Scientific Notation Objectives: SWBAT convert between standard notation and scientific notation by hand and by calculators.

Scientific Notation - Usefulness Scientific notation is used to express very large or very small numbers. A number in scientific notation is written as the product of a number (integer or decimal) and a power of 10.

Examples Ex.- there are approximately 7,000,000,000 humans on earth. This number could be written in scientific notation as 7x10 9.

More Ex. A drop of water contains about 1,700,000,000,000,000,000,000 molecules → 1.7 x The size of a E. coli bacteria meter long → 2 x m.

Converting numbers to Scientific Notation Proper exponent can be found by counting how many times the decimal point must be moved to bring it to its final position; so that the number (coefficient) is between 1 and 10 e.g. the number is 1 or above but less than 10.

Negative Exponent When the decimal point is moved to the right, the exponent is written as a negative number → 2.25 x 10 -3

Positive Exponent When the decimal point is moved to the left, the exponent is written as a positive number. 707 → 7.07 x 10 2

Problems Convert standard into scientific notation. 1) 32,700 2) 1, ) )

Converting Scientific Notation into standard notation If the exponent is a positive number, move the decimal point the same number of places to the right as the number of the exponent. Example: 7.19 x 10 6 → 7,190,000

Converts the Scientific Notation into Standard Notation – cont. If the exponent is a negative number, move the decimal point the same number of places to the left as the number of the exponent Example: 8.16 x →

Converts the Scientific Notation into Standard Notation 1) 2.5 x g 2) x 10 0 mL 3) x m 4) 8.7 x kg 5) x 10 4 cm