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Numbers are among the most basic concepts of mathematics. Children get introduced to numbers in the kindergarten curriculum. As they grow up, they advances to different types of numbers such as whole numbers, natural numbers, decimal numbers, rational numbers etc. All these numbers are based on decimal number system with a base of ten and it uses the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9.
Kids relate natural numbers and whole numbers to things they see around them. Decimal numbers are something they get introduced at a later stage. It is highly recommended to use good math manipulatives like base 10 blocks, 10 by 10 grids and other place value models for introducing the topic. This gives a better visual understanding of the topic that stays deeper.
Using math games for 4th graders for further practice of the topic is also recommended. This enables kids to get a repeated practice resulting in computational fluency.
SplashLearn deals with the decimals topic in a very detailed manner with a lot of worksheets and practice problems in various sections.
By grade 4, children are already comfortable with the concept of place values for whole numbers.
To revise it, consider the whole number 489.
The number at the right most, 9 is at one's place, the number 8 at ten’s place and the number 4 at the hundred’s place.
That is, there are 4 hundreds, 8 tens and 9 ones in the number 489.
The number can be decomposed as 
.
In whole numbers, as you go from right to left, the place value gets multiplied by 10. In other words, as you go from left to right, the place value gets divided by 10. What happens if we go further right to the one's place? As per the logic so far, the place value should get divided by another 10. Let us use this logic to extend the place value system to non-whole numbers, in this context, to decimal numbers.
Going further to the right of one's place, the place value should get reduced by one-tenth as it gets divided by 10. This place value of decimals is called tenths. When you move another place to the right, the place value further gets divided by 10, with a value of one-hundredth. This place value is called hundredth.
So, the place value till the one’s place is greater than one and the place values of the numbers right to it are less than one. To mark this segregation a dot called a decimal point is used. The numbers right to the decimal point is called the decimal part and the numbers on the left are called the integral part or whole number part.
Thus, the structure of the base-ten system is uniform. A place value chart with decimals for first two decimal places can be represented as below.
A decimal number can be written as an integral part, decimal point, and a decimal part. For example, the number 32.45 where 4 has a place value of tenths and 5 has hundredths is a decimal number.
Thus, the number 32.45 can be decomposed as 
.
There are 4 one-tenths in the decimal number 32.45. Each one-tenth can be shown as a shaded part when the whole is divided equally into 10 parts.
Similarly, 4 one-tenth or 
can be represented by shading 4 parts.
There are 5 one-hundredths in the decimal number 32.45. Each one-hundredth can be shown as a single shaded square when the whole is divided equally into hundred as a 10 by 10 grid.
So, 5 one-hundredth or 
can be represented by shading 5 squares in the 10 by 10 grid.
Whole numbers also can be written as decimals with zero decimal parts. That is, number 4 as a decimal can be written as 4.00. Similarly, 10 as a decimal can be written as 10.00.
Decimals smaller than 1 may be written with or without zero before the decimal point. That is, both 0.25 and .25 are correct ways to write the decimal.
Children learn about non-terminating decimals and how to round decimals at a later stage. For example, when you write one third as a decimal, it does not terminate. Rounding decimal is an option to find the approximate value there.
SplashLearn has decimal place value worksheets for numbers less than 1 and for the numbers greater than 1 separately in detail.
Once the children are comfortable with the definition of decimals, they can be introduced to its connection with fractions.
Consider the decimal 0.34. According to the base-ten place value system, there are 3 tenths and 4 hundredths in the number 0.34. That is, it can be expanded as 0 ones + 3 tenths + 4 hundredths.
= 
Now, the fraction 
can be represented by shading 3 parts of a whole divided equally into 10.
This is equivalent to 30 small squares shaded in the 10 by 10 grid.
Therefore, 
or in words, 3 tenths is equivalent to 30 hundredths. So, 0.3 and 0.30 are equivalent decimals.
The above result can also be explained using equivalent fractions. To find a fraction equivalent to , the numerator and the denominator have to be multiplied by the same number. Multiply the numerator and denominator by 10. 
Thus, 
and 
are equivalent fractions.
