Decimal Fractions - Advanced - Examples, Exercises and Solutions

First let's fill in the zeros in the empty spaces as follows:

$21.52\\+03.40\\$Note that the decimal points are written one below the other.

Therefore, the positions of the decimal points correspond and thus the exercise is written in the correct form.

First let's fill the zeros in the empty space as follows:

$006.310\\+216.222\\\$

Here We should note that the decimal points are written one below the other.

Therefore, the exercise is written in the appropriate form.

Note that the decimal points are not written one below the other. They do not correspond.

Therefore, the exercise is not written correctly.

Note that the decimal points are not written one below the other. They do not correspond.

Therefore, the exercise is not written correctly.

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:

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

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 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 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 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:

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

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

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

Let's solve the exercise in order.

First, we'll subtract the tenths after the decimal point:

$1-0=1$

Then, we'll subtract the whole numbers before the decimal point accordingly:

$2-2=0$

$2-1=1$

We obtain:

$22.1\\-12.0\\10.1$

Let's solve the exercise in order:

We'll add up the hundredths after the decimal point:

$8+1=9$

We'll add up the tenths after the decimal point:

$3+4=7$

Finally, we'll add up the whole numbers before the decimal point accordingly:

$1+3=4$

$2+1=3$

And we get:

$21.38\\+13.41\\34.79$