Question Video: Solving Problems in Scientific Notation | Nagwa Question Video: Solving Problems in Scientific Notation | Nagwa

# Question Video: Solving Problems in Scientific Notation Mathematics • First Year of Preparatory School

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An electron has a mass of approximately 9 × 10⁻³¹ kg. The Sun has a mass of approximately 2 × 10³⁰ kg. How many times heavier is the Sun than an electron? Give your answer in the form 𝑎 × 10^(𝑏) where 𝑎 is a whole number.

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### 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.

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