We've seen how to convert fractions to decimals. We can also convert from decimals to fractions.
To demonstrate, let's find a decimal fraction equivalent to the following decimal:
The number of decimal places gives us the number of zeros in our fraction's denominator. In this case, has decimal place. So, is our fraction's denominator:
Then, we put everything to the right of the decimal point in the numerator:
Earlier, we saw that we can represent the decimal as a decimal fraction as follows:
We can also write as a decimal fraction with a denominator of by multiplying the numerator and denominator by
However, the denominator should be the smallest possible power of ten when expressing decimals as decimal fractions. So, while is a valid decimal fraction representing the preferred answer is
Express as a decimal fraction.
Notice that has decimal places. So, we can write it as a fraction with in the denominator as follows:
Express $0.7$ as a decimal fraction.
|
a
|
$\dfrac{7}{100}$ |
|
b
|
$\dfrac{10}{70}$ |
|
c
|
$\dfrac{7}{10}$ |
|
d
|
$\dfrac{100}{7}$ |
|
e
|
$\dfrac{10}{7}$ |
Express $0.967$ as a decimal fraction.
|
a
|
$\dfrac{100}{967}$ |
|
b
|
$\dfrac{967}{10}$ |
|
c
|
$\dfrac{1,000}{967}$ |
|
d
|
$\dfrac{967}{100}$ |
|
e
|
$\dfrac{967}{1,000}$ |
Express as a decimal fraction.
Notice that has decimal places. So, we can write it as a fraction with in the denominator as follows:
Express $0.06$ as a decimal fraction.
|
a
|
$\dfrac{6}{1,000}$ |
|
b
|
$\dfrac{60}{100}$ |
|
c
|
$\dfrac{60}{10}$ |
|
d
|
$\dfrac{6}{100}$ |
|
e
|
$\dfrac{6}{10}$ |
Express $0.003$ as a decimal fraction.
|
a
|
$\dfrac{30}{1,000}$ |
|
b
|
$\dfrac{3}{100}$ |
|
c
|
$\dfrac{30}{100}$ |
|
d
|
$\dfrac{3}{1,000}$ |
|
e
|
$\dfrac{300}{100}$ |
Sometimes, when we convert a decimal into a fraction, the fraction is not in its simplest form.
For instance, notice that has decimal place. So, we can write it as a decimal fraction with in the denominator:
However, this fraction is not in its simplest form. To simplify, we divide the numerator and denominator by
Therefore, as a fraction in its simplest form is
Which fraction is equivalent to
Notice that has decimal places. So, we can write it as a fraction with in the denominator:
We then reduce this fraction to its simplest form:
Therefore, is equivalent to
Which fraction is equivalent to $0.5?$
|
a
|
$\dfrac{2}{3}$ |
|
b
|
$\dfrac{1}{2}$ |
|
c
|
$\dfrac{1}{20}$ |
|
d
|
$\dfrac{1}{5}$ |
|
e
|
$\dfrac{3}{2}$ |
Which fraction is equivalent to $0.35?$
|
a
|
$\dfrac{5}{6}$ |
|
b
|
$\dfrac{9}{25}$ |
|
c
|
$\dfrac{7}{20}$ |
|
d
|
$\dfrac{3}{5}$ |
|
e
|
$\dfrac{2}{7}$ |