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## 8th grade (Eureka Math/EngageNY)

### Unit 1: Lesson 2

Topic B: Magnitude and scientific notation- Scientific notation examples
- Scientific notation example: 0.0000000003457
- Scientific notation
- Multiplying in scientific notation example
- Multiplying & dividing in scientific notation
- Multiplying three numbers in scientific notation
- Multiplying & dividing in scientific notation
- Subtracting in scientific notation
- Adding & subtracting in scientific notation
- Simplifying in scientific notation challenge
- Scientific notation word problem: red blood cells
- Scientific notation word problem: U.S. national debt
- Scientific notation word problem: speed of light
- Scientific notation word problems
- Scientific notation review

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# Scientific notation review

CCSS.Math:

Review the basics of scientific notation and try some practice problems.

## Scientific notation

A number is written in scientific notation when there is a number greater than or equal to 1 but less than 10 multiplied by a power of 10.

The following numbers are written in scientific notation:

- 5, point, 4, times, 10, cubed
- 8, point, 013, times, 10, start superscript, minus, 6, end superscript

*Want to learn more about scientific notation? Check out this video.*

## Writing numbers in scientific notation

### Numbers greater than 10

If we have a number greater than 10, we move the decimal point to the

**left**until we have a number between 1 and 10. Then, we count the number of times we moved the decimal and write that as an exponent over a base of 10. Finally, we write our number multiplied by the power of 10.**Example**

Let's write 604, comma, 000 in scientific notation.

If we move the decimal left once, we get 60, comma, 400, point, 0. We need to keep moving the decimal until we get a number between 1 and 10.

We have to move the decimal left a total of start color #a75a05, 5, end color #a75a05 times.

Now, we have 6, point, 04.

Finally, we multiply 6, point, 04 times 10, start superscript, start color #a75a05, 5, end color #a75a05, end superscript:

604, comma, 000 in scientific notation is 6, point, 04, times, 10, start superscript, start color #a75a05, 5, end color #a75a05, end superscript.

### Numbers less than 1

If we have a number less than 1, we move the decimal point to the

**right**until we have a number between 1 and 10. Then, we count the number of times we moved the decimal and write that as a**negative**exponent over a base of 10. Finally, we write our number multiplied by the power of 10.**Example**

Let's write 0, point, 0058 in scientific notation.

If we move the decimal

**right**start color #1fab54, 3, end color #1fab54 times, we get a number between 1 and 10.Now, we have 5, point, 8.

Finally, we write 5, point, 8 times 10, start superscript, start color #1fab54, minus, 3, end color #1fab54, end superscript:

0, point, 0058 in scientific notation is 5, point, 8, times, 10, start superscript, start color #1fab54, minus, 3, end color #1fab54, end superscript.

## Want to join the conversation?

- I get confused on which way I should move the decimal for each exponent. Does anyone Have a trick or saying that helps them remember this.

Thanks.(35 votes)- A positive exponent means move to the right, and a negative exponent means move to the left.(7 votes)

- Is this for seventh graders?(15 votes)
- You Learn maybe before 8th grade, but you learn around 8th grade (or pre-algebra at OLP)(4 votes)

- Is it possible for a number to have an infinite answer?(15 votes)
- Yes, for example, x(2+3) = 2x+3x, once you simplify the first expression you get 2x+3x = 2x+3x, which means it has infinite solutions.(2 votes)

- This is so hard how do you know neg and pos(6 votes)
- If your original number in standard form is a large number, then you get a positive exponents.

For example: 5,000,000 = 5 x 10^6

If your original number in standard form was a decimal, then you would have a negative exponent.

For example: 0.00006 = 6 x 10^(-5)

Hope this helps.(6 votes)

- How do you write scientific notation in standard form? I still don't get it even after watching the videos.(5 votes)
- for writing scientific notation in standard form we have to remove 10 exponent ; if exponent is in negative then we have to move decimal to left;{ 5.4*10^-1= 0.54} and if power of exponent is positive then we move decimal to right{ 2.456 *10^2= 245.6} hope it helps(3 votes)

- why did people make scientific notation?(1 vote)
- In order to simplify numbers that are to big(6 votes)

- is it possible to have a negative pi(6 votes)
- Every real number has an opposite, so negative pi exists.(2 votes)

- i am still confused how to solve questions of this type -

9 ten thousandths ; 10 hundred thousandths

please help me out ..(4 votes)- Hi there. you may be familiar with ten thousand or one hundred thousand. however, what you are talking about is decimal places. For example, 1000 would be one thousand. if you were to have a decimal which is basically a more specific version of a fraction. ".1" would be one-tenth, .01 would be one-hundredths, .001 would be one-thousandths, and so on. so if I had 1.5 it would be one and 5 tenths or 1 and a half.(6 votes)

- I have trouble using Scientific notation to the problems that I have at school for work.Any advice will be helpful.(7 votes)
- Ask your teacher for help and work it out together.(0 votes)

- Hi

(I didn't know how to google this.)

I'm wondering what the word/term I sould use to describe the difference between 1 x 10^⁻9 and 1 x 10^⁻8 (they differ by a zero doesn't sound so good)

Thanks in advance!(3 votes)- Well, the difference is

10^(−8) − 10^(−9) = 10 ∙ 10^(−9) − 10^(−9) = 9∙10^(−9)

However, when comparing the sizes of two numbers we often rather use their*ratio*.

10^(−8)∕10^(−9) = 10,

which of course means that 10^(−8) is ten times as big as 10^(−9), and we say that they differ by a factor of 10.(5 votes)