Multiplying In Scientific Notations

Review how to multiply values in scientific notation. During this lesson, you will review exponent rules for multiplication which will be applied to solve. This video shows 4 quick examples.

Multiplying Values In Scientific Notation

Let's say we want to multiply \(3.2 \times 10^4\) and \(2.5 \times 10^3\). Here's how we do it:

1. Write the values in standard scientific notation format:
   \[3.2 \times 10^4 \quad \text{and} \quad 2.5 \times 10^3\]

2. Multiply the coefficients (the numbers in front):
   \[3.2 \times 2.5 = 8.0\]

3. Add the exponents (the powers of 10):
   \[10^4 \times 10^3 = 10^{4+3} = 10^7\]

4. Write down the result in scientific notation:
   \[8.0 \times 10^7\]

So, \(3.2 \times 10^4\) multiplied by \(2.5 \times 10^3\) equals \(8.0 \times 10^7\).

Multiplying Values In Scientific Notation When The Coefficient Is 10 Or Greater.

Of course! Let's multiply two values in scientific notation where the coefficient is 10 or greater, which requires adjustment at the end. 

Let's multiply \(6.4 \times 10^5\) and \(8.5 \times 10^3\). Here's how we do it:

1. Write the values in standard scientific notation format:
   \[6.4 \times 10^5 \quad \text{and} \quad 8.5 \times 10^3\]

2. Multiply the coefficients (the numbers in front):
   \[6.4 \times 8.5 = 54.4\]

3. Add the exponents (the powers of 10):
   \[10^5 \times 10^3 = 10^{5+3} = 10^8\]

4. Write down the result in scientific notation:
   \[54.4 \times 10^8\]

5. Adjust the coefficient to ensure it's between 1 and 10:
   Since the coefficient is greater than 10, we need to adjust it. We can rewrite \(54.4 \times 10^8\) as \(5.44 \times 10^9\).

So, \(6.4 \times 10^5\) multiplied by \(8.5 \times 10^3\) equals \(5.44 \times 10^9\).

Dividing Numbers In Scientific Notation

Certainly! Let's divide two values in scientific notation step by step using MathJax formatting.

Let's divide \(4.2 \times 10^7\) by \(2.1 \times 10^3\). Here's how we do it:

1. Write the values in standard scientific notation format:
   \[4.2 \times 10^7 \quad \text{and} \quad 2.1 \times 10^3\]

2. Divide the coefficients (the numbers in front):
   \[\frac{4.2}{2.1} = 2.0\]

3. Subtract the exponents (the powers of 10):
   \[10^7 \div 10^3 = 10^{7-3} = 10^4\]

4. Write down the result in scientific notation:
   \[2.0 \times 10^4\]

So, \(4.2 \times 10^7\) divided by \(2.1 \times 10^3\) equals \(2.0 \times 10^4\).

 

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