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Adding Or Subtracting Numbers In Scientific Notation




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

Related Topics: More Scientific Notation Lessons

Scientific Notation: Addition and Subtraction

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)



How to add and subtract numbers in scientific notation with same or different exponents and negative exponents?
This video explains how to add and subtract numbers written in scientific notation, whether or not they have the same exponent.
Examples:
(3.769 × 105) + (4.21 × 105)
(8.14 × 10-2) - (2.01 × 10-2)
(7.58 × 105) + (2.871 × 106)
(2.9785 × 10-8) - (5.72 × 10-10)
(4.86 × 103) - (4.72 × 103) Why you have to make sure the exponents are the same?
This video explains why when adding and subtracting numbers in scientific notation, you have to make sure the exponents are the same.
Example: (7.1 × 103) + (5 × 102)


 
Rules for scientific notation
This video reviews scientific notation and shows how to add and subtract in Scientific Notation.
Rule for scientific notation:
If the exponent goes down, the decimal point goes right.
If the decimal point goes right, the exponent goes down.
If the exponent goes up, the decimal goes left.
If the decimal point goes left, the exponent goes up.

Scientific Notation - Addition and Subtraction Rules

This video explains how to do add and subtract in scientific notation without the use of a calculator.
• The powers of 10 must be the same in both terms in order to add/subtract.
• Once the power of 10 matches, just add or subtract.
• Adjust the answer to scientific notation.

Adding and Subtracting Numbers in Scientific Notation

This video shows how to add and subtract numbers in different bases by rewriting their exponents to be the same.
Example: (5.4 × 103) + (1.2 × 105)

Scientific Notation - Adding and Subtracting

Learn how to add and subtract in scientific notation. Example: (3.5 × 104) + (3.1 × 105)


 
Scientific Notation Calculator

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.


You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.


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