of numbers from least to greatest ( ascending order)- solutions

POWERS of 10

Write 6 million as power of 10 Write as power of 10 Write as power of 10

An ordinary penny contains about 20,000,000,000,000,000,000,000 atoms. The average size of an atom is about centimeters across. The length of these numbers in standard notation makes them awkward to work with. Scientific notation is a shorthand way of writing such numbers.

The sign of the exponent tells which direction to move the decimal. A positive exponent means move the decimal to the right, and a negative exponent means move the decimal to the left. Helpful Hint In scientific notation the number of atoms in a penny is 2.0  10 22, and the size of each atom is 3.0  10 –8 centimeters across. An ordinary penny contains about 20,000,000,000,000,000,000,000 atoms. The average size of an atom is about centimeters across.

Translating Standard Notation to Scientific Notation Think: The decimal needs to move left to change 7.09 to , so the exponent will be negative Move the decimal to get a number between 1 and  10 Set up scientific notation. Think: The decimal needs to move 3 places. Check 7.09  10 –3 = 7.09  = Write in scientific notation. So written in scientific notation is 7.09  10 –3.

Try This: Example 2 Think: The decimal needs to move left to change 8.11 to , so the exponent will be negative Move the decimal to get a number between 1 and  10 Set up scientific notation. Think: The decimal needs to move 4 places. Check 8.11  10 = 8.11  = –4 Write in scientific notation. So written in scientific notation is 8.11  10 –4.

A pencil is 18.7 cm long. If you were to lay 10,000 pencils end to end, how many millimeters long would they be? Write the answer in scientific notation. 187 mm  10,000 1 centimeter = 10 millimeters, so 18.7 centimeters = 187 millimeters Find the total length. 1,870,000 mm Additional Example 3: Application

Think: The decimal needs to move 6 places. The 10,000 pencils would be 1.87  10 6 mm long, laid end to end. This is about one mile long. Additional Example 3 Continued 1.87  10 Set up scientific notation. Think: The decimal needs to move right to change 1.87 to 1,870,000, so the exponent will be positive. 1,870,000 mm

An oil rig can hoist 2,400,000 pounds with its main derrick. It distributes the weight evenly between 8 wire cables. What is the weight that each wire cable can hold? Write the answer in scientific notation. 2,400,000 pounds ÷ 8 cables = 300,000 pounds per cable Each cable can hold 300,000 pounds. Try This: Example 3 Find the weight each cable is expected to hold by dividing the total weight by the number of cables. Now write 300,000 pounds in scientific notation.

Think: The decimal needs to move right to change 3.0 to 300,000, so the exponent will be positive. Think: The decimal needs to move 5 places. Each cable can hold 3.0  10 pounds  10 Set up scientific notation. Try This: Example 3 Continued

Multiplying and Dividing numbers in Scientific Notation form What is the product of: And (use index laws) and express answer in SN

X Same base, different exponent or index If same base number, add the index Write them out so that same base numbers are next to each other Multiply the whole numbers

Dividing numbers in SN form 1. Rewrite it as one over the other 2. Use index laws: if dividing same base numbers, subtract the indices 3. Complete operation with index numbers 4. Divide whole numbers

Lesson Quiz Write in standard notation   10 – ,000,000 17,  10 –3 5.7  10 7 Write in scientific notation. 5. A human body contains about 5.6 x 10 6 microliters of blood. Write this number in standard notation. 5,600,000

6. Evaluate and express in SN 7. Evaluate and express in SN

135,  100,000 Think: Move the decimal right 5 places. A   = 100,000 5 Additional Example 1A: Translating Scientific Notation to Standard Notation Write the number in standard notation.

2,870,000,  1,000,000,000 Think: Move the decimal right 9 places. A   = 1,000,000,000 9 Write the number in standard notation. Try This: Example 1A

Divide by the reciprocal. 2.7  100 Think: Move the decimal left 3 places. 2.7  10 –3 B. 2.7  10 –3 10 = –  Write the number in standard notation. Additional Example 1B: Translating Scientific Notation to Standard Notation Continued

C. –2.01  10 4 –20,100 Think: Move the decimal right 4 places. –2.01  = 10,000 4 –2.01  10,000 Additional Example 1C: Translating Scientific Notation to Standard Notation Continued Write the number in standard notation.

1.9  10, Divide by the reciprocal. Think: Move the decimal left 5 places. 1.9  10 –5 B. 1.9  10 –5 – = 10,000 Write the number in standard notation. 1.9  1 10,000 Try This

10 = 100,000,000 8 –5.09  10 8 –5.09  100,000,000 C. –5.09  10 8 Write the number in standard notation. Try This –509,000,000 Think: Move the decimal right 8 places.

Write in scientific notation x x x x 10 5

Write (2.8 x 10 3 )(5.1 x ) in scientific notation x x x x 10 11

Write x 10 5 in scientific notation x x x x x x x 10 8