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Ordering Decimals
In ordering decimals we will learn how to compare two or more decimals.
(i) Convert each of them as like decimals.
(ii) Compare these decimals just as we compare two whole numbers ignoring decimal point.
1. Which is greater of 0.89 and 2.01?
Since whole number part 2 > whole number part 0
Therefore, 2.01 > 0.89
2. Arrange in increasing order: 4.91, 13.01, 12.1, 18.123, 13.9, 4.53
Largest decimal places are in 18.123 that is 3
Therefore, convert each of the decimal number into like decimals with 3 decimal places.
4.91 = 4.910 ....... 2
13.01 = 13.010 ....... 4
12.1 = 12.100 ....... 3
18.123 = 18.123 ....... 6
13.9 = 13.900 ....... 5
4.53 = 4.530 ....... 1
4.53, 4.91, 12.1, 13.01, 13.9, 18.123
3. Write the decimal numbers in ascending order using
< sign:
(i) 4.926, 18.324, 18.428, 18.528, 18.234
The given decimal numbers are like decimals with 3 decimal places.
To arrange the decimal numbers in ascending order, first check the whole number part of all the decimal numbers. We see 4 is the smallest whole number part so, 4.926 is the smallest decimal number.
The rest of the decimal numbers have the same whole number part i.e. 18. Now we will compare the decimal part of 18.324, 18.428, 18.528 and 18.234 just as we compare the whole numbers ignoring the decimal points.
Clearly, we see 234 < 324 < 428 < 528
i.e. 18.234 < 18.324 < 18.428
< 18.528
Therefore, 4.926 < 18.234 < 18.324 < 18.428 < 18.528
(ii) 72.09, 72.19, 72.91, 72.17, 72.81
The given decimal numbers are like decimals with 2 decimal places and they have the same whole number part i.e. 72.
Now we will compare the decimal part of 72.09, 72.19, 72.91, 72.17 and 72.81 just as we compare the whole numbers ignoring the decimal points.
Clearly, we see 09 < 17 < 19 < 81 < 91
Therefore, 72.09 < 72.17 <
72.19 < 72.81 < 72.91
(iii) 301.13, 301.03, 301.31, 301.30
Since the whole number part of all the decimal numbers are same here we need to compare the decimal part just as we compare the whole numbers ignoring the decimal points.
301.13, 301.03, 301.31, 301.30
Clearly, we see 03 < 13 < 30 < 31
Therefore, 301.03 < 301.13 < 301.30 <
301.31
(iv) 107.08, 107.81, 107.80, 107.88
These decimal numbers are like decimals with the same whole
number part so we compare these decimals just as we compare the whole numbers
ignoring decimal point.
107.08, 107.81, 107.80, 107.88
Clearly, we see 08 < 80 < 81 < 88
Therefore, 107.08 < 107.80 < 107.81 < 107.88
4. Arrange 32.21, 2.324, 14.73, 6.4 in ascending order.
Solution:
On converting the decimal fractions into like decimals, we get
32.210, 2.324, 14.730,6.400
Now, 2.324 is the smallest decimal. The next decimal greater than 2.324 is 6.400. The other decimals in ascending order are: 14.730, 32.210.
Then, the given decimals in ascending order are:
2.324, 6.400, 14.730, 32.210, i.e., 2.324, 6.4, 14.73, 32.21.
5. Arrange 2.49, 7.16, 23.5, 5.35 in descending order.
Solution:
The greatest decimal is 23.5. The next decimal smaller than 23.5 is 7.16. The other decimals in descending order are 5.35 and 2.49.
Hence, the given decimals in descending order are:
23.5, 7.16, 5.35, 2.49.
