Why 10^{0} = 1 ? Please keep reading to see the explanation in the end of this lesson.
Since 0.06 = 6 × 10^{-2} , we get the following:Example #2:
Convert 0.014 to a fraction.
Follow all the steps above again. First, convert 0.014 to scientific notation.
0.014 = 14 × 10^{-3}
10^{-2} = 1 / 10^{2}, so 10^{-3} = 1 / 10^{3}
In general, 10^{-n} = 1 / 10^{n}
14 × 10^{-3} = 14 × 1 / 10^{3}
14 × 10^{-3} = (14 / 1) × (1 / 10^{3})
14 × 10^{-3} = (14 × 1) / (1 × 10^{3})
14 × 10^{-3} = 14 / 10^{3}
14 × 10^{-3} = 14 / 1000
Notice that you could have gotten to the result a little faster bu using the shortcut below. However, we wanted to show you first all the steps again so you understand deeply!
Example #3:
Convert 0.10252 to a fraction. First, convert 0.10252 to scientific notation.
0.10252 = 10252 × 10^{-5}
10^{-5} = 1 / 10^{5}
10252 × 10^{-5} = 10252 × 1 / 10^{5}
10252 × 10^{-5} = (10252 / 1) × (1 / 10^{5})
10252 × 10^{-5} = (10252 × 1) / (1 × 10^{5})
10252 × 10^{-5} = 10252 / 10^{5}
10252 × 10^{-5} = 10252 / 1000
Once again, you could also just use the shortcut below:
Why 10^{0} = 1?
In order to see why 10^{0} is equal to 1, we need to make the following two important observations:
Observation #1: 10^{n} / 10^{n} = 1
Observation #2: 10^{n} / 10^{n} = 10^{n-n} = 10^{0}
Therefore, 10^{n} / 10^{n} = 1 = 10^{n-n} = 10^{0}
1 = 10^{0}
Mar 29, 23 10:19 AM
Mar 15, 23 07:45 AM