Reduction and Expansion of Decimal Fractions - Examples, Exercises and Solutions

Since there are two digits after the decimal point, we divide 75 by 100:

$\frac{75}{100}$

Now let's find the highest number that divides both the numerator and denominator.

In this case, the number is 25, so:

$\frac{75:25}{100:25}=\frac{3}{4}$

Since there are two digits after the decimal point, we divide 36 by 100:

$\frac{36}{100}$

Now let's find the highest number that divides both the numerator and denominator.

In this case, the number is 4, so:

$\frac{36:4}{100:4}=\frac{9}{25}$

Since there are two digits after the decimal point, we divide 58 by 100:

$\frac{58}{100}$

Now let's find the highest number that divides both the numerator and denominator.

In this case, the number is 2, so:

$\frac{58:2}{100:2}=\frac{29}{50}$

Since there is one digit after the decimal point, we divide 8 by 10:

$\frac{8}{10}$

Now let's find the highest number that divides both the numerator and denominator.

In this case, the number is 2, so:

$\frac{8:2}{10:2}=\frac{4}{5}$

Since there is one digit after the decimal point, we divide 5 by 10:

$\frac{5}{10}$

Now let's find the highest number that divides both the numerator and the denominator.

In this case, the number is 5, so:

$\frac{5:5}{10:5}=\frac{1}{2}$

Since there are three digits after the decimal point, we divide 350 by 1000:

$\frac{350}{1000}$

Now let's find the highest number that divides both the numerator and denominator.

In this case, the number is 50, so:

$\frac{350:50}{1000:50}=\frac{7}{20}$

Since there are three digits after the decimal point, we divide 630 by 1000:

$\frac{630}{1000}$

Now let's find the highest number that divides both the numerator and denominator.

In this case, the number is 10, so:

$\frac{630:10}{1000:10}=\frac{63}{100}$

Let's write the decimal fraction as a mixed fraction.

Since there is one digit after the decimal point, we divide 4 by 10 and add 1 which represents one whole number, as follows:

$1+\frac{4}{10}$

Now let's divide the simple fraction by the highest number that can divide both the numerator and denominator, in this case the number is 2:

$1+\frac{4:2}{10:2}=1+\frac{2}{5}=1\frac{2}{5}$

Let's write the decimal fraction as a mixed fraction.

Since there is one digit after the decimal point, we divide 6 by 10 and add 2, as follows:

$2+\frac{6}{10}$

Now let's divide the simple fraction by the highest number that can divide both the numerator and denominator, in this case the number is 2:

$2+\frac{6:2}{10:2}=2+\frac{3}{5}=2\frac{3}{5}$

Let's write the decimal fraction as a mixed fraction.

Since there is one digit after the decimal point, we'll divide 9 by 10 and add 6, as follows:

$6+\frac{9}{10}$

Since it can't be simplified further, the answer is:

$6\frac{9}{10}$

Let's write the decimal fraction as a mixed fraction.

Since there is one digit after the decimal point, we will divide 3 by 10 and add 11, as follows:

$11+\frac{3}{10}$

Since it cannot be simplified further, the answer is:

$11\frac{3}{10}$

Let's write the decimal fraction as a mixed fraction.

Since there is one digit after the decimal point, we divide 4 by 10 and add 16, as follows:

$16+\frac{4}{10}$

Now let's divide the simple fraction by the highest number that can divide both the numerator and denominator, in this case the number is 2:

$16+\frac{4:2}{10:2}=16+\frac{2}{5}=16\frac{2}{5}$

In order to compare which is greater, we will compare the numbers by adding 0 to 0.30 in the following way:

$0.305\text{?}0.300$

Note that before the decimal point we have 0 in both numbers

After the decimal point in both numbers we have the number 3 and then the number 0

The different numbers are the last numbers 5 and 0

Since 5 is greater than 0 the appropriate sign is:

0.305 > 0.300

To compare which is greater, we will compare the numbers by adding 0 to 0.8 as follows:

$0.80\text{?}0.08$

Let's note that before the decimal point, we have 0 in both numbers

After the decimal point, we have 8 versus 0

Since 8 is greater than 0, the appropriate sign is:

0.80 > 0.08

In order to compare which is larger, we'll compare the numbers by adding 0 to 0.08 in the following way:

$0.008\text{?}0.080$

Note that before the decimal point we have 0 in both numbers

After the decimal point in both numbers we have 0

The different numbers are the following ones, 0 versus 8

Since 8 is greater than 0, the appropriate sign is:

0.008 < 0.080