Scientific Notation

Scientific Notation Week 2 (September 13 – 17, 2010)

Scientific notationis a shorthand way of writing really big or really small numbers – instead of standard notation. An ordinary quarter contains about 97,700,000,000,000,000,000,000 atoms. The average size of an atom is about 0.00000003 centimeters across. These very long numbers are written in **STANDARD NOTATION** **The length of these numbers in standard notation makes them awkward to work with.

Writing a number in standard notationfrom scientific notation: • The exponent on the 10 tells you how many spaces you will move the decimal • If the exponent is POSITIVE move RIGHT • If the exponent is NEGATIVEmove LEFT EXAMPLES: 3.75 x 109 = 3,750,000,000 (really big #) 8.62 x 10-6 = .00000862 (really small #) (5.23 X 107)

-2.01  104 Remember: Move the decimal right4 places. **Because 4 is POSITIVE** Change the number from Scientific Notation to Standard Form -2.01  104 HINT: ***It doesn’t matter that the number (-2.01) is negative – only the exponent changes things -201 00 Two extra zero’s were added to complete the number -20,100 Place your comma and you are DONE!

Helpful Hint A positive exponent means move the decimal to the right, and a negative exponent means move the decimal to the left. 0.0027 Change the number from Scientific Notation to Standard Form 2.7  10–3 **Remember** the exponent is negative so we move the decimal to the left 3 spaces 2.7  10–3

To express any number in scientific notation from standard form: • Always use a number greater than 1 and less than 10 rounded to the 100ths place (2 spaces after decimal) – place your decimal • These are called significant digits • Always multiply by 10 to a power • Count the # of spaces you moved from new decimal point to old decimal • -Did you move right? – Your Exponent is Positive • -Did you move left?- Your exponent is Negative.

EXAMPLE: 92,300,000,000 • 9.23 (place our decimal to make the number between 1 & 10.) • 2. 9.23 X 10 (multiply by 10) • We moved 10 places to get to the end so the exponent is 10. • 4. The original number is much larger than 1… so 10 is positive: (know the sign) • 9.23 X 1010 (You moved RIGHT)

In scientific notation the number of atoms in a quarter is(97,700,000,000,000,000,000,000) or • 9.77  1022 • The size of each atom is (0.00000003)or • 3.0  10–8 centimeters across.

So 0.00709 written in scientific notation is 7.09  10–3. Write 0.00709 in scientific notation. Place the decimal to so you get a number between 1 and 10 rounded to the nearest 100th. . 0.00709 (*you want only one number in front of the decimal) Count the spaces to get back to original decimal point to tell you your power of 10. - Which way do you move? 7.09  10-3 There are 3 spaces so it is 10-3. Remember The decimal needs to move left to change 7.09 to 0.00709, so the exponent will benegative. *Note, it is a really small number

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. • Hint: • Convert from cm to mm • Find the length of 10,000 pencils K H D M D C M 1 cm = 10 mm 18.7 cm = 187 mm Multiply each side by 10 Find the total length. 187 mm  10,000 1,870,000 mm

In scientific notation the 10,000 pencils would be 1.87  106 mm long, laid end-to-end. 1,870,000 Set up scientific notation. Remember: The decimal needs to move right to change 1.87 to 1,870,000, so the exponent will be positive. The decimal needs to move 6 places.

5.3  10–3 5.7  107 Quiz: Write each number in standard notation. 1. 1.72  104 17,200 2. 6.9  10–3 0.0069 Write each number in scientific notation. 3. 0.0053 4. 57,000,000 5. Order the numbers from least to greatest: 2  10–4 , 9  10–5 , 7  10–5 7  10–5, 9  10–5, 2  10–4

Scientific Notation