How to Multiply a Whole Number by a Scientific Notation

By Peter Flom

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.

About the Author

Peter Flom is a statistician and a learning-disabled adult. He has been writing for many years and has been published in many academic journals in fields such as psychology, drug addiction, epidemiology and others. He holds a Ph.D. in psychometrics from Fordham University.