Question

Find the sum of the numbers. Express your answer in scientific notation. (2.04 times 10 Superscript 10 Baseline) + (6.45 times 10 Superscript 11) 6.654 times 10 Superscript 10 8.49 times 10 Superscript 10 6.654 times 10 Superscript 11 8.49 times 10 Superscript 11

Answer 1

Taking into account the scientific notation, the result of the sum is 6.654×10¹¹.

Scientific notation

Scientific notation is a quick way to represent a number using powers of base ten.

The numbers are written as a product:

a×10ⁿ

where:

• a is a real number greater than or equal to 1 and less than 10, to which a decimal point is added after the first digit if it is a non-integer number.
• n is an integer, which is called an exponent or an order of magnitude. Represents the number of times the comma is shifted. It is always an integer, positive if it is shifted to the left, negative if it is shifted to the right.

Sum in scientific notation

You want to add two numbers in scientific notation:

2.04×10¹⁰ + 6.45×10¹¹

It should be noted that when the numbers to be added do not have the same base 10 exponent, the base 10 power with the highest exponent must be found. In this case, the highest exponent is 11.

Then all the values ​​are expressed as a function of the base 10 exponent with the highest exponent. In this case: 2.04×10¹⁰= 0.204×10¹¹

Taking the quantities to the same exponent, all you have to do is add what was previously called the number "a". In this case:

0.204×10¹¹ + 6.45×10¹¹= (0.204 + 6.45)×10¹¹= 6.654×10¹¹

Finally, the result of the sum is 6.654×10¹¹.

Learn more about scientific notation:

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