Q: How is the number 82,120 written in Scientific Notation?

Why is 82,120 written as 8.212 x 10⁴ in scientific notation?

The purpose of scientific notation is for scientists to write very large, or very small, numbers with ease.

Calculating scientific notation for a positive integer is simple, as it always follows this notation:

a x 10^b

Follow the steps below to see how 82,120 is written in scientific notation.

Step 1

To find a, take the number and move a decimal place to the right one position.

• Original Number: 82,120
• New Number: 8.2120

Step 2

Now, to find b, count how many places to the right of the decimal.

New Number:	8	.	2	1	2	0
Decimal Count:			1	2	3	4

There are 4 places to the right of the decimal place.

Step 3

Building upon what we know above, we can now reconstruct the number into scientific notation.

Remember, the notation is: a x 10^b

a = 8.212 (Please notice any zeroes on the end have been removed)

b = 4

Now the whole thing:

8.212 x 10⁴

Step 4

Check your work:

10⁴ = 10,000 x 8.212 = 82,120

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