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The Patterns in zeros exercise used to appear under the 5th grade (U.S.) Math Mission, but was apparently removed due to reordering, renaming, or other changes. This exercise practices exploring the idea of multiplying by powers of ten and the implications it has for the numbers of zeroes and moving decimal spots.

Types of Problems

There are four types of problems in this exercise:

  1. How many zeroes: This problem has a number written in a form involving a power of ten. It asks the user to report how many zeroes the number would have if it were expanded.
    Piz1

    How many zeroes

  2. How does it move: This problem provides a hypothetical where a number is multiplied or divided by a power of ten. The user is asked how many spots, and in what direction the decimal will be moved.
    Piz2

    How does it move

  3. Do operation and tell how many zeroes: This problem describes an arithmetic problem. Users are supposed to perform the problem and then report how many zeroes there would be after the operation.
    Piz3

    Do operation and tell how many zeroes

  4. What number is this: This problem has either a power of ten as an exponential expression or expanded. The user is to select the corresponding version from a multiple choice list.
    Piz4

    What number is this

Strategies

This exercise is easy to get accuracy badges because all the problems deal with powers of ten or place value which is easy to understand when mastered. The speed badges are easy because although there are four types, it is easy to tell which problem type it is quickly and answer appropriately.

  1. On How many zeroes the answer is always the exponent on the power of ten.
  2. On How does it move, the number of place it moves is always the exponent and multiply connect with right, divide connect with left.
  3. On Do operation and tell how many zeroes simply count the zeroes in the number provided and subtract the exponent of the power of ten, users are dividing by (until they start to bring in multiply problems, then add).
  4. Although it can go either direction, What number is this can also be done nicely by counting zeroes.


Real-life applications

  1. As it can be inferred, scientific notation has many applications in the sciences.
  2. Scientific notation is useful for representing very large or very small quantities.

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