What are “like” place values in decimals?
As we have learned before, every digit in a number has a place value. While referring to decimals, a number consists of a whole number and a fractional part, separated by a decimal point. “Like” place values in decimals are for those decimal numbers that have the same number of digits after the decimal point. It is suitable for arithmetic operations such as addition and subtraction. For example, 5.36 and 7.82 are like decimals as they both have 2 decimal places after the decimal point.
What is Regrouping?
In simple terms, regrouping is for creating groups of tens during addition and subtraction. Regrouping is done either by carrying over or borrowing. In regrouping, each group can be grouped by 10 and be moved to the immediate left as 1 group. For example, 10 hundredths will be grouped to form 1 tenths and that group will be moved to the left, thereby increasing the tenths by 1.
What is estimating in Decimals
Estimating numbers makes calculations easier. When we estimate decimals, we round them to the nearest whole number. For example, 4.68 can be rounded to 5, and 7.3 can be rounded to 7. When we estimate numbers, we also obtain an approximate answer to a specific mathematical operation. If we need to add 4.68 and 7.3, when rounded off, the estimate will be five added to seven, which is 12. However, the actual answer of 4.68 added to 7.3 is 11.98, quite close to the estimated answer of 12.
Solved Examples
1) Add: 45.76 + 28.18
Answer: First, let us line up the like place values to line up the decimal points.
45.76
+ 28.18
Now, we will begin adding the hundredths and the tenths. We will regroup, wherever necessary. In this sum, we regroup 14 hundredths as 1 tenths and 4 hundredths. After that, we add the ones and then the tens.
The answer is 69.94.
2)Add 42.46 + 49.39 and then round it to the nearest number.
Answer: First, we will line up the like place values to line up the decimal points.
42.46
+ 49.39
Now, we will begin adding the hundredths and the tenths. We will regroup, wherever necessary. In this sum, we will regroup 15 hundredths as 1 tenths and 5 hundredths. We will carry over the 1 to the tenths place.
Now, we will add the ones, and then the tens. We will regroup, wherever necessary. We will regroup 11 ones to 1 tens and 1 ones.
The answer is 91.85. We will round it to the nearest whole number, which is 92.
3) Subtract: 17.83 – 6.55
Answer: Let us first line up like place values to line up the decimal points.
17. 8 3
– 6. 5 5
Now, we will begin the subtraction with the hundredths, and then the tenths place. We will regroup wherever necessary. We will regroup 3 hundredths as 13 hundredths and 8 tenths as 7 tenths.
After this, we will subtract the ones and then the tens.
11.28 is the answer.
4) Sophie received $25.50 as her weekly allowance. Out of that, she bought coloring books for $12.15 and donated $2.09 for a marathon. How much money is Sophie left with?
Answer: Total amount of money Sophie has = $25.50
Amount of money Sophie spent on coloring books = $12.15
Amount of money Sophie donated for the marathon = $2.09
Thus, the amount of money Sophie is left with = Total amount of money Sophie originally had – total amount of money Sophie spent.
Amount of money Sophie is left with = Total amount of money Sophie originally had – (Amount of money spent on coloring books + Amount of money donated for the marathon).
Let us use the order of operations to solve this sum.
First, we will add 12.15 + 2.99
12 . 1 5
+ 2 . 0 9
Now, we will begin adding the hundredths and the tenths. We will regroup, wherever necessary. In this sum, we will regroup 14 hundredths as 1 tenth and 4 hundredths. Then we will continue the addition by adding the ones and the tens.
In the second step, we will subtract 25.50 – 14.24
Let us now begin the subtraction with the hundredths, and then the tenths place. We will regroup wherever necessary. We will regroup 0 hundredths as 10 hundredths and 5 tenths as 4 tenths. Then we will subtract the ones and the tens.
Sophie is thus left with $11.26 in total.
Decimal numbers and whole numbers can be added together in a simple way. We can place a decimal point after the whole number and add zeros after the decimal point to make both the numbers like decimals. Both the numbers should be aligned as per their place value. For example, if we add 2 and 3.56, it will look like this:
3.56
+ 2.00
————
5.56
We are adding two zeros after the whole number 2, to convert the whole number into a decimal.
Here are a few things that you should know about the addition and subtraction of decimals:
- The numbers should be written vertically, and the decimal points should be lined up accordingly. You can add in zeros as placeholders to balance the two sides of the decimal points.
- Carry over (for addition) or borrow (for subtraction), wherever necessary.
- When you’re finding the answer, make sure you line up the decimal point with the numbers that you added or subtracted.