Coming back to the addition:
Therefore, 0.34 = 
.
It can be read as 34 hundredths or 3 tenths 4 hundredths.
The converting fraction worksheets provided by SplashLearn has a handful of questions that models tenths and hundredths using fractional strips.
The conversion from decimal to a fraction is explained using the area models and decimal place value chart in the above section.
Converting fractions to decimal can be done in two ways. One way is to write the fraction with a denominator as multiple of 10.
For example, to write the fraction 1/5 as a decimal, multiply the numerator and the denominator of the fraction by 2.
Now, 2 tenths can be converted to decimal easily as 0.2. Thus, 
.
To write 5/4 as a decimal, multiply the fraction by 25/25.
The whole number 125 can be written as 125.0 as a decimal. When you divide a number by 100, the decimal point is shifted 2 decimal places to the left.
That is:
Thus, 
.
Another method is to divide the numerator of the fraction by the denominator.
To write 2/5 as a decimal, divide 2 by 5.
The child can either use a decimal calculator or find the quotient by long division.
Thus, 2/5 as a decimal can be written as 0.4.
Note that, the fractions with denominator 10 or 100 also goes through the same process when written in decimal. To write 3/10 as a decimal, divide 3 by 10 resulting in the shift of decimal point one decimal place to the left. Thus 3/10 = 0.3.
The integral parts of a mixed fraction and the corresponding decimal are the same. So, to convert mixed number to decimal, first write down the same integral part. Further, the fractional part has to be converted to decimal. Consider the mixed number 
to convert to decimal. The fraction 
is equivalent to the decimal .2. Thus, 
.
Similarly, the number 5.82 can be converted to a fraction as 
.
Once the children are familiar with the conversions between the decimals and fractions, it is easy to mark decimals on a number line. The child’s previous knowledge about rounding numbers can be used in rounding decimals to locate the approximate place on a number line.
Given a decimal number, say 0.35, the child estimates that it is a number between zero and 1 and it is closer to 0 than 1. The number has 3 at the tenth decimal place and 5 at the hundredth decimal place. Since 0.35 is equivalent to 35 hundredths the point can be plotted on the 35th mark when the unit measure from 0 to 1 on a number line is divided equally into 100 parts. In a simplified form, the number can be plotted right at the middle of 0.3 and 0.4 when the whole from 0 to 1 is divided equally into 20 parts.
The worksheets for representing decimals in different ways give a good practice for kids.
Another skill learned at the grade 4 level is comparing decimals based on their sizes.
One needs to realize that comparisons are valid only when the two decimals refer to the same whole. Logically it is very easy to understand using fractional strips.
Here, the two wholes divided into equally into 10 parts each are shown. In the first whole, the 4 parts are shaded and in the second one, 6 are shaded. But if you compare the area of shaded parts, though 4 < 6, the area shaded in the first whole is more than that of the second. So, the comparison is not valid.
Consider the another set of wholes as shown:
The wholes are equal in size but the first whole is divided into 10 equal parts and the second whole into 100.
The number of parts shaded in the first one is 4 and in the second one is 30. Though 30>4, it is clear that the shaded area in the first is greater than that in the second. It is because the first whole is divided into 10 equal parts and the second whole is divided into 100 equal parts. The shaded region in the first whole is 4 tenths and that in the second one is 30 hundredth. 4 tenths are equivalent to 40 hundredths and 40 hundredths are greater than 30 hundredths. Thus, the comparisons are valid only when the two decimals refer to the same whole.
For example, compare the decimals 0.8 and 0.28.
When you convert the decimals to fractions, 
and 
the two fractions do not have the same whole.
The decimal 0.8 is 8 tenths and 0.28 is 28 hundredths. To compare the decimals the child need to write 8 tenths as 80 hundredths. Now, the two, 80 hundredths and 28 hundredths refer to the same whole.
Since 80 > 28, 80 hundredths is greater than 28 hundredths and thus 0.8 > 0.28.
Comparing decimals less than 1 can be practiced at SplashLearn.
To make the kids understand the real world applications of the topic, decimal word problems can be illustrated.
Evaluation:
Ans: 3.12
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Ans: 0.6
