Related Pages
Converting Scientific Notation
Multiplying Scientific Notation
Dividing 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.)
A number is in scientific notation when it is in the form
A × 10n where
To add or subtract numbers in scientific notation, the exponents must be the same. If they are different, you must adjust one (or both) numbers to match before performing the operation.
The following diagram shows how to add or subtract numbers in scientific notation. Scroll down the page for more examples on adding and subtracting with scientific notation.
Scientific Notation Worksheets:
Practice your skills with the following scientific notation worksheets:
Online & Printable Scientific Notation Worksheets
Steps to add or subtract numbers in scientific notation
Before you can add or subtract the significands, the exponents of 10 must be the same. To do this, you might need to adjust one or both numbers.
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 exponent to equal the larger exponent).
If you move the decimal point to the left, increase the exponent by the number of places moved.
If you move the decimal point to the right, decrease the exponent by the number of places moved.
Step 2: Add or subtract the significands.
Once the powers of ten are the same, you can add or subtract the significands. Treat the 10n part as a common factor.
a × 10n + b × 10n = (a + b) × 10n
a × 10n - b × 10n = (a - b) × 10n
Step 3: Adjust the Result to Proper Scientific Notation (if necessary)
The result from Step 2 might not be in proper scientific notation. If necessary, adjust the decimal point in the significand and change the exponent accordingly:
If the significand is less than 1: Move the decimal point to the right until it is between 1 and less than 10, and decrease the exponent by the number of places moved.
If the significand is 10 or greater: Move the decimal point to the left until it is between 1 and less than 10, and increase the exponent by the number of places moved.
Example:
Evaluate 2 × 103 + 3.6 × 104, giving your answer in
scientific notation.
Solution:
Example:
Evaluate 7 × 105 – 5.2 × 104, giving your answer in
scientific notation.
Solution:
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)
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)
This video reviews scientific notation and shows how to add and subtract in Scientific Notation.
Rule for scientific notation:
This video explains how to do add and subtract in scientific notation without the use of a calculator.
Learn how to add and subtract in scientific notation.
Add and subtract numbers in different bases by rewriting their exponents to be the same.
Example:
(3.5 × 104) + (3.1 × 105)
Try the free Mathway calculator and
problem solver below to practice various 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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