1Cademy - Converting $$\frac{43}{22}$$ to a Decimal

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Procedure for Converting a Fraction to a Decimal

Example

Converting $\frac{43}{22}$ to a Decimal

Convert $\frac{43}{22}$ to decimal form by dividing $43$ by $22$ :

Perform long division, appending zeros to the dividend as needed:

$22$ into $43$ : $1$ time ( $22$ ), remainder $21$ .
Bring down $0$ : $22$ into $210$ : $9$ times ( $198$ ), remainder $12$ .
Bring down $0$ : $22$ into $120$ : $5$ times ( $110$ ), remainder $10$ .
Bring down $0$ : $22$ into $100$ : $4$ times ( $88$ ), remainder $12$ .
Bring down $0$ : $22$ into $120$ : $5$ times ( $110$ ), remainder $10$ .

At this point the remainders $12$ and $10$ have started cycling, so the digit pair $54$ will repeat forever. The quotient is $1.9545454\ldots$ , written with a repeating bar as:

$\frac{43}{22} = 1.9\overline{54}$

This example illustrates that when a fraction's denominator has prime factors other than $2$ and $5$ , the decimal expansion will not terminate — it will eventually repeat.

Updated 2026-04-21

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OpenStax Elementary Algebra

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