Q: How is the number 5,200,461 written in Scientific Notation?

Why is 5,200,461 written as 5.200461 x 10⁶ 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 5,200,461 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: 5,200,461
• New Number: 5.200461

Step 2

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

New Number:	5	.	2	0	0	4	6	1
Decimal Count:			1	2	3	4	5	6

There are 6 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 = 5.200461

b = 6

Now the whole thing:

5.200461 x 10⁶

Step 4

Check your work:

10⁶ = 1,000,000 x 5.200461 = 5,200,461

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