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.
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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.
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