Worksheet on Comparing and Ordering Decimals:
1. Compare the following pairs of decimals:
(i) 8.27 and 3.26
(ii) 5.312 and 5.407
(iii) 3.21 and 0.513
(iv) 35.146053 and 1.067
(v) 23.07 and 21.156
(vi) 0.467 and 0.87
Answer:
1. (i) 8.27 > 3.26
(ii) 5.312 < 5.407
(iii) 3.21 > 0.513
(iv) 35.146053 > 1.067
(v) 23.07 > 21.156
(vi) 0.467 < 0.87
2. Arrange the following decimals in descending order:
(i) 6.6, 23.94, 7.96, 35.275
(ii) 12.05, 42.14, 16.50, 8.69
(iii) 36.75, 58.5, 48.6, 9.7
(iv) 86.351, 205.25, 346.87, 87.4
Answer:
2. (i) 35.275, 23.94, 7.96, 6.6
(ii) 42.14, 16.50, 12.05, 8.69
(iii) 58.5, 48.6, 36.75, 9.7
(iv) 346.87, 205.25, 87.4, 86.351
3. Arrange the following decimals in ascending order:
(i) 26.5, 5.07, 82.008, 23.4
(ii) 27.6, 24.63, 39.532, 76.943
(ⅲ) 47.6, 31.085, 37.54, 142.514
(iv) 0.33, 0.3, 3.03, 3.033
Answer:
3. (i) 5.07, 23.4, 26.5, 82.008
(ii) 24.63, 27.6, 39.532, 76.943
(iii) 31.085, 37.54, 47.6, 142.514
(iv) 0.3, 0.33, 3.03, 3.033
4. Arrange the following in ascending order.
(i) 2.35, 0.98, 2.53, 5.25, 3.25, 1.35, 5.68
(ii) 4.627, 4.067, 3.798, 6.297, 4.729, 3.628, 4.236
(iii) 0.9, 0.92, 0.29, 0.39, 0.93, 0.039, 0.835, 0.49
(iv) 423.5, 234.5, 542.3, 324.5, 204.73, 624.38, 322.22
4. (i) 0.98 < 1.35 < 2.35 < 2.53 < 3.25 < 5.25 < 5.68
(ii) 3.628 < 3.798 < 4.067 < 4.627 < 4.729 < 6.297
(iii) 0.039 < 0.29 < 0.39 < 0.49 < 0.835 < 0.9 < 0.92
(iv) 204.73 < 234.5 < 322.22 < 324.5 < 423.5 < 542.3
5. Arrange the following in descending order.
(i) 31.5, 16.7, 16.9, 3.004, 16.07, 24.38, 18.57, 14.32
(ii) 31.0, 24.3, 23.4, 42.3, 4.234, 18.26, 24.09, 25.43
(iii) 4.008, 4.803, 4.308, 3.840, 4.830, 6.038, 4.380, 4.038
(iv) 12.0, 13.4, 12.7, 21.4, 13.03, 17.09, 19.9, 24.62
Answer:
5. (i) 31.5 > 24.38 > 18.57 > 16.9 > 16.7 > 16.07 > 14.32 > 3.004
(ii) 42.3 > 31.0 > 25.43 > 24.3 > 24.09 > 23.4 > 8.26 > 4.234
(iii) 6.038 > 4.830 > 4.803 > 4.380 > 4.308 > 4.038 > 4.008 > 3.840
(iv) 24.62 > 21.4 > 19.9 > 17.09 > 13.4 > 13.03 > 12.7 > 12.0
6. Arrange the following in ascending order.
(i) 132.45, 123.54, 213.54, 312.9, 132.74
(ii) 87.94, 78.89, 118.93, 109.76, 98.79
(iii) 204.03, 240.3, 24.003, 420.3
Answer:
6. (i) 123.54, 132.45, 132.74, 213.54, 312.9
(ii) 78.89, 87.94, 98.79, 109.76, 118.93
(iii) 24.003, 204.03, 240.3, , 420.3
7. Arrange the following in descending order.
(i) 105.89, 523.52, 215.43, 314.69, 105.08
(ii) 72.35, 172.35, 117.53, 97.17, 107.35
(iii) 411.32, 421.12, 411.23, 432.11
Answer:
7. (i) 523.52, 314.69, 215.43, 105.89, 105.08
(ii) 172.35, 117.53, 107.35, 97.17, 72.35,
(iii) 432.11, 421.12, 411.32, 411.23
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