How to Add Decimal Numbers: 8 Steps (with Pictures)

Video: How to Add Decimal Numbers: 8 Steps (with Pictures)

Video: How to Add Decimals | Math with Mr. J 2024, December

2024 Author: Jason Gerald | [email protected]. Last modified: 2024-01-15 08:07

Adding decimal numbers is almost like adding regular integers. All you have to do is align the decimal marks (commas), and make sure the decimal marks are also written in the summed numbers.

Step

Part 1 of 2: Basic Concepts

Skip this section if you are familiar with decimal numbers.

Step 1. Understand place value

An ordinary number can consist of one digit, each of which has place value different.

The number 472, for example, consists of a 2 in the “ones place”, a 7 in the “tens place”, and a 4 in the “hundreds place”.
That means 2 is only worth 2, but 7 (in the tens place) is worth ten times, so it's actually worth 70. 4 in the hundreds place is worth a hundred times, and that's 400.

Step 2. Understand decimal numbers

If a number added to the left of a number has an increasing place value, it makes sense that a number added to the right of a number will have a smaller place value. To indicate that we are using a place value less than 1, a decimal sign is written after the ones place. Just as the number on the left has a place value that increases with a base 10 multiple, the number after the decimal sign has a place value divided by a base 10 multiple; so that the further to the right, the smaller the place value.

Example: 1, 65 consists of 1 in the ones place, 6 in the tenths place, and 5 in the hundredths place. The number 6 is worth one tenth of the value of the ordinary 6 (0, 6), and the number 5 is one hundredth of the value of the ordinary 5 (0.05)

Part 2 of 2: Adding Decimal Numbers

Step 1. Align the decimal marks in the numbers that are added up

Each time you add decimal numbers, write each number on a separate line vertically. Always align the decimal point, so that each number in a column has the same place value.

Example: to calculate 31.8 + 0.45, write 31.8 over 0.45, where 1 is above 0 (both are in the ones place) and 8 is above 4 (both are in the tenth place)

Step 2. Add zeros to the numbers for alignment, if necessary

Sometimes numbers don't align neatly, because they don't have the same number of digits or don't use numbers in the same place value. If that's the case, add a 0 before and/or after the number to make the total number the same. This method does not change the value of the number, because there is no value in the place value.

Example: You can rewrite 31, 8 + 0.45 to 31, 80 + 00, 45 so that they are parallel to each other

Step 3. Lower the decimal sign

Write a decimal mark in the answer line, just below the decimal mark that has been aligned in the problem, before you do the addition.

Step 4. Add up the numbers starting from the far right

At this point, do the math the same way you would a regular addition problem. Add up the numbers starting from the far right, and write the answer in the answer line, just below the summed numbers.

Example: to calculate 31, 80 + 00, 45, start with 0 + 5. Write the answer, 5, under the column. 31, 80 + 00, 45 = _ _, _ 5.

Step 5. Move to the left, and repeat, bringing up 1 point if you get an answer of 10 or greater

Remember, just like regular addition, if you get a two-digit answer, you must "carry 1 number" to the next column on the left.

In our example problem, the next column to add up is 8 + 4. The answer is 12, which cannot be included in the 1-digit answer. Write the number 2 in the answer row, and carry the number 1 to the next column on the left; write it as a small number above the column.
31⁺¹, 80 + 00, 45 = _ _, 2 5.

Step 6. Continue until all the columns have been added up

Continue the same as when working on regular addition problems, until all the numbers have been added up. Don't forget to bring "excess numbers" to the next column on the left of the addition problem.

Sum the next column in our example problem: 31⁺¹, 80 + 00, 45 = _ 2, 2 5.
By adding the last column (3 + 0), we get the answer 32, 25.

Example

Try solving the following questions yourself, then highlighting the space to the right of the equals sign to check your answer. The most difficult questions are those at the bottom.

2, 25 + 1 = 3, 25
7, 66 + 0, 3 = 7, 96
0, 478 + 0, 032 = 0, 51
0, 042 + 0, 0601 = 0, 1021
2, 3 + 4, 55 + 1, 19 = 8, 04

Tips

If you get a 0 to the right of the decimal point as the last digit in the answer number, the 0 can be omitted. For example, 31, 00 equals 31. However, do not omit the number 0 to the left of a decimal sign (example: 400, 54), between a decimal sign and a number (0, 002), or between a number (304, 102).
You can add as many decimal numbers as you want in one problem. Just write down all the numbers in one tall stack vertically, with all the decimal points positioned parallel to each other.

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