Rename an Eighth as a Decimal

Supplied materials

• Paper or a browser scratch area; a calculator is optional unless rounding is requested.
• Supplied teaching case: Write 2/8 as an exact decimal. Candidate answers: (A) 0.025 (B) 0.25 (C) 0.5 (D) 4.
• Independent check inputs: Write 3/8 as an exact decimal. Candidate answers: (A) 0.0375 (B) 0.375 (C) 0.75 (D) 2.6667.

Learn the idea

Rational numbers can be represented as ratios of integers with nonzero denominator. Their decimal forms terminate or repeat, and negative quantities can be compared by their positions to the left of zero. A denominator built from factors two and five can be renamed as a power of ten. This connects exact fraction values to decimal place value without rounding.

Here is the method on the supplied teaching case. Divide 2 by 8, or rename the denominator as 1000: 2/8=250/1000=0.25.

A decimal with three displayed places need not be approximate. Distinguish an exact terminating value from a shortened decimal; dividing numerator by denominator preserves the fraction’s value.

1. Write or sketch the supplied teaching case, labeling its quantities and restrictions.
2. Apply the method shown in the worked solution, keeping each intermediate equality or justified inference.
3. Solve the independent check with its changed inputs before revealing feedback.
4. Complete the three practice cases; explain which mathematical rule rules out one distractor in each case.

Check your reasoning

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Take it further

Changed-input task: Write 9/8 as an exact decimal. Candidate answers: (A) 0.1125 (B) 0.8889 (C) 1.125 (D) 2.25. Show the mathematical reason, not only the selected answer. Expected result: 1.125. Divide 9 by 8, or rename the denominator as 1000: 9/8=1125/1000=1.125.

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