Q: How is the number 642,125,419 written in Scientific Notation?

Why is 642,125,419 written as 6.42125419 x 10⁸ 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 642,125,419 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: 642,125,419
• New Number: 6.42125419

Step 2

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

New Number:	6	.	4	2	1	2	5	4	1	9
Decimal Count:			1	2	3	4	5	6	7	8

There are 8 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 = 6.42125419

b = 8

Now the whole thing:

6.42125419 x 10⁸

Step 4

Check your work:

10⁸ = 100,000,000 x 6.42125419 = 642,125,419

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