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Lesson 12: Scientific notation word problems

# Numbers and operations: FAQ

## What are repeating decimals?

Repeating decimals are when a pattern of numbers repeats over and over after the decimal point. For example, the fraction $\frac{1}{3}$ is equivalent to the decimal $0.\stackrel{―}{3}$, which is a repeating decimal.
The bar over the $3$ means that it repeats forever: $0.\stackrel{―}{3}=0.333333\dots$

## What are square roots and cube roots?

Square roots and cube roots are used all the time in math and science. When we want to find the side length of a square with a given area, we use square roots. When we want to find the length of a cube with a given volume, we use cube roots.

## What are irrational numbers?

Irrational numbers are numbers that can't be written as a fraction of two integers. For example, $\sqrt{2}$ is an irrational number, because no matter how hard we try, we can't find two integers that will give us $\sqrt{2}$ when we divide them.

## What does "approximating irrational numbers" mean?

When we approximate an irrational number, we're finding a rational number that is close to the irrational number. For example, we could say that $\sqrt{2}\approx 1.414$.

## What are exponent properties?

Exponent properties are rules that we can use to simplify expressions that contain exponents.
Product rule: ${x}^{a}×{x}^{b}={x}^{a+b}$. For example, ${x}^{2}×{x}^{3}={x}^{5}$.
Power rule: $\left({x}^{a}{\right)}^{b}={x}^{ab}$. For example, $\left({x}^{2}{\right)}^{3}={x}^{6}$.
Quotient rule: $\frac{{x}^{a}}{{x}^{b}}={x}^{a-b}$. For example, $\frac{{x}^{5}}{{x}^{2}}={x}^{3}$.
Zero exponent rule: ${x}^{0}=1$. For example, ${7}^{0}=1$.

## What is scientific notation?

Scientific notation is a way of writing really big or really small numbers in a way that makes them easier to work with. For example, $0.000000000005$ is hard to read, but when we put it in scientific notation, we get $5×{10}^{-12}$. This is much easier to read and work with.

## Where is scientific notation used in the real world?

Scientific notation is used in many different fields, especially in the sciences. Scientists often work with very large or very small numbers, and using scientific notation makes calculations and comparisons much easier.
For example, in chemistry, scientists use scientific notation to express the mass of atoms and molecules in grams, which usually have values much smaller than $1$.
Another example: we might want to calculate the distance that light travels in one year. We can use scientific notation to express the speed of light as $3×{10}^{8}$ meters per second and multiply that by the number of seconds in a year to get our answer.

## Want to join the conversation?

• Im khanfused with this math
• just use prodigy math game to help
• What is an easy way to remember scientific notation?
• One way to remember it is you multiply ten by the number that you have. Another way is to remember to add the zeros after (or before) the number. That's how I remember it. Hope that helps!
• why is everyone saying salami khan....
• Why does it fell like Khan Academy is trying to kill us with math?
• Sometmes it's to easy and sometimes it's so hard!
• what's an easy way to remember scientific notation
• Watch the videos.