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

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 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'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:

$11\frac{3}{10}$

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

To compare which is greater, we'll compare the numbers by adding 0 to 0.35 as follows:

$0.350\text{?}0.135$

We notice that before the decimal point, we have 0 in both numbers

After the decimal point, we have 3 versus 1

Since 3 is greater than 1, the appropriate sign is:

0.350 > 0.135

Let's compare the numbers in the following way:

We notice that before the decimal point, both numbers start with 1

Then we have the number 9 versus the number 7

Since 9 is greater than 7, the appropriate sign is:

19.88 > 17.10

Let's compare the numbers in the following way:

We notice that before the decimal point, both numbers start with 1 and then 0

After that, the numbers are different, 1 versus 2

Since 2 is greater than 1, the appropriate sign is:

101.0 < 102.1

Let's compare the numbers in the following way:

We notice that before the decimal point, both numbers start with 202

After the decimal point, we notice that the number is 1 versus 0

Since 1 is greater than 0, the appropriate sign is:

202.1 > 202.01

Let's compare the numbers in the following way:

We notice that before the decimal point, we have the number 66 versus the number 6

Since 66 is greater than 6, the appropriate sign is:

66.101 > 6.6101

Let's compare the numbers in the following way:

We notice that before the decimal point, we have the numbers 2 and 20

Since 20 is greater than 2, the appropriate sign is:

2.021 < 20.21

Let's compare the numbers in the following way:

We notice that before the decimal point, both numbers start with 24

After the decimal point, we have the number 3

Then the numbers are 0 versus 1

Since 1 is greater than 0, the appropriate sign is:

24.305 < 24.315

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:

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