The Understanding place value exercise appears under the 4th grade (U.S.) Math Mission, Pre-algebra Math Mission and Mathematics III Math Mission. This exercise explores the concept of place value and comparison of place value via multiplying by tens.

Types of Problems

There are five types of problems in this exercise:

  1. Solve the word problem: This problem describes a word problem and the user types the correct solution on the appropriate spot.

    Solve the word problem

  2. Compare digits within number: This problem has an integer with a repeated digit. The user is asked hoe many times larger or smaller the first or second occurrence is than the other.

    Compare digits within number

  3. Multi-step comparison: This problem asks usersto compare two numbers that are different by a factor of ten. The answer two drop down questions and at the end a final question.

    Multi-step comparison

  4. Other representations: This problem takes an integer and asks the user to write out alternative representations of the number in the place value system.

    Other representations

  5. Compare digits between numbers: This problem has two numbers with a common digit. Users are to answer how many times larger or smaller the digit is in one number compared to the other.

    Compare digits between numbers


Knowledge of place value is highly recommended to have success while doing this exercise.

  1. On problem type one the answer always seems to be ten times whatever number shows up in the word problem.
  2. On problem type two, the similar digits always seems to be consecutive, thus the answer is ten each time.
  3. On problem type three, Small -> Right and Large -> Left can help with the answers.
  4. On problem type three, the fill in the answer problem appears to always be ten.
  5. On problem type four, write the spots out first, then decrease the first column by one as you increase the second column by ten. You should end with 0 in the first column.
  6. On problem type five the answer always seems to be 10, in other words, the digits are in consecutive 'places.'

Real-life Applications

  1. Place value is used for writing checks.
  2. A common example of place value is money (example: $1.69 means that there is 1 whole (dollar), 6 tenths (dimes), and 9 hundredths (pennies)).

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