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Powers of ten
Description
Exercise Name: Powers of ten
Math Missions: 5th grade (U.S.) Math Mission
Types of Problems: 2

The topic Powers of ten is a topic under the 5th grade (U.S.) Math Mission. This exercise experiments with the powers of ten and explores how they relate via multiplication and division.

## Types of Problems

There are two types of problems in this exercise:

1. Perform the operation with powers of ten: This problem has a multiplication or division problem involving powers of ten. The user is asked to find the correct answer to the problem and write it in the space provided.
2. Find the value of the power of ten: This problem has a power of ten written at the beginning. The user is asked to select the correct value of the power of ten from a multiple choice list of possibilities.

## Strategies

Basic exponentiation and the multiplicative structure of the numbering system can help to do this problem quickly and correctly.

1. The value of ${10^n}$ is a one followed by ${n}$ zeros.
2. Multiplying powers of ten is a 1 followed by the sum of the number of the zeros in both of the numbers that are being multiplied together.
3. Division will result in a fraction (1 over a power of ten) if the first number is smaller than the second, and an integer if the first number is larger. The number of zeroes will be the absolute value of the difference of the numbers of zeros in the numbers.

## Real-life Applications

1. Exponential Growth is a critically important aspect of Finance, Demographics, Biology, Economics, Resources, Electronics and many other areas.
2. Exponents are often used to describe a computer's memory.