Anonymous A. answered • 06/01/22
Math and Chemistry Nerd, Software Engineer, and Patient Teacher
I believe your question is write 0.0474 × 106 in scientific notation.
Scientific notation is always written in the form "number × 10some power" where number is between 1 and 10.
So in order to write this 0.0474 in scientific notation, we need to move the decimal place around until the result is between 1 and 10. So let's move the decimal one step at a time.
- 0.0474 - no moves
- 0.474 - 1 decimal place over
- 4.74 - 2 decimal places over
Now we have a number between 1 and 10. But we have to adjust the exponent on the 10 since we moved decimals around to keep the expression equal. How many decimal places over did we move the decimal? 2.
So we are changing the exponent on the 10 by 2. But is it positive or negative? Well, originally we had 0.0474 which is smaller than 4.74. What do we have to multiply 4.74 by in order to get 0.0474? 1/100 or 10-2. Which moves the decimal place correctly to the left. So now we have
4.74×10-2×106
But we can add the powers of the exponents of the 10s together. So that's -2 + 6 = 4. Which gives us our final answer of
4.74×104
And this answer meets scientific notation. Let's check our work! Is our new answer equal to the original question? In other words is 4.74 ×104 the same as 0.0474 × 106? Let's multiply and find out!
4.74 × 104
47.4 × 103
474 × 102
4740 × 101
47400 × 100 = 47400 × 1 = 47400
And now, let's check the original numbers
0.0474 × 106
0.474 × 105
4.74 × 104
47.4 × 103
474 × 102
4740 × 101
47400 × 100 = 47400 × 1 = 47400
And the numbers do match indeed! So we know we have the right answer.
