Of course, this alternative method can be cumbersome if the numbers you are working with are very large or very small, and may not be possible if the calculator you are using won't display the results in regular notation. The other way to multiply scientific notations is to convert the notations to real numbers, perform the multiplication, and then convert the number back to scientific notation, like the following: Alternative Multiplication Method (3 x 10 6) x (6 x 10 4) = (3 x 1000000) x (6 x 10000) = 3000000 x 60000 = 180000000000 = 1.8 x 10 11 Multiplication Steps (3 x 10 6) x (6 x 10 4) Group like terms: = (3 x 6) x (10 6 x 10 4) Multiply coefficients and add exponents: = (18) x (10 10) Convert to proper SN: = 1.8 x 10 11 Here are the steps to solving the above problem. To divide powers of 10, subtract the exponents that is, subtract the exponent of the second number (the divisor) from the exponent of the first number (the dividend).ĭivide the following and leave the answers in powers of ten.ġ,000 ÷ 100 = 10 3 ÷ 10 2 = 10 (3 – 2) = 10 1or 10ġ00 ÷ 10,000 = 10 2 ÷ 10 4 = 10 (2 – 4) = 10 –2ġ ÷ 0.01 = 10 0 ÷ 10 –2 = 10 = 10 (0 + 2)= 10 2Ġ.001 ÷ 0.01 = 10 –3 ÷ 10 –2 = 10 = 10 (–3 + 2)= 10 –1ġ0,000 ÷ 0.To multiply two SN's you basically just multiply the coefficients and add the exponents, and then convert that result to proper scientific notation format (if not already).Įxample multiplication problem: (3 x 10 6) x (6 x 10 4) To multiply powers of ten, add the exponents. Since our number system is based on powers of ten, you should understand the notation and how to work with these powers, as follows: Quiz: Variables and Algebraic Expressions.Variables Algebraic Expressions and Simple Equations.Quiz: Arithmetic Progressions and Geometric Progressions.Quiz: Calculating Measurements of Basic Figures.Calculating Measurements of Basic Figures.Customary System, Metric System, and Converting Units of Measure Rationals (Signed Numbers Including Fractions).Quiz: Rationals (Signed Numbers Including Fractions).Quiz: Changing Percents, Decimals, and Fractions, and Important Equivalents.Changing Percents, Decimals, and Fractions.Quiz: Changing Fractions to Decimals, Changing Terminating Decimals to Fractions, and Changing Infinite Repeating Decimals to Fractions.Changing Infinite Repeating Decimals to Fractions.Changing Terminating Decimals to Fractions.Quiz: Simplifying Fractions and Complex Fractions.Simplifying Fractions and Complex Fractions.Quiz: Multiplying and Dividing Fractions and Mixed Numbers.Multiplying Fractions and Mixed Numbers.Quiz: Adding and Subtracting Fractions and Mixed Numbers.Quiz: Proper and Improper Fractions, Mixed Numbers, and Renaming Fractions.Quiz: Factors, Primes, Composites, and Factor Trees.Factors, Primes, Composites, and Factor Trees.Quiz: Estimating Sums, Differences, Products, and Quotients.Estimating Sums, Differences, Products, and Quotients.Quiz: Grouping Symbols and Order of Operations.Ways to Show Multiplication and Division.Grouping Symbols and Order of Operations.Quiz: Properties of Basic Mathematical Operations.Properties of Basic Mathematical Operations.Quiz: Ways to Show Multiplication and Division, Multiplying and Dividing by Zero, and Common Math Symbols.
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