Adding And Subtracting In Scientific Notation

Learn how to add and subtract values in scientific notation. This video shows 4 examples and how you have to make the exponents the same before adding and subtracting.

Adding and subtracting expressions in scientific notation involves several steps, including ensuring that the exponents are the same and then performing the operation on the coefficients. Here are the steps:

1. Align the exponents: Write both numbers in scientific notation with the same exponent.
2. Perform the operation on the coefficients: Add or subtract the coefficients.
3. Normalize the result: If the coefficient is 10 or greater, adjust the coefficient and exponent accordingly by moving the decimal point.

Let's illustrate these steps with examples:

Addition Examples:

1. \(3.5 \times 10^4 + 2.1 \times 10^3\)

   Align the exponents: \(3.5 \times 10^4\) and \(0.21 \times 10^4\) (rewrite \(2.1 \times 10^3\) as \(0.21 \times 10^4\)).

   Perform the operation on the coefficients: \(3.5 + 0.21 = 3.71\).

   Normalize the result: \(3.71 \times 10^4\).

2. \(7.2 \times 10^5 + 8.9 \times 10^4\)

   Align the exponents: \(7.2 \times 10^5\) and \(0.89 \times 10^5\) (rewrite \(8.9 \times 10^4\) as \(0.89 \times 10^5\)).

   Perform the operation on the coefficients: \(7.2 + 0.89 = 8.09\).

   Normalize the result: \(8.09 \times 10^5\).

Subtraction Examples:

1. \(5.6 \times 10^4 - 1.2 \times 10^3\)

   Align the exponents: \(5.6 \times 10^4\) and \(0.12 \times 10^4\) (rewrite \(1.2 \times 10^3\) as \(0.12 \times 10^4\)).

   Perform the operation on the coefficients: \(5.6 - 0.12 = 5.48\).

   Normalize the result: \(5.48 \times 10^4\).

2. \(9.3 \times 10^6 - 6.5 \times 10^5\)

   Align the exponents: \(9.3 \times 10^6\) and \(0.65 \times 10^6\) (rewrite \(6.5 \times 10^5\) as \(0.65 \times 10^6\)).

   Perform the operation on the coefficients: \(9.3 - 0.65 = 8.65\).

   Normalize the result: \(8.65 \times 10^6\).

In both addition and subtraction examples, we ensure that the exponents are the same, perform the operation on the coefficients, and then normalize the result if necessary by adjusting the coefficient and exponent.

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