A man finds that he has a mass of 100.6 kg. He goes on a diet for several months and later he finds that he has a mass of 96.4 kg. Express each number in scientific notation, and calculate the number of kilograms the man has lost by dieting.
We are asked to express each of the numbers in scientific notation and to also calculate the number of kilograms the man lost through dieting. Scientific notation expresses a large number as a decimal multiplied by an exponential factor of ten. The numbers are shown below in scientific notation.
100.6 = 1.006 x 10^2
96.4 = 9.64 x 10^1
To find the number of kg's the man lost, we can do this by subtracting the numbers in regular form or in scientific notation. In regular form:
100.6 kg - 96.4 kg = 4.2 kg
For scientific notation, we need the exponent of the factor of 10 to be the same for both numbers, so we can convert 9.64 x 10^1 into 0.964 x 10^2.
1.006 x 10^2 kg - 0.964 x 10^2 kg = 0.042 x 10^2 kg
This value is the same as 4.2 kg as calculated above.