Terminating Decimals

Divide · factor · predict · verify

Mode

Decimal laboratory

Visual model

Numerator3

Denominator8

Repeating digits shown6

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Ready · 10 visual chapters.

Chapters

Learning objectives

Define a terminating decimal and identify its stopping point.
Convert fractions through long division and powers of ten.
Use the simplified denominator factor test.
Predict the maximum number of decimal places.

Key ideas

A simplified fraction terminates exactly when its denominator has no prime factors except 2 and 5. Long division terminates when its remainder becomes zero.

If the simplified denominator is 2 to power a times 5 to power b, the decimal needs at most the larger of a and b places.

Try these experiments

Compare 3/8 with 1/6 in the factor scanner.
Change 3/8 into a denominator of 1000.
Predict the places required by 7/40.
Display 1/4 on the hundred grid.
Generate a challenge and justify the result.

Questions

Why must a fraction be simplified first? What does remainder zero prove? Why are 2 and 5 special in our base-ten number system?

Seven-question check

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Ten independent pages. Works with touch, stylus, mouse, Android devices and interactive smart boards.