Q: How is the number 42,638 written in Scientific Notation?

Why is 42,638 written as 4.2638 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 42,638 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: 42,638
• New Number: 4.2638

Step 2

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

New Number:	4	.	2	6	3	8
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 = 4.2638

b = 4

Now the whole thing:

4.2638 x 10⁴

Step 4

Check your work:

10⁴ = 10,000 x 4.2638 = 42,638

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