Analysis: Let\"s usage our understanding of combined numbers to aid us analysis this problem.

You are watching: Do you line up decimals when adding

52.3 = 

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 and 973.41=
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Recall that a decimal number deserve to have a whole-number part and a fractional part. When adding decimals, you should first line up all the decimal clues in a column. Lining up the decimal point out ensures that each digit is in the appropriate place-value position. Once each digit is in the proper place-value position, the whole-number parts are inside wall up through each other, and also the fractional parts are inside wall up through each other. This is presented in the table below.

PLACE VALUE and DECIMALS
\"*\"
 
 
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\"*\"
\"*\"
 
\"*\"
 
\"*\"
 
\"*\"
\"*\"
 
\"*\"
\"*\"
 
\"*\"
\"*\"
 
 
\"*\"
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     52.3     
    973.41    
----------- Whole-Number component ----------- ---------- Fractional part -----------

Now the we have lined increase the decimal points, friend will notice that the number being included do not have the same number of decimal digits. Let\"s look at this trouble on record without a place-value chart.

52.3+ 973.41

You can write one extra zero to the ideal of the critical digit the the very first decimal so that both decimals have the same number of decimal digits.

52.30+ 973.41

Just just like whole numbers, start on the right, and include each column in turn. Keep in mind that friend are adding digits in the same place-value position.

52.30+ 973.41 1025.71

Place the decimal allude in the sum.

52.30+ 973.41 1025.71

Answer: The amount of 52.3 and also 973.41 is 1025.71.

Example 2: Add: 0.078 + 3.09 + 0.6

0.078 3.090+ 0.600

Analysis: If you need to carry (i.e. If a columns adds increase to much more than 9), mental to include the 10s digit that that shaft to the next column.

 1 0.078 3.090+ 0.600 3.768

Answer: The sum of 0.078 and 3.09 and also 0.6 is 3.768.

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Example 3: Add: $77.23 and $88

Analysis: every of these numbers represents money; however, the 2nd is composed as a totality number. Adjust the second number so that it has actually two decimal digits, and also then do the addition.

$ 77.23+ $ 88.00 $165.23

Answer: The sum of $77.23 and also $88 is $165.23.

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Procedure: To include decimals, follow this steps:

Line up all the decimal point out in a column.When needed, create one or more extra zeros to the appropriate so the both decimals have actually the same number of decimal digits.Start ~ above the right, and include each pillar in turn. (Add number in the exact same place-value position.)If you need to carry, mental to add the 10s digit of that shaft to the next column.Place the decimal point in the sum.

Example 4: Add: 28.5 + 34.5

Analysis: you will need to carry much more than once. Accordingly, the addition will be split into three procedures to display the process of carrying.

 1 1 1 1 1 28.5 28.5 28.5+ 34.5 + 34.5 + 34.5 .0   3.0   63.0

Answer: The sum of 28.5 and 34.5 is 63.

Example 5: Add: 3.986 + 37 + 25.902

 1 1 1 1 1 3.986 3.986 3.986 37.000 37.000 37.000+ 25.902 + 25.902 +25.902 .888   6.888  66.888

Answer: The sum of 28.5 and also 34.5 is 66.888.

Example 6: Add: $12.95 + $67.89 + $54.55

1 2 1 1  2 1 $ 12.95 $ 12.95 $ 12.95 $ 67.89 $ 67.89 $ 67.89+ $ 54.55 + $ 54.55    + $ 54.55 .39   $ 5.39   $135.39

Answer: The amount of $12.95 and also $67.89 and $54.55 is $135.39.

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Example 7: A dime rolling 5.8794 cm and also then rolled 7.48 cm. How much did it roll altogether?

 1 1 1 1 1 1 5.8794 5.8794 5.8794+ 7.4800 + 7.4800 + 7.4800 .3594   3.3594   13.3594

Answer: The sum of 5.8794 cm and also 7.48 cm is 13.3594 cm.

Summary: When adding decimals, you must first line up all the decimal point out in a column. Lining up the decimal point out ensures that each digit is in the suitable place-value position. You have the right to then add digits in the same place-value place to find the sum.

Exercises

Directions: read each concern below. You might use record and pencil to help you add. Click when in an answer BOX and form in your answer; then click ENTER. After friend click ENTER, a message will appear in the results BOX to suggest whether her answer is exactly or incorrect. To begin over, click CLEAR.

1.Add: 46.907 + 2.0184ANSWER BOX:   

RESULTS BOX: 

2.Add: 504.6 + 13.7 + 0.029ANSWER BOX:   

RESULTS BOX: 

3.Add: $234.50 + $187.95ANSWER BOX: $  

RESULTS BOX: 

4.

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Add: 15.419 + 0.3 + 297.0651ANSWER BOX:   

RESULTS BOX: 

5.Jill bought two sweaters because that $19.99 each and a pair of jeans for $27. Just how much walk she pay completely (assuming there to be no sales tax)?ANSWER BOX: $  

RESULTS BOX: