DECIMAL NUMBERS – ROUNDING WITH SUBTRACTION

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

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 Subtracting Rounded Decimals: Use subtraction to find the difference between two numbers or amounts. The answer to a subtraction equation is called the difference. Follow these steps to subtract decimals.

Steps for Subtracting Rounded Decimals

Step 1 | Write the larger decimal above the smaller decimal. Align the decimal points.
Step 2 | Start with the column furthest to the right. Subtract the numbers in that column, placing the result underneath the Results Line in that column. When a digit in the bottom number is greater than the digit above it, you must borrow from the column to the left.
Step 3 | Work from right to left, subtracting the numbers in each column. Whenever a digit in the bottom number is greater than the digit above it, you must borrow from the top number to the left.
Step 4 | Check your answer by adding the difference and the number you subtracted. The sum should equal the top number in the original problem.

Example for Subtracting Rounded Decimals: Subtract 0.2438 from 0.5025

Step 1 | Write the larger decimal (0.5025) above the smaller decimal (0.2438). Align the decimal points. | 0.5 0 2 5 0.2 4 3 8
Step 2 | Start with the column furthest to the right. Subtract the numbers in the that column, placing the result underneath the Results Line, in the ones column. Oops! Note that you can not subtract 8 from 5, because 8 is greater than 5. You therefore need to borrow. | 0.5 0 2 5 – 0.2 4 3 8
Step 3 | Whenever a digit in the bottom number is greater than the digit above it, you must borrow from the column to the left. Since you can not subtract 8 from 5, because 8 is greater than 5, you need to borrow 1 from the tens column in 0.5025. That drops the value in the tens column from 2 to 1, and raises the value in the ones column from 5 to 15. Write these new values above the original values. | 1 15 0.5 0 2 5 –0.2 4 3 8
| Now complete the subtraction in the ones column: 15 – 8 = 7. | 1 15 0.5 0 2 5 – 0.2 4 3 8 7
| Since you work from right to left, subtracting the numbers in each column as you go, you must now subtract the tens column, 1 – 3. Oops! Again you must borrow from the column to the left, since 3 is greater than 1. The value of the digit in the hundreds column of 5025 is 0. We can not borrow anything from 0. For that reason you must now borrow from the thousands column. | 1 15 0.5 0 2 5 – 0.2 4 3 8 7
| The value of the digit in the thousands column will now go from 5 to 4, and the value of the digit in the hundreds column of 5025 will now become 10. | 4 10 1 15 0.5 0 2 5 –0.2 4 3 8 7
| Next, borrow from the hundreds column. The value in the hundreds column goes from 10 to 9. The value in the tens column goes from 1 to 11. | 9 11 4 10 1 15 0.5 0 2 5 – 0.2 4 3 8 7
| Complete the subtraction in the tens column: 11 – 3 = 8. | 9 11 4 10 1 15 0.5 0 2 5 –0.2 4 3 8 8 7
| Now, move to the hundreds column. Complete the subtraction in the hundreds column: 9 – 4 = 5 | 9 11 4 10 1 15 0.5 0 2 5 – 0.2 4 3 8 5 8 7
| Finally, move to the thousands column. Complete the subtraction in the thousands column: 4 – 2 = 2. | 9 11 4 10 1 15 0.5 0 2 5 – 0.2 4 3 8 2 5 8 7
| Our answer is: 5 0 2 5 – 2 4 3 8 = 2587 | 9 11 4 10 1 15 0.5 0 2 5 –0.2 4 3 8 2 5 8 7
Step 4 | Check your answer by adding the difference (2587) and the number which you subtracted (2438). The sum (5025) should equal the top number in the original problem. | 1 1 1 2587 + 2438 5025