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 𝑎 times 10 raised to
the power of 𝑛, where the absolute value of 𝑎 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 𝑎 times 10 raised to the power of 𝑛 with these
restrictions.
Since 𝑛 is an integer, we are
multiplying or dividing 𝑎 by factors of 10. We know that this has the effect of
moving the digits of 𝑎. This means that the digits of 𝑎
must be the same as the digits in 0.00447. However, the digits can be
shifted. We need 𝑎 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.
