Video Transcript
An electron has a mass of
approximately nine multiplied by 10 to the power of negative 31 kilograms. The Sun has a mass of approximately
two multiplied by 10 to the power of 30 kilograms. How many times heavier is the Sun
than an electron? Give your answer in the form 𝑎
multiplied by 10 to the power of 𝑏, where 𝑎 is a whole number.
We begin by recalling that any
number written in the form 𝑎 multiplied by 10 to the power of 𝑏 is written in
scientific notation, also known as standard form, where the absolute value of 𝑎
must be greater than or equal to one and less than 10 and 𝑏 is an integer. In this question, we are given the
approximate mass of two objects in kilograms, written in scientific notation. The mass of an electron is given as
nine multiplied by 10 to the power of negative 31 kilograms. And the mass of the Sun is given as
two multiplied by 10 to the power of 30 kilograms. We are asked to calculate how many
times heavier the Sun is than an electron.
In order to calculate this, we need
to divide the mass of the Sun by the mass of an electron. We have two multiplied by 10 to the
power of 30 over nine multiplied by 10 to the power of negative 31. This can be rewritten as a
multiplication of two fractions: two-ninths multiplied by 10 to the power of 30 over
10 to the power of negative 31. Simplifying each fraction
separately, we recall that two-ninths is equal to 0.2 recurring. And using the quotient rule for
exponents, 10 to the power of 30 over 10 to the power of negative 31 is equal to 10
to the power of 61. Therefore, we get 0.2 recurring
multiplied by 10 to the power of 61.
Since the absolute value of 𝑎 must
be greater than or equal to one, we can rewrite 0.2 recurring as 2.2 recurring
multiplied by 10 to the power of negative one. As such, our answer simplifies to
2.2 recurring multiplied by 10 to the power of 60.
Finally, since we’re asked to give
𝑎 as a whole number, we round the answer to two multiplied by 10 to the power of
60. And we can therefore conclude that
the mass of the Sun is approximately two multiplied by 10 to the power of 60 times
heavier than the mass of an electron.
