Answer
Decimal Notation: 0.0042; Scientific Notation: $4.2$$\times$$10^{-3}$
Decimal Notation: 315,171,000; Scientific Notation: $3.15171$$\times$$10^{8}$
Decimal Notation: 0.000000000018; Scientific Notation: $1.8$$\times$$10^{-11}$
Decimal Notation: 1,232,000; Scientific Notation: $1.232$$\times$$10^{6}$
Work Step by Step
To convert from decimal notation to scientific notation, place a decimal after the first nonzero value. For 315,171,000, place a decimal after the 3 and then move it over to the right as many times as needed until the correct amount of zeros are added as place fillers. The number of decimal movements is the exponent attached to the base power of 10. For 1,232,000, place a decimal after the 1 so that 1.232 will have to be multipled by 10 to a positive power to bring it back to its decimal notation form. Move the decimal place over to the right, adding zeros as place fillers until the original value is reached. The number of decimal movements is the exponent needed for scientific notation. When converting from scientific notation to decimal notation, move the decimal place over to the left or right as indicated by the power attached to the base of 10. The decimal for 4.2 will be moved over 3 places to the left, adding zeros as necessary. The same can be done for 1.8, in which the decimal is moved over 11 times to the left.
