DECIMAL NUMBERS – ROUNDING WITH ADDITION

There are two steps to solving these problems. First, round the numbers. Then add.

Concept for Rounding Decimals: Use rounding to make difficult calculations easier to perform, especially when you do not need exact numbers in your calculations.

Steps for Rounding Decimals

Step 1 | Find the digit you want to round to. Call it the target digit.
Step 2 | Look at the digit to the right of the target digit.
Step 3 | If the digit to the right of the target digit is 5 or more, add 1 to the target digit. If the digit to the right of the target digit is less than 5, do not change the target digit.
Step 4 | In either case, drop all digits to the right of the target digit.

Example of Rounding Decimals: Round 0.774168 to the nearest thousandths

Step 1 | Find the digit you want to round to. Call it the target digit. In this case we are targeting the thousandths digit which is a 4 in 0.774168. | 0.77 4 168
Step 2 | Look at the digit to the right of the target digit. That digit is a 1. | 0.774 1 68
Step 3 | If the digit to the right of the target digit is a 5 or more, add 1 to the target digit. If the digit to the right of the target digit is less than a 5, do not change the target digit. 1 is less than 5, so we will not change the target digit. Our target digit remains a 4. | 0.77 4 1 68
Step 4 | In either case, drop all digits to the right of the target digit . 0.774168 rounded to the nearest thousandths is 0.774 000. | 0.774 000

Concept for Adding Rounded Decimals: Use addition to combine quantities, or find a total, or a sum. The answer to an addition equation is called the sum. Follow these steps to add whole numbers.

Steps for Adding Rounded Decimals

Step 1 | Arrange the decimals being added so digits with the same place value are aligned.
Step 2 | Start with the column furthest to the right. Add the numbers in that column, placing the result underneath the Results Line in that column.
Step 3 | Working from right to left, add the numbers in each column. When a column of digits has a sum greater than 9, carry to the next column on the left.

Example of Adding Rounded Decimals: Combine 0.2990 and 0.2858

Step 1 | Arrange the decimals being added so digits with the same place value are aligned. | 0.2990 0.2858
Step 2 | Start with the column furthest to the right. Add the numbers in that column, placing the result underneath the Results Line in that column. | 0.299 0 +0.285 8 8
Step 3 | Working from right to left, add the numbers in each column, placing the result underneath the Results Line in that column. When a column of digits has a sum greater than 9, carry to the next column on the left. | 1 0.29 9 0 +0.28 5 8 4 8
| Working from right to left, add the numbers in each column, placing the result underneath the Results Line in that column. | 1 1 0.2 9 9 0 +0.2 8 5 8 8 4 8
| Working from right to left, add the numbers in each column, placing the result underneath the Results Line in that column. | 1 1 0.2 9 9 0 +0.2 8 5 8 0.5 8 4 8
| 0.2990 combined with 0.2858 equals 0.5848 | 1 1 0.2 9 9 0 +0.2 8 5 8 0.5 8 4 8