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a. Write the numbers one million and one millionth in scientific notation.b. By what number must we multiply one millionth to get one million?
a. $1.0 \times 10^{6}$, $1.0 \times 10^{-6}$b. $1.0 \times 10^{12}$
Algebra
Chapter 5
Exponents and Polynomials
Section 3
Scientific Notation
Polynomials
Harvey Mudd College
Baylor University
University of Michigan - Ann Arbor
Lectures
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Let's write one millionth in scientific notation to start out. We should write it in terms of numbers instead of words. So using our decimal place photos, we have 10th hundreds, thousands, 10,300 thousands and finally, millionths where we'll put a one since there's one million. So let's convert this number of scientific notation to start out we need to move. The decimal point is that there is only one significant digit to the left of it that is right here after the one. So we now have 1.0, and with any scientific notation, we're multiplying by 10 raised to some power. So we can add this times 10 to the something. So what is this power To figure it out? We just have to count the number of decimal points that we moved the decimal that is 12345 six. So it's not going to be the sixth power, though. But the negative sixth power since we moved the decimal point to the right, that is, our initial number was very small and made it larger. We have to use a negative exponents of the 10 meaning one millionth is in scientific notation is one times 10 to the negative sixth power
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