# Reading and Writing Scientific Notation 04:40 minutes

**Video Transcript**

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Transcript
**Reading and Writing Scientific Notation**

Dorothy is a really hardworking student. She has an internship at the prestigious Frank N. Stein Laboratory! At the lab, she works in the biology department, and her job is to observe how different types of bacteria grow. How fascinating!

### Scientific Notation

It’s the end of Dorothy's internship, and she needs to write a final report about what she learned. She has all the facts, so she just needs to write up her findings in a neat report. Can you believe there are about 5 **million, trillion, trillion** bacteria on Earth? Wow! That's a lot of bacteria and that’s too many zeros to write down – her report is a mess. There’s another way! Dorothy can write this huge number in **scientific notation***! Let’s review how to read and write numbers in scientific notation.

### Simplifying very big and very small numbers

Just to review, scientific notation makes really BIG and really SMALL numbers easy to read and interpret. To write numbers in scientific notation, we write 'n', the **coefficient**, **times 10**, the **base**, **raised to the power of 'a'**, which is the **exponent**. N' must be greater than or equal to 1 and less than 10. 10 raised to the 'a' power represents the number of times we must multiply 'n' by 10 to get back to the original number, the really big number with all the zeros.

To make this easier to understand, let’s look at an example: We'll write the number one million in scientific notation. To do this, move the **decimal** over until you have a coefficient that is greater than or equal to 1 and less than 10. Now, count the number of times you moved the decimal. Each time you move the decimal over one place value to the left, it's the same as multiplying by ten. So, since you moved the decimal six places to the left, we can write this as 1 x 10⁶.

### Scientific Notation of really big Numbers

Let’s help Dorothy write her report. We’ll use the same process to this write this **really big number** in scientific notation. Scoot the decimal point over til you have a coefficient that is greater than or equal to 1 but less than 10, so this makes 'n' equal to 5.12. Now count the number of times you moved the decimal to the left and use that number to write the exponent using 10 as the base. We moved the decimal 30 places to the left. So we can write the number in scientific notation as 5.12 x 10³⁰.

### Scientific Notation of really small Numbers

During her internship, Dorothy also observed the mass of various bacteria cells, and she learned that one really, really small bacteria has a teeny-tiny small mass. This critter is really small! Luckily for Dorothy, she can use scientific notation to write really small numbers too. We use the same process as before, but this time we move the decimal in the opposite direction. Each time you move the decimal over one place value to the right, it's the same as **dividing** by ten.

Remember, when the number in **standard form** is less than 1, the exponent is always a **negative number**. Our new number, 1.46, is greater than or equal to 1 but less than 10. Now count the number of places you moved the decimal point to the right, and write that number as the negative exponent. In scientic notation, the number is 1.46 x 10⁻¹⁴.

### Converting from Scientific Notation to the Standard Form

How do you convert a number written in scientific notation to the standard form? As an example, let’s use 2.25 x 10⁴. We know this is 2.25(10)(10)(10)(10), but there's an easier way. Since the exponent is a positive number, we know the **standard form** will be a bigger number, so move the decimal over four places to the right 2.25 x 10⁴ is the same as 22,500.

Now that Dorothy used scientific notation to write her report, it’s much easier to read. Just look at that last fact. Wow! These particular bacteria have a very fast rate of growth. Now that's what I call a 'cultured' party!

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2 commentsThanks! We hope sofatutor continues to meet your educational needs! If you have any further comments or questions, you can always e-mail us at mathematics@sofatutor.com.

Great video!