
Warm Up Standard to Scientific Scientific to Standard
Warm Up How would you simplify the following expressions? 1. 2 x 101 2. 3.5 x 104 3. 3.5 x 1015 2 x 10 = 20 3.5 x 10 x 10 x 10 x 10 = 35,000 3.5 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 = 3,500,000,000,000,000
Vocabulary scientific notation a shorthand method of writing very large or very small numbers by using the powers of 10
An ordinary penny contains about 20,000,000,000,000,000,000,000 atoms. The average size of an atom is about 0.00000003 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.
In scientific notation the number of atoms in a penny is 2.0 1022, and the size of each atom is 3.0 10–8 centimeters across. Put this in your notes! It’s like on a number line: Negative Positive
Translating Scientific Notation to Standard Notation Write the number in standard notation. 2.64 x 107 2.64 x 10,000,000 26,400,000 B. 1.35 x 104 1.35 x 1/10,000 1.35 / 10,000 = 0.000135 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.
5,800,000 5.8 1,000,000 Think: Move the decimal right 6 places. A. 5.8 106 Additional Example 1A: Translating Scientific Notation to Standard Notation Write the number in standard notation.
0.0027 Divide by the reciprocal. 2.7 1000 Think: Move the decimal left 3 places. B. 2.7 10 –3 Write the number in standard notation. Additional Example 1B: Translating Scientific Notation to Standard Notation Continued
C. –2.01 104 –20,100 Think: Move the decimal right 4 places. Additional Example 1C: Translating Scientific Notation to Standard Notation Continued Write the number in standard notation.
2,870,000,000 2.87 1,000,000,000 Think: Move the decimal right 9 places. A. 2.87 109 Write the number in standard notation. Try This: Example 1A
1.9 100,000 0.000019 Divide by the reciprocal. Think: Move the decimal left 5 places. B. 1.9 10–5 Write the number in standard notation. Try This: Example 1B
Translating Standard Notation to Scientific Notation Think: The decimal needs to move left to change 7.09 to 0.00709, so the exponent will be negative. 0.000002 Move the decimal to get a number between 1 and 10. 2 Set up scientific notation. Think: The decimal needs to move 3 places. Write 0.000002 in scientific notation. Number less than 1 = negative exponent Number greater than 1 = positive exponent
Additional Example 2: Translating Standard Notation to Scientific Notation Think: The decimal needs to move left to change 7.09 to 0.00709, so the exponent will be negative. 0.00709 Move the decimal to get a number between 1 and 10. 7.09 Set up scientific notation. Think: The decimal needs to move 3 places. Write 0.00709 in scientific notation.
Try This: Example 2 Think: The decimal needs to move left to change 8.11 to 0.000811, so the exponent will be negative. 0.000811 Move the decimal to get a number between 1 and 10. 8.11 Set up scientific notation. Think: The decimal needs to move 4 places. Write 0.000811 in scientific notation.
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. Additional Example 3 Continued 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.
Lesson Quiz Write in standard notation. 1. 1.72 104 2. 6.9 10–3 4. 57,000,000 17,200 0.0069 3. 0.0053 Write in scientific notation. 5. A human body contains about 5.6 x 106 microliters of blood. Write this number in standard notation. 5,600,000 Number less than 1 = negative exponent Number greater than 1 = positive exponent
If I want to try this on a calculator… If my answer looks like this… 8.22 x 102 Then it means… E2 = 102 E3 = 103 E6 = 106
by jlindemuth  Modified: 6 years ago
Language: English (Detected)  Topic: Education
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