6.2 Small Numbers
When small numbers are written in standard form they have a negative value for n. For example, 10-2. A negative power can be written in the form as 1 divided by the positive power; 1/ 102. Here are the first 5 negative power of 10.
Place the 0.004 in standard form:
The first step is to choose our value of A. The value of A for 0.004 would be 4. We then need to work out what we multiply 4 by to turn it into 0.004.
- 100 = 1
- 10-1 = 1/101 = 1/10 = 0.1
- 10-2 = 1/102 = 1/100 = 0.01
- 10-3 = 1/103 = 1/1,000 = 0.001
- 10-4 = 1/104 = 1/10,000 = 0.0001
- 10-5 = 1/105 = 1/100,000 = 0.00001
Place the 0.004 in standard form:
The first step is to choose our value of A. The value of A for 0.004 would be 4. We then need to work out what we multiply 4 by to turn it into 0.004.
The second way is to see how far the 4 is away from the units column. 4 is 3 units away from the units column and it is smaller than one, which means that the value for n will be negative (n = -3).
Let’s have another example. Write 0.000095 in standard form.
Our value for A will be 9.5. 9 is 5 places away from the units column and as it is smaller than 1 the value for n is -5. The answer to this question is.
Converting Small Numbers from Standard Form to Numbers
Find 7.6 x 10-3 without standard form:
With this question, we need to move 7, 3 places to the right. This is because n is -3 (you can also view this as moving the decimal place to the left). This results in the answer becoming: