In the previous section we discussed about the addition of decimals. We also saw decimals which have a 'whole number part' before the decimal point. This whole number part can take any high value. There is no upper limit. But there is a definite lower limit. This lower limit is '1'. Because, if it is less than 1, it is a proper fraction. A proper fraction, when written in the decimal form, will not have any digits before the decimal point. In this section we will discuss the comparison of decimals with whole number part. We will also see how to represent decimals on a number line. And later in this section we will see subtraction of decimals.
We have seen the place values of each digit after the decimal point. We have learnt the place values of each digit in whole numbers in lower classes. We can now combine the two. The fig.6.19 below shows an example.
Now we will learn how to mark decimals on a number line. Consider for example 0.4
We have seen the place values of each digit after the decimal point. We have learnt the place values of each digit in whole numbers in lower classes. We can now combine the two. The fig.6.19 below shows an example.
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| Fig.6.19 |
Now we will learn how to mark decimals on a number line. Consider for example 0.4
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| Fig.6.20 |
In the number line, 1, 2 etc, marked with thick lines represent 'whole numbers'. The space between these whole numbers is divided into 10 equal parts. Thus each part will represent 0.1. So 0.4 can be easily marked as shown in the fig.6.20
Let us mark another decimal number. This time 1.6. It comes after '1'. Six small divisions after 1 will represent 1.6 as shown in the fig. 6.21 below:
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| Fig.6.21 |
In the two examples that we saw above, both the decimals had only one digit after the decimal point. We know that, this first digit after the decimal point represents 'tenths'. If there is a second digit, it will represent hundredths. We will have to divide the space between whole numbers into '100 equal parts'. It is not convenient to do so in ordinary sized sheets of paper. We will require large sheets of paper to mark such divisions. But if we have a 'graph paper', we will be able to mark hundredths. Because, very small spaces are already marked on graph papers.
Now let us see the comparison of decimals 'with whole number parts' before the decimal point. Consider 15.19 and 16.099. We can pick out the larger of the two with out any difficulty: The larger is 16.099. This is because in the 'whole number part' 16 is greater than 15. We do not even have to see the values in the decimal part for making the comparison.
But consider 15.19 and 15.099. Here things are different. Both have 15 before the decimal point. So the larger number will be decided by the values after the decimal point. We have already discussed the 'comparison of the decimal parts' in the previous section. Based on that, we will be able to find that 0.19 is larger than 0.099. Thus 15.19 is larger than 15.099
Subtraction of Decimals
Just like addition, subtraction can also be done using the 'usual subtraction procedure'. Let us see some examples: (i) Subtract 3.57 from 7.89 (ii) Subtract 4.31 from 16.52 (iii) Subtract 14.315 from 29.579: |
| Fig.6.22 |
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| Fig.6.23 |
In the next section we will see some practical applications of decimals.
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