Adding Or Subtracting Numbers In Scientific Notation

In this lesson, we will look at some examples of adding and subtracting numbers in scientific notation (also called standard form in the UK)

To add or subtract two numbers in scientific notation:

Step 1: Adjust the powers of 10 in the 2 numbers so that they have the same index. (Tip: It is easier to adjust the smaller index to equal the larger index).

Step 2 : Add or subtract the numbers.

Step 3 : Give the answer in scientific notation.

Example :

Evaluate 2 × 10³ + 3.6 × 10⁴, giving your answer in scientific notation.

Solution:

Text Box: 2 × 103 + 3.6 × 104 = 0.2 × 104 + 3.6 × 104 (change to the same indices) = (0.2 + 3.6) × 104 (add the numbers) = 3.8 × 104 (answer in scientific notation)

Example :

Evaluate 7 × 10⁵ – 5.2 × 10⁴, giving your answer in scientific notation.

Solution:

Text Box: 7 × 105 – 5.2 × 104 = 70 × 104 – 5.2 × 104 (change to the same indices) = (70 – 5.2) × 104 (subtract the numbers) = 64.8 × 104 = 6.48 × 105 (answer in scientific notation)

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