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) 4248 42÷6=748÷6=8 42÷48=0.875
2) 90120 90÷3=3120÷30=4 90÷120=0.75
3) 1680 16÷16=180÷16=5 16÷80=0.2
  1. Construct a number line and plot the values below.

9.749032816, 9.25, 768

Harriet and Alexander are working together on a math assignment. They need to classify the value 16.871871. Harriet wants to classify 16.871871 as a rational number, but Alexander disagrees. Alexander wants to classify 16.871871 as an irrational number because it has a lot of decimal places.

  1. 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.

  1. Determine if each number is placed correctly, then justify your answer.
Image3
  Placed Correctly (Yes, No) Reason
12 Yes 12 is a natural number greater than 0 that can be used for counting objects.
53.175175 No 53.175175 is a repeating decimal, so it is not an irrational number. Repeating decimals are rational numbers.
19 No Negative numbers are not classified as whole numbers. Whole numbers are positive numbers beginning with 0.
7813 Yes This fraction simplifies to 66 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.
226 No 226 simplifies to the decimal 3.67. Decimals are not classified as integers.
99 Yes 99 is a positive whole number greater than 0.
18.90432176505384... Yes 18.90432176505384... is an irrational number.

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