01Bdecimals

=** Decimals **= toc

All fractions will convert into either a **finite decimal** or a ** recurring decimal **.

Finite Decimals
A finite decimal terminates after several decimal places without having been rounded. It is exact.

math \text{For example, } \; 0.75 \textit{ is a finite decimal} math

To convert a fraction into a decimal,
 * find the numerator divided by the denominator.

** Example 1 **
{On the calculator, type 5 ÷ 8 = }

To convert a finite decimal into a fraction,
 * the digits of the decimal become the numerator
 * the denominator is "1" followed by a number of "0"s equal to the number of digits after the decimal point.
 * simplify if possible

Recurring Decimals
A ** recurring decimal ** continues to infinity with a pattern of one or more repeating digits.

A recurring decimal can be represented by a bar (or dots) over the repeating digits.

math \\ \text{For example, } \; 0.33333333 ... = .\overline{3} \qquad \qquad \textit{ is a recurring decimal} \\ \\ . \qquad \qquad \qquad 5.10232323 ... = 5.10\overline{23} \qquad \textit{ is a recurring decimal} math


 * Note: ** To indicate a repeating pattern, we always use 3 dots ... (never 2 dots or 4 dots, always 3 dots}

To convert a fraction into a decimal,
 * find the numerator divided by the denominator (continue until the pattern is clear}

** Example 3 **


{on the calculator, type 5 ÷ 6 = }

To convert a recurring decimal into a fraction,


 * Let x = the recurring decimal in expanded form
 * Call this Equation 1
 * Multiply equation 1 by 10 if there is a single repeated digit
 * multiply by 100 if there are 2 repeated digits,
 * multiply by 1000 if there are 3 repeated digits, etc
 * Call this Equation 2
 * Find Eqn 2 minus Eqn 1 (this gets rid of the recurring part of the decimal)
 * Solve the resulting equation for x
 * write the answer as a fraction in its simplest form

** Scientific Calculator **
To change from finite decimal to fraction {Most scientific calculators will only do this for a limited number of decimal places. Mine can cope with up to 6 decimal places}
 * Enter the decimal,
 * Press =
 * Press the **[a b/c]** button

Most scientific calculators can't convert a recurring decimal to a fraction. You'll have to do it by hand (see above examples).

To change from fraction to decimal Either Or
 * Enter the fraction using the **[a b/c]** button
 * Press =
 * Press the **[a b/c]** button
 * Enter the fraction as a division using the [**÷]** button

** Casio Classpad **



 * In the main screen, enter the fraction or decimal
 * Highlight the value
 * Click on the left icon in the row at the top of the screen

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