How to Multiply a Whole Number by a Scientific Notation

Scientific Notation reduces the number of zeroes in large numbers.
••• Jupiterimages, Brand X Pictures/Brand X Pictures/Getty Images

In scientific notation, numbers are represented as a * 10^b, where "a" is a number between 1 and 10 and "b" is an integer. For example, 1,234 in scientific notation is 1.234 * 10^3. Scientific notation can also be used with negative exponents to express small numbers. For example, you can write 0.000123 in scientific notation as 1.23 * 10^-4.

So scientific notation is efficient for expressing very large or very small numbers. It is easier, for example, to see that 1.23 * 10^-4 is different from 1.23 * 10^-5 than it is to tell that 0.0000123 is different from 0.000123.

    Multiply the whole number by the coefficient of the number in scientific notation. For example, if you want to multiply 2.5 * 10^3 by 6, multiply 2.5 by 6 to get 15.

    Determine if this number is between 1 and 10. In the example, 15 is not between 1 and 10.

    Divide the number by a power of 10 to make it between 1 and 10. In the example, dividing 15 by 10^1 yields 1.5, which is between 1 and 10.

    Add the power of 10 to the exponent in the original number in scientific notation. In the example, 3 (the starting exponent) + 1 (the power of 10 from Step 3) = 4.

    Write the number from Step 3 multiplied by 10 raised to the exponent from Step 4. This is the result in scientific notation. Concluding the example, you would have 1.5 * 10^4.

Related Articles

How to Calculate the Midpoint Between Two Numbers
How to Calculate F-Values
Rules for Multiplying Scientific Notation
How to Write a Repeating Decimal As a Fraction
How to Find the Line of Symmetry in a Quadratic Equation
How to Determine Less Than & Greater Than in Fractions
How to Factorise a Quadratic Expression
The Difference Between Scientific & Engineering Notation
How to Write Expressions as Radicals
How to Factor Monomials
How to Measure a Flagpole
Adding & Subtracting Fractions
How to Convert Negative Celsius to Fahrenheit
How Do I Find Multiples of a Number?
How to Easily Convert Celsius to Fahrenheit
How to Calculate Incline
How to Find the Area of a Rectangular Prism
How to Calculate 1/6th of Something
How Can I Add Repeating Decimals?
How to Insert an Absolute Value in a Scientific Calculator

Dont Go!

We Have More Great Sciencing Articles!