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Scientific notation
Description
Exercise Name: Scientific notation
Math Missions: 8th grade (U.S.) Math Mission, Pre-algebra Math Mission, Algebra basics Math Mission, Mathematics I Math Mission
Types of Problems: 2

The Scientific notation exercise appears under the 8th grade (U.S.) Math Mission, Pre-algebra Math Mission, Algebra basics Math Mission and Mathematics I Math Mission. This exercise strengthens the ability to transfer between scientific notation and the standard form of numbers.

## Types of Problems

There are two types of problems in this exercise:

1. Change into scientific notation: This problem provides a number written in the typical standard form. The student is asked to rewrite the number in scientific notation.
2. Write in standard form: This problem provides a number written in scientific notation. The student is expected to expand the number into the standard form.

## Strategies

Order of operations is useful for expansion, but knowledge and familiarity with scientific notation is really key.

1. A number is in scientific notation if it is written in the form of ${a\times 10^n}$ where n is an integer and a is a number such that ${1 \leq a <10}$.
2. To make a number into scientific notation, move the decimal to the spot immediately to the right of the first non-zero digit reading from the left. This is a. The number of spots moved is n if you moved it left, and -n if you moved it right.
3. To expand a number into standard form, move the decimal the magnitude of the value of n. Move to the right if n is positive and to the left if n is negative.
4. Small numbers tend to have a negative n, whereas big numbers tend to have a high n.

## Real-life applications

1. Scientific notation has many applications in the sciences.
2. Scientific notation is useful for representing very large or very small quantities.