How to Multiply and Divide in Scientific Notation

How to Multiply and Divide in Scientific Notation

This article teaches you how to Multiply and Divide Scientific Notations into a few simple steps.

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Step by step guide to Multiply and Divide Scientific Notations

Multiplying numbers that are in the form of a scientific notation is relatively simple because multiplying by coefficients of ten is simple.

To multiply two numbers in scientific notation:

  • Step 1: Multiply their coefficients which may be a decimal number or an integer.
  • Step 2: Multiply the two exponential numbers (with a base of 10) by adding their powers together.

To divide two numbers in scientific notation:

  • Step 1: divide their coefficients which may be a decimal number or an integer.
  •  Step 2: divide the two exponential numbers (with a base of 10) by subtracting their powers from each other.

The answer must be converted to scientific notation.

Multiplication and Division in Scientific Notation Example 1:

Write the answers in scientific notation. \((2.2\times 10^6) (4\times 10^{ \ -3})=\)

Solution:

First, multiply the coefficients: \(2.2\times 4=8.8\)

Add the powers of \(10\): \(10^6\times 10^{ \ -3}=10^3\)

Then: \((2.2\times 10^6) (4\times 10^{ \ -3})=8.8\times 10^3\)

Multiplication and Division in Scientific Notation Example 2:

Write the answers in scientific notation. \(\frac{7.5\times 10^9}{1.5\times 10^5}\)

Solution:

First, divide the coefficients: \(\frac{7.5}{1.5}=5\)

Subtract the power of the exponent in the denominator from the exponent in the numerator: \(\frac{10^9}{10^5}=10^{9-5}=10^4\)

Then: \(\frac{7.5\times 10^9}{1.5\times 10^5}=5\times 10^4\)

Multiplication and Division in Scientific Notation Example 3:

Write the answers in scientific notation. \((1.1\times 10^9) (9\times 10^{ \ -4})=\)

Solution:

First, multiply the coefficients: \(1.1\times 9=9.9\)

Add the powers of \(10\): \(10^9\times 10^{ \ -4}=10^5\)

Then: \((1.1\times 10^9) (9\times 10^{ \ -4})=9.9\times 10^5\)

Multiplication and Division in Scientific Notation Example 4:

Write the answers in scientific notation. \(\frac{4.5\times 10^{-7}}{5\times 10^2}\)

Solution:

First, divide the coefficients: \(\frac{4.5}{5}=0.9\)

Subtract the power of the exponent in the denominator from the exponent in the numerator: \(\frac{10^{-7}}{10^2}=10^{-7-2}=10^{-9}\)

Then: \(\frac{4.5\times 10^{-7}}{5\times 10^2}=0.9\times 10^{-9}\)

Now, convert the answer to scientific notation: \(0.9\times 10^{-9}=9\times 10^{-10}\)

Exercises for Multiplying and Dividing Scientific Notations

Write the answers in scientific notation. 

  1. \(\color{blue}{(4.2\times 10^6) (3\times 10^{ \ -9})=}\)
  2. \(\color{blue}{(5\times 10^8) (3.6\times 10^{ \ -6})=}\)
  3. \(\color{blue}{(4.9\times 10^7) (2\times 10^{ \ -5})=}\)
  4. \(\color{blue}{\frac{6.3\times 10^{-9}}{9\times 10^5}}\)
  5. \(\color{blue}{\frac{8.8\times 10^9}{4\times 10^2}}\)
  6. \(\color{blue}{\frac{9.6\times 10^{-5}}{3\times 10^4}}\)
  1. \(\color{blue}{1.26\times 10^{-2}}\)
  2. \(\color{blue}{1.8\times 10^3}\)
  3. \(\color{blue}{9.8\times 10^2}\)
  4. \(\color{blue}{7\times 10^{-15}}\)
  5. \(\color{blue}{2.2\times 10^7}\)
  6. \(\color{blue}{3.2\times 10^{-9}}\)

Related to "How to Multiply and Divide in Scientific Notation"

How to Add and Subtract  in Scientific Notations
How to Add and Subtract in Scientific Notations
How to Solve Function Notation
How to Solve Function Notation
How to Solve Scientific Notation
How to Solve Scientific Notation
How to Add and Subtract Decimals
How to Add and Subtract Decimals

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