Video Transcript
Express 874,527,893 in scientific notation.
In this question, we are asked to express a given number in scientific notation.
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 lies between one and 10 and 𝑛 is an integer.
We know that multiplying and dividing a number by 10 is the same as shifting the position of its digits. This means that when we want to express a number in scientific notation, the value of 𝑎 is found by shifting the digits of the number so that its absolute value lies between one and 10. In this case, the value of 𝑎 is 8.74527893.
To find the value of 𝑛, we need to determine how many times we need to multiply 𝑎 by 10 to obtain the original number. We know that each time we multiply by 10, we move the digits over one place left. This is the same as moving the decimal point one place to the right. We see that we need to move the decimal point eight places to the right to get back to our original number. Hence, the value of 𝑛 is eight, and we have shown that 874,527,893 is equal to 8.74527893 times 10 raised to the power of eight in scientific notation.
