Question Video: Dividing Two Numbers in Scientific Notation Form | Nagwa Question Video: Dividing Two Numbers in Scientific Notation Form | Nagwa

# Question Video: Dividing Two Numbers in Scientific Notation Form Mathematics • First Year of Preparatory School

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Calculate (8.2 × 10⁴) ÷ (4.1 × 10²), giving your answer in scientific notation.

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### Video Transcript

Calculate 8.2 multiplied by 10 to the fourth power divided by 4.1 multiplied by 10 to the second power, giving your answer in scientific notation.

In this question, we’ve been given two values to divide, each in scientific notation, or standard form. This means that these numbers have been written in the form 𝑎 multiplied by 10 to the 𝑛th power, where the modulus of 𝑎 is greater than or equal to one and less than 10 and 𝑛 is an integer.

Let’s begin by rewriting the expression in this way: 8.2 multiplied by 10 to the fourth power over 4.1 multiplied by 10 to the second power. Writing it in this way helps us to then rewrite the division as a multiplication of two fractions. This is 8.2 over 4.1 multiplied by 10 to the fourth power over 10 to the second power. Now, let’s simplify each of these two fractions.

Firstly, we can evaluate 8.2 over 4.1. That gives us two. Then, we can evaluate 10 to the fourth power over 10 to the second power. To do this, let’s recall the exponent quotient rule. That is, 𝑥 to the 𝑚 power over 𝑥 to the 𝑛 power equals 𝑥 to the 𝑚 minus 𝑛 power. Therefore, 10 to the fourth power over 10 to the second power is 10 to the four minus two power. And because four minus two is two, this is 10 to the second power or 10 squared.

So, our answer is two multiplied by 10 to the second power. Remember that we were asked to give our answer in scientific notation, so let’s just check that this is in scientific notation. Well, because two is between one and 10 and our exponent, two, is an integer, this answer is in scientific notation. So, this is our final answer.

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