How to Multiply a Whole Number by a Scientific Notation

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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.

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