If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

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 start fraction, 1, divided by, 3, end fraction is equivalent to the decimal 0, point, start overline, 3, end overline, which is a repeating decimal.
The bar over the 3 means that it repeats forever: 0, point, start overline, 3, end overline, equals, 0, point, 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, square root of, 2, end square root is an irrational number, because no matter how hard we try, we can't find two integers that will give us square root of, 2, end square root 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 square root of, 2, end square root, approximately equals, 1, point, 414.

## What are exponent properties?

Exponent properties are rules that we can use to simplify expressions that contain exponents.
Product rule: x, start superscript, a, end superscript, times, x, start superscript, b, end superscript, equals, x, start superscript, a, plus, b, end superscript. For example, x, squared, times, x, cubed, equals, x, start superscript, 5, end superscript.
Power rule: left parenthesis, x, start superscript, a, end superscript, right parenthesis, start superscript, b, end superscript, equals, x, start superscript, a, b, end superscript. For example, left parenthesis, x, squared, right parenthesis, cubed, equals, x, start superscript, 6, end superscript.
Quotient rule: start fraction, x, start superscript, a, end superscript, divided by, x, start superscript, b, end superscript, end fraction, equals, x, start superscript, a, minus, b, end superscript. For example, start fraction, x, start superscript, 5, end superscript, divided by, x, squared, end fraction, equals, x, cubed.
Zero exponent rule: x, start superscript, 0, end superscript, equals, 1. For example, 7, start superscript, 0, end superscript, equals, 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, point, 000000000005 is hard to read, but when we put it in scientific notation, we get 5, times, 10, start superscript, minus, 12, end superscript. 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, times, 10, start superscript, 8, end superscript meters per second and multiply that by the number of seconds in a year to get our answer.