Decimal Fractions - Advanced - Examples, Exercises and Solutions

Determine whether the exercise is correctly written or not.

The position of the decimal point corresponds..

Let's fill in the zeros in the empty space as follows:

$006.310\\+216.222\\\$We should note that the decimal points are written one below the other.

Therefore, the exercise is written in the appropriate form.

True

Determine whether the exercise is correctly written or not.

The position of the decimal point corresponds.

Let's fill in the zeros in the empty space as follows:

$21.52\\+03.40\\$

Note that the decimal points are written one below the other

Therefore, the exercise is written in the correct form

True

Determine whether the exercise is correctly written or not.

The position of the decimal point corresponds.

La posición del punto decimal coincide.

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

Therefore, the exercise is not written correctly.

Not true

Determine whether the exercise is correctly written or not.

The position of the decimal point corresponds.

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

Therefore, the exercise is not written correctly.

Not true

Solve the following exercise and circle the appropriate answer:

Let's solve the exercise in order:

We'll subtract the tenths after the decimal point:

$1-0=1$

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

$2-2=0$

$2-1=1$

And we get:

$22.1\\-12.0\\10.1$

10.1

Fill in the missing sign:

$66.101\text{ }_{—\text{ }}6.6101$

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

>

Fill in the missing sign:

$2.021\text{ }_{—\text{ }}20.21$

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

<

$8.5+5.2+8.4=$

We will break down each of the factors in the exercise into a whole number and its remainder.

We get:

$8+0.5+5+0.2+8+0.4=$

Now we'll combine only the whole numbers:

$8+5+8=13+8=21$

Now we'll calculate the remainder:

$0.5+0.2+0.4=0.7+0.4=1.1$

And now we'll get the exercise:

$21+1.1=22.1$

22.1

$10.1x+5.2x+2.4x=$

We will factor each of the terms in the exercise into a whole number and its remainder.

We get:

$10x+0.1x+5x+0.2x+2x+0.4x=$

Now we'll combine only the whole numbers:

$10x+5x+2x=15x+2x=17x$

Now we'll calculate the remainder:

$0.1x+0.2x+0.4x=0.3x+0.4x=0.7x$

And now we'll get the exercise:

$17x+0.7x=17.7x$

17.7X

$4.1\cdot1.6\cdot3.2+4.7=\text{?}$

We begin by converting the decimal numbers into mixed fractions:

$4\frac{1}{10}\times1\frac{6}{10}\times3\frac{2}{10}+4\frac{7}{10}=$

We then convert the mixed fractions into simple fractions:

$\frac{41}{10}\times\frac{16}{10}\times\frac{32}{10}+\frac{47}{10}=$

We solve the exercise from left to right:

$\frac{41\times16}{10\times10}=\frac{656}{100}$

This results in the following exercise:

$\frac{656}{100}\times\frac{32}{10}+\frac{47}{10}=$

We solve the multiplication exercise:

$\frac{656\times32}{100\times10}=\frac{20,992}{1,000}$

Now we get the exercise:

$\frac{20,992}{1,000}+\frac{47}{10}=$

We then multiply the fraction on the right so that its denominator is also 1000:

$\frac{47\times100}{10\times100}=\frac{4,700}{1,000}$

We obtain the exercise:

$\frac{20,992}{1,000}+\frac{4,700}{1,000}=\frac{20,992+4,700}{1,000}=\frac{25,692}{1,000}$

Lastly we convert the simple fraction into a decimal number:

$\frac{25,692}{1,000}=25.692$

25.692

What is the number of the tenths?

1.3

3

What is the number of the ones?

0.4

0

What is the number of the ones?

0.07

0

What is the hundredth?

0.96

6

What is the number of the ones?

0.81

0