Section 2: Scientific Notation

Chapter 2: Measurement and Problem Solving

Learning ObjectivesExpress very large and very small numbers using scientific notation.

Scientific Notation Scientific notation allows us to express very

large or small numbers without having to write down all of the digits 15,000,000,000 = 1.5 x 1010

0.00000264 = 2.64 x 10-6

When expressing numbers in scientific notation, always keep the same number of sigfigs as in the original measurement.

Scientific Notation To express a number written in

standard notation in scientific notation: Move the decimal until one nonzero digit

appears to the left of the decimal. The exponent represents the number of

decimal places you moved▪ A positive exponent represents a value larger than one▪ A negative exponent represents a value less than one

Scientific Notation Include all significant figures▪1.5 x 105 = 150,000

▪2.93 x 10-7 = 0.000000293

If the decimal point is moved to the left, the exponent is positive.

If the decimal point is moved to the right, the exponent is negative.

Scientific NotationA number written in scientific notation has two parts: A decimal part

An exponential part

Scientific NotationThe 2013 U.S. population was estimated to be 315,000,000 people. Express this number in scientific notation.

Scientific NotationThe total U.S national debt in 2013 was approximately $16,342,000,000,000. Express this number in scientific notation.

Scientific NotationThe radius of a carbon atom is approximately 0.000000000070 m. Express this number in scientific notation.

Scientific NotationExpress the number 0.000038 in scientific notation.