Question Video: Writing Decimal Numbers in Scientific Notation Form Mathematics • 8th Grade

Express 0.00447 in scientific notation.


Video Transcript

Express 0.00447 in scientific notation.

In this question, we are asked to express a given number in scientific notation. To do this, let’s start by recalling what is meant by scientific notation. It’s the form π‘Ž times 10 raised to the power of 𝑛, where the absolute value of π‘Ž is greater than or equal to one and less than 10 and 𝑛 is an integer. This means that we want to write 0.00447 in the form π‘Ž times 10 raised to the power of 𝑛 with these restrictions.

Since 𝑛 is an integer, we are multiplying or dividing π‘Ž by factors of 10. We know that this has the effect of moving the digits of π‘Ž. This means that the digits of π‘Ž must be the same as the digits in 0.00447. However, the digits can be shifted. We need π‘Ž to be equal to 4.47 so that its absolute value lies in the correct range. We can use this to find the value of 𝑛. We know that each time we divide by 10, we will shift the digits to the right by one. We can see that we need to shift the digits three places to the right. This is the same as moving the decimal point three places left to make the numbers the same.

Hence, the value of 𝑛 is negative three, and we have shown that 0.00447 is equal to 4.47 times 10 raised to the power of negative three in scientific notation.

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