Place value charts
A place value chart ensures that the digits are in their proper places. It helps with the comparison, addition, and subtraction of numbers. The place value of each digit can be easily shown through a place value chart. The value of a place is 10 times the value of the place to its right. Also, the value of each place is one-tenth \(\left(\frac{1}{10} \right)\) the value of the place to its left.
What are Decimal places?
The places to the right of the decimal point are called the decimal places. Tenths, hundredths, thousandths, and so on, are decimal places.
For example, in 3.2, 3 is in the ones place and 2 is in the tenths place.
Steps for adding and subtracting Decimals
We have to follow some basic steps to add decimal numbers, and the steps are as follows:
Step 1: Align the decimal numbers according to their place values first, such that their decimal points are lined up.
Step 2: If necessary, convert decimals to like decimals.
Step 3: Add or subtract the numbers and place the decimal point in the sum or difference according to the numbers added or subtracted, such that all the decimal points are aligned.
Example: Add: 55.23 + 12.41
Solution: First, let us line up the like place values, which leads to the lining up of the decimal places.
55.23
+ 12.41
Now, we will begin adding from the extreme right.
55.23
+ 12.41
—————
67.64
The answer is 67.64.
Example: Subtract: 77.14 – 8.62
Solution: Let us first line up like place values and line up the decimal places.
77.14
– 8.62
Now, we will begin the subtraction from the extreme right.
The answer is 68.52.
How do we solve problems involving both the addition and subtraction of decimals?
In case a problem involves both operations simultaneously, some rules need to be followed:
Step 1: Always perform the operation in the parentheses first.
Step 2: Once the above step is completed, then proceed with the addition of decimals.
Step 3: Finally, proceed with subtraction.
Solved Addition and Subtraction of Decimals Examples
Example 1: Add: 25.23 + 2.41
Solution: First, let us line up the like place values to line up the decimal points.
25.23
+ 2.41
Now, we will begin adding from the extreme right.
25.23
+ 2.41
—————
27.64
The answer is 27.64.
Example 2: Subtract: 17.14 – 8.62
Solution: Let us first line up like place values to line up the decimal points.
17. 14
– 8.62
Now, we will begin the subtraction from the extreme right.
The answer is 8.52.
Example 3: John has $100, with which he intends to buy various games. He first buys a game based on dice for $8.99 and then bowling pins for $33.50. His mother gave him an additional $20 so he could buy an archery target, but he got one for $16.50. How much money does he have remaining in total?
Solution:
Initial money that John has = $100
The cost of the game based on dice = $8.99
The cost of bowling pins = $33.50
Money remaining = 100 – (33.50 + 8.99)
Money given by John’s mother = $20
The cost of the archery target = $16.50
Money remaining in total (R) = 100 – (33.50 + 8.99) + 20 – 16.50
Step 1: Operation in parentheses
R =100 – 42.49 + 20 – 16.50
Step 2: Add
R =120 – 42.49 – 16.50
R =120 – (42.49 + 16.50)
Step 3: Subtract
R = $61.01
So, John is left with a total of $61.01.
A decimal number is the combination of an integral part and a decimal part. The decimal point is a point or dot used to separate the integral and the decimal part of a number.
When we do not line up the decimal points while adding or subtracting, it makes the addition or subtraction a bit difficult to solve and get the answer. It is essential that the decimals are aligned according to their place values before addition or subtraction, and if not, the answer may be incorrect.
Like decimals are decimals that have the same number of decimal places.
When the decimals are not like decimals, we add the required number of zeros to the right of the decimal to convert it to like decimals. This is done to make the addition or subtraction process easier.