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Convert a Fraction to a Decimal

To convert a fraction to a decimal, divide the numerator by the denominator using long division. For example, let's convert $\frac{3}{25}$ to a decimal: As we can see, $\frac{3}{25} = 0.12.$

Convert a Decimal to a Fraction

To convert a decimal to a fraction, place the decimal above the number $1$. Then multiply the top and bottom by $10$ the same number of times, until the numerator is a whole number. How many times do you have to do this? It depends how many digits are after the decimal point of the original numerator. In this example, $0.38$ has two digits after the decimal point. This lets us find the numerator and denominator. Best of all, we haven't changed the value of anything!

Then, just simplify the fraction, if it's necessary! As an example, let's convert $0.38$ into a fraction: $$\begin{align} 0.38 &= \dfrac{0.38}{1}\\ &=\dfrac{0.38 \times 100}{1\times 100}\\ &=\dfrac{38}{100}\\ &=\dfrac{19}{50} \end{align}$$

The last step is where we reduced the fraction. We could reduce it because $38$ and $100$ share a factor of $2$. There are no other factors to cancel though. This is because $2$ is the greatest common factor of $38$ and $100$.

So, $0.38 = \frac{19}{50}$. We found a technique that converts a decimal number to a fraction!

Be careful, however. Some decimals that go on forever without a pattern can't be written as a fraction. These are called the irrational numbers. Otherwise the number is called rational.

We can also convert a repeating decimal to a fraction.

Let's do a couple more examples!

To convert the fraction $\frac{7}{50}$ into a decimal, we just need to divide the numerator, $7,$ by the denominator, $50$. As we can see, $\frac{7}{50} = 0.14$.

Here's another example of the same type of problem for you to try.

To convert $0.725$ to a fraction, place the decimal above $1$. Then multiply the numerator and denominator by $10$ the same number of times, until the numerator is a whole number. Then, just simplify the resulting fraction! $$\begin{align} 0.725 &= \dfrac{0.725}{1}\\ &=\dfrac{0.725 \times 1000}{1\times 1000}\\ &=\dfrac{725}{1000}\\ &=\dfrac{29(25)}{40(25)}\\ &=\dfrac{29\cancel{25}}{40\cancel{25}}\\ &=\dfrac{29}{40}\\ \end{align}$$ So, $0.725 = \boxed{\frac{29}{40}}$.

(Video) Convert any Fraction to a Decimal

by Math Antics

Here's a video by mathantics that explains how to convert any fraction into an equivalent decimal. There will only be one way to do this. However, we can't always turn a decimal into a fraction, perhaps if the number is irrational.

$\large{\text{Summary}}$

Fractions are another way to write out division. We can convert a fraction to a decimal by dividing the numerator by the denominator. Sometimes we can do this by hand, often by first writing the fraction in simplest form. Other times we need a calculator.

Suppose we want to convert the fraction $\frac12$ into a decimal. Start by turning it into a division problem where the numerator is divided by the denominator. But wait, $2$ doesn't go into $1$. This means, we need to break out a decimal point. Begin by turning $1$ into $1.0$ (we're not changing the value of anything). We know that $2$ goes into $10$ a total of $5$ times. In other words, $10$ is the fifth positive multiple of $2$. Thus, we can solve this division problem.

Fraction to Decimal

To convert a fraction to a decimal just divide the numerator by the denominator.

That's pretty much it. It can be a pain and division sucks, but there's really only one step. Sometimes that one step is long division, though.

Let's say we want to know the decimal equivalent of the fraction $\frac{13}{84}$. To start, we divide $13$ by $84$. This is one of those problems we do using long division. It's too complicated to do in your head.

As you can see this continues on, seemingly forever. In fact, it does go on forever, so just stop when you see a pattern. It will actually come out to be $0.15\overline{476190}$. As a decimal though, we can get a clearer picture as to how big it really is. It is more difficult to compare fractions when the denominators are different. Even if the denominators are the same it is worthwhile to convert to a decimal. In some cases we can also convert to a percent.

To solve this problem, you should have used long division to turn $\frac{14}{33}$ and $\frac{30}{73}$ into decimals. You should have gotten

$$\begin{align} \frac{14}{33} &= 0.\overline{42} \\ \frac{30}{73} &= 0.41095... \end{align}$$

We only have to look at the first few digits to see that $\frac{14}{33}$ is bigger.