Lesson 1 Test: Classifying Numbers Solutions
Simplify each fraction below, then convert each fraction to a decimal. Show your work.
Simplified Fractions | Decimal Form | |
1) | ||
2) | ||
3) |
- Construct a number line and plot the values below.

Harriet and Alexander are working together on a math assignment. They need to classify the value . Harriet wants to classify as a rational number, but Alexander disagrees. Alexander wants to classify as an irrational number because it has a lot of decimal places.
- Who is correct? Use your knowledge of rational and irrational numbers to justify your choice.
Harriet is correct. The number is a repeating decimal. Repeating decimals can be classified as rational numbers. The number of digits a number has does not determine if it is rational or irrational.
Evaluate the placement of each number on the Classifying Numbers Diagram below.
- Determine if each number is placed correctly, then justify your answer.

Placed Correctly (Yes, No) | Reason | |
12 | Yes | 12 is a natural number greater than 0 that can be used for counting objects. |
No | is a repeating decimal, so it is not an irrational number. Repeating decimals are rational numbers. | |
No | Negative numbers are not classified as whole numbers. Whole numbers are positive numbers beginning with 0. | |
Yes | This fraction simplifies to . can be classified as an integer. | |
26.27 | Yes | 26.27 is a terminating decimal. Terminating decimals are rational numbers. |
0 | No | Natural numbers begin with 1. 0 is a whole number but not a natural number. |
No | simplifies to the decimal 3.67. Decimals are not classified as integers. | |
99 | Yes | 99 is a positive whole number greater than 0. |
Yes | is an irrational number. |