Decimal number is a number. It has two parts. That is whole number part and a fractional part. The “.” is called the decimal point.
Ordering decimals:
Suppose if we have a two or more decimal, we need to arrange the decimals using tenths, hundreds and thousands place.
Comparing decimals:
Suppose if we have a two decimal numbers we can compare them. Normally one number is greater than, less than or equal to another number. Here we are going to see some examples for how to compare and order decimal values.
Mathematical Concepts in Comparing and Ordering Decimals
- To compare decimals start at the left and compare digits in the same places, find first the place where the decimals differs,
- Equal decimals can be written by adding zeros or deleting zeros from the right of the last non zero digit.
- Adding zeros at the end of the decimal does not change it value. On the other hand, adding zeros before the first decimals digit changes its value.
- To compare and order decimals having different number of digits, put zeros at the end of the shorter decimals to have the same number of digits, then compare and order the numbers as if the decimal points.
Comparing and Ordering Decimals:
- Compare and order decimals through hundred thousandths.
- Use the symbols >, <, or = correctly in comparing decimals.
- List decimal in the order least to greatest.
Problem in comparing and ordering decimals
When you compare decimals, think about place value you can add or remove zeros at the end of the decimal without changing its meaning.
0.2 = 0.20 =0.200 =0.2000
0.54 = 0.540 = 0.5400 = 0.54000
3.5 = 3.50 = 3.500 = 3.5000
The ordering decimal is 3.5, 0.2,0.54.
Rule : To compare two decimals, first convert the given decimals into like decimals and then compare the whole number parts. The decimal with greater whole number part is greater. If the whole number parts are equal, then compare the tenths digits. The decimal with the bigger digit at tenths place is greater. If the tenths digits are equal, then compare the hundredth digits and so on.
i)In 2.5 and 3.5
Here we can notice that both are like decimals number and the tenths place is same so, comparing the whole number parts of two decimals, we have 3 > 2
Hence, 3.5 > 2.5
ii) In 15.12 and 15.39
Here we can notice that both are like decimals num
ber so, comparing the whole number parts of two decimals, we have 15=15
Now comparing the digits at tenths place, we have 1 <>
Hence, 15.12 <>
iii)In 5.147 and 5.14
Here we need to convert the unlike decimal to like decimal i.e., 5.14 = 5.140, so compare 5.147 and 5.140
Comparing the whole number parts of two decimals, we have 5 = 5
Now, comparing the digits at tenths place, we have 1 = 1
Next, comparing the digits at hundredths place, we have 4 = 4
Finally, comparing the digits at thousandths place, we have 7 > 0
Hence, 5.147 > 5.14.
iv)In 3.159 and 3.15
Here we need to convert the unlike decimal to like decimal i.e., 3.15 = 3.150, so compare 3.159 and 3.150
Comparing the whole number parts of two decimals, we have 3 = 3
Now, comparing the digits at tenths place, we have 1 =1
Next, comparing the digits at hundredths place, we have 5 = 5
Finally, comparing the digits at thousandths place, we have 9 > 0
Hence, 3.159 > 3.150.
5)Arrange 12.4, 135.25, 14.648, 115.35 in ascending order and descending order.
Converting the given decimals into like decimals, we have,
12.400, 135.250, 14.648, 115.350.
Here we notice that in all the numbers the whole number part is different so we need to arrange the whole number from smaller to bigger.
Thus arranging in ascending order, 12.400 <>
Hence, the given decimals in ascending order are :
12.400 <>
Thus arranging in descending order we need to arrange the whole number from bigger to smaller,
135.250 > 115.350 > 14.648 > 12.400 since 135 > 115>14>12.
Hence, the given decimals in descending order are :
135.250 > 115.350 > 14.648 > 12.400 (descendingorder).
Comparing Decimals:
This step explains the kids that how to compare the decimal valuesWhen 0's are add to the right of the decimal number, the number is not changed.
To compare decimals, we compare the values,
Step 1: Start at the left side; Solve the first place where the numbers are different
Step 2: Compare the digits that are different.
If there are two decimal numbers we can compare them. One number is either greater than, less than or equal to the other number.
A decimal number is just a fractional number. Comparing 0.7 and 0.07 is clearer if we compared 7/10 to 7/100. The fraction 7/10 is equivalent to 70/100 which is clearly larger than 7/100.
Therefore, when decimals are compared start with tenths
place and then hundredths place, etc. If one decimal has a higher number in the tenths place then it is larger than a decimal with fewer tenths. If the tenths are equal compare the hundredths, then the thousandths etc. until one decimal is larger or there are no more places to compare. If each decimal place value is the same then the decimals are equal.
Place Value
To understand decimal numbers you must first know about
When we write numbers, the position (or "place") of each number is important.
In the number 327:
- the "7" is in the Units position, meaning just 7 (or 7 "1"s),
- the "2" is in the Tens position meaning 2 tens (or twenty),
- and the "3" is in the Hundreds position, meanin g 3 hundreds.
From Units, to Tens, to Hundreds
... and ...
And that is a Decimal Number!
Decimal Point
The decimal point is the most important part of a Decimal Number. It is exactly to the right of the Units position. Without it, we would be lost ... and not know what each position meant.
Now we can continue with smaller and smaller values, from tenths, to hundredths, and so on, like in this
example:
Large and Small
So, our Decimal System lets us write numbers as large or as small as we want, using the decimal point. Numbers can be placed to the left or right of a decimal point, to indicate values greater than one or less than one.
17.591The number to the left of the decimal point is a whole number
As we move further left, every number place gets 10 times bigger.
The first digit on the right means tenths (1/10).
As we move further right, every number place gets 10 times smaller (one tenth as big).
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