Scientific notation is very easy to use; it was designed to be.\u00a0 To start with, we need to realize the “everyday” way we write numbers is called “float” (aka “normal”).<\/p>\n
Another point to bear in mind is that scientists\u00a0commonly\u00a0space numbers in groups of three.\u00a0 Therefore, 0.03445 might also be written as 0.034 45.\u00a0 Similarly, 3467 might be written 3 467.<\/p>\n
Example:\u00a0 write 34 200 in scientific notation.<\/strong><\/p>\n Solution: 3.4200×104<\/span><\/sup><\/p>\n So we see that 34 200 is 3.4200×104<\/span><\/sup> in scientific notation.<\/p>\n Example:\u00a0 write 0.024 132 in scientific notation. The point to realize is that in scientific, you always write the decimal after the leftmost digit, then write x10p<\/b><\/span><\/sup>. The value of p<\/b> is the number of places you need to move the decimal to return to its “normal” place. If you need to move the decimal to the left, p<\/b> is negative.<\/p>\n Going from scientific back to float is easy as well; an example or two may help solidify the whole idea.<\/p>\n Example: write 3.24×10-5<\/span><\/sup> in float.<\/strong><\/p>\n Solution: The exponent tells us to move the decimal five jumps to the left.\u00a0\u00a0\u00a0It turns out the number is\u00a00.000 032 4\u00a0in float.<\/p>\n Example: write 7.59×106 <\/span><\/sup>in float. Good luck with this new way of seeing numbers.<\/p>\n
\n<\/strong>
\nSolution: 2.413 2×10-2<\/span><\/sup><\/p>\n
\n<\/strong>
\nSolution: The exponent tells us to move the decimal six jumps to the right. We arrive at 7 590 000 in float notation.<\/p>\n