Repeating Decimals Worksheet printable pdf download

Repeating Decimals Worksheet

Middle Grades Activity:

Repeating Decimals #2 – Delayed Repetends

CALCULATOR:

Casio fx-300ES

INTRODUCTION:

A repeating decimal is a decimal that does not terminate (end), but

eventually reaches a continuous pattern of digits. Examples are:

and

0.3 0.3333333...

25.4126 25.41262626...

The portion of the decimal that repeats is called the repetend.

A delayed repetend is defined for the purposes of this activity as a repetend

that does not begin its pattern immediately after the decimal point; rather,

there is at least one digit after the decimal point that does not repeat.

All repeating decimals are members of the set of rational numbers. All

rational numbers can be written as a ratio of two integers (an improper

fraction).

PROCEDURE:

Turn the calculator [ON].

Make sure the fx-300ES is set up correctly for this activity by pressing the

following key sequences:

[SHIFT]-[SETUP] [1] to enter Math Input/Output mode;

[SHIFT]-[SETUP] [8] [1] to enter Normal Display 1;

[SHIFT]-[SETUP] [ ] [2] to force fractions to display as improper

fractions.

¸ ” , then press [=]. The fx-300ES will display the fraction

Type “ 1 6

Press the [S D] key. Notice that the fraction

is equivalent to the

repeating

decimal 0.1666666..., or 0.16 . This decimal has a repetend delayed by

one digit.

Let’s see if we can find a pattern amongst all repetends delayed by one digit.

Type “0.266666...” until the top line of the screen is filled with 6’s. Then

press [=]. Notice that the fx-300ES interprets this as a repeating decimal,

and outputs

Repeating Decimals Worksheet