# Intermediate Algebra Problems With Answers - Sample 5 - Scientific Notation

 A set of intermediate algebra problems, related to scientific notation, with answers, are presented. The solutions are at the bottom of the page. Review: A number x is written in scientific notation when it is written in the form: x = a × 10 N with 1 ≤ |a| < 10 and N is an integer. Convert from decimal notation to scientific notation. a) 234 b) 0.000052 c) -220,000 d) -0.00000000000000182 Convert from scientific to decimal notation. a) 1.01 × 10 2 b) 8.2 × 10 -6 c) 3.456 × 10 10 d) -1.2 × 10 -8 Perform the multiplication and write the result in scientific notation. a) (5 × 10 2)(7 × 10 5) b) (1.2 × 10 -6)(3.5 × 10 14) c) (-4.5 × 10 -7)(8.62 × 10 10) d) (-7.2 × 10 -6)(0.00039) Perform the division and write the result in scientific notation. a) (4 × 10 13) / (5 × 10 -4) b) 0.000012 / (2.4 × 10 -8) c) (-1.2 × 10 -6) / (1.5 × 10 -10) d) 0.00000065 / 0.000013 Evaluate and express in scientific notation. a) (1.3 × 10 -6) 2 b) (1.5 × 10 -8) 2(2.1 × 10 5) c) [ (1.144 × 10 2)(6 × 10 7) ] / (2.2 × 10 4) d) [ (0.00001)(2,500) ] / [ (0.0003)(150,000) ] Evaluate in scientific notation. a) The diameter of an atom: 0.0000000000001 meter b) diameter of earth = 12,756,000 meters c) 1 billion: 1000,0000,000 d) 1 micron: 0.000001 meter e) 1 trillion: 1000,000,000,000 f) Diameter of earth / diameter of atom g) Speed of light: 300,000,000 m/sec h) Distance travelled by light in one year.