TenMarks teaches you how to write large numbers in scientific notation.
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Learn about Numbers in Scientific Notation In this lesson we will learn how to right large numbers in scientific notation, we’ve got two problems the first problem wants us to write the number 143 followed by nine zeros in scientific notation. Now scientific notation was design to represent really large numbers, now the way a scientific notation works is you’ve got the first number multiplied by the second number it usually written as two numbers which I multiply. The first number is between one and ten and the second number is ten raise to the power of something, so lets learn how to do this, in order to convert this number which is fairly large number into scientific notation what we do is we follow a few steps. Step one is we place a decimal point after the first digit so in this case it would be 143000000000 so after the first digit I place a decimal point. Step two is we measure or we count digits to the right of the decimal point, how many do we have so in this case we have eleven taking a little bit of extra space what we do now, now that we’ve done this, Step three we drop all zeros so what I’m left with 1.43 cause I drop all the zeros. Step four I multiply by 1011 which is the count that I got here, so what do we get final answer is 1.43 * 1011 now this eleven is what we place here fairly simple step one we take the number we put the decimals point after the first digit, second we count the digits to the right of the decimal which are eleven in this case I drop all the zeros so I’m left with 1.43 and then I replace the rest with 1011 which is the count here and I noticed that our rule have said that the number typically has a number between one and ten which is what we have here and then the second part is ten to the power of something that’s exactly what we have a number between one and ten and ten raise to the power of something. Now let’s try the second problem which is 0.0000033 that’s what we have to show in scientific form. What we do is we count first thing we do is step one is we find the first number, remember a scientific notation has the first number multiplied by the second number, the second number is usually ten to the power of something so lets find the first number. In order to find the first number let me create a little bit of extra space, what I do is I move the is I move the decimal spot to the first digit which is not a zero, so place or move the decimal point after the first digit that is not equal to zero, so in this case I have 0.0000033 first digit that’s not a zero is this so the new decimal spot should be placed here so that’s done. Step two is I have to drop all the zeros so this becomes 3.3 because I just simply drop all the zeros. Step three we have to find the power of ten remember that the second number is always ten to the power of something, power of ten can be computed by how many digits or how many places did I move the decimal spot. Here how many places that I move it, it used to be here I moved it here which was 6 spots the answer to this is 6, so if we moved it six spots to the right. Step four is I right the scientific notation which is I take this number 3.3 x 106 but if I moved the decimal spot to the right I put -6, since I move it as most part to the right, I make it to -6 so the final answer is 3.3 x 10-6 . Again to recap this what we’ve learned is if we got a number that is a large number, I can apply the principle and move it to scientific notation represent it at scientific notation, a scientific notation ahs two numbers the first number which is always between one and ten and the second number that is usually ten to the power of something , so 143 followed by nine zeros I can place the decimals after the first digit that’s not a zero which is right here and drop all the zeros, I did that second I look at how many digits did I move the decimal spot, so it used to be here I moved it eleven spaces or how many digits are their after the decimal spot on the original number e