1.7 C) Adding & Subtracting
- Take the numbers out of standard form
- Complete the calculation (addition or subtraction)
- Place the answer back into standard form
Let’s have a few examples.
Example 1
What is:
The first step is to take each of these two terms out of standard form. Both of the numbers have a positive value for n, and this means that we will be moving the decimal points to the right. The working for taking the numbers out of standard form is shown below.
The calculation now becomes:
The final step is to place this number into standard form. The value of A for this number is 5.22 (the value of A must satisfy 1 ≤ A < 10). We now need to find out how many places we move the decimal point.
We move the decimal point 5 places to the left, which means that n is 5. Therefore, the answer to this question is 5.22 x 105.
Example 2
What is:
Like the example before, the first step is to take both of these terms out of standard form. The working is shown below:
The sum becomes:
The final step is to give our answer in standard form. A is going to be 8.127. We now need to find out how many places the decimal point has moved.
The decimal point has moved 6 places to the left, thus meaning that n is 6. Therefore, the answer to this question in standard form is 8.127 x 106.
Example 3
What is:
The first step is to take these two terms out of standard form. Both of the powers of 10 are negative. This means that we are going to move the decimal point to the left. The working is shown below.
The calculation becomes:
I am going to use column subtraction to calculate the answer to this question.
We now need to get 0.00445 into standard form. A is going to be 4.445. We are moving the decimal point 3 places to the right and this means that the value of n is -3.
Therefore, the answer is 4.45 x 10-3.