Solve Scientific Notation Problems

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How many times does to the decimal how to move from its original position to get just after the 7?

It has to move ten places to the right, so the answer is basically means that you are now dividing 7.53 by ten, ten times which would in fact give us the original number.

This is correct because if we actually multiplied 2.389 by ten five times we would in fact get the original number of 238,900. The mass of a dust particle is 0.000 000 000 753 kg.

The zeroes to the left of 753 are not significant because leading zeroes never are. We place the decimal after the seven giving us 7.53.

How many times did we have to move the decimal to get it from it’s understood or assumed location after the last zero in 238,900 to just after the 2?

It moved five times to the left so we write the scientific notation as .Step 1: Put the decimal after the first significant digit.Step 2: Indicate how many places the decimal moved by the power of 10.Let’s say we wanted to know how many electrons would flow past a point in a circuit carrying 1 amp of electric current in 25 seconds.If we know the number of electrons per second in the circuit (which we do), then all we need to do is multiply that quantity by the number of seconds (25) to arrive at an answer of total electrons: However, if we want to hold to standard convention for scientific notation, we must represent the significant digits as a number between 1 and 10.Thinking about decimal arithmetic, the requirement that we have the same powers makes sense, because that guarantees that all of the place values are lined up properly.Example: (4.5 × 10 We see that this solution is not in standard scientific notation form because the decimal part has more than one digit in front of the decimal point. We need to rewrite 532.5 as 5.325 × 10 Subtraction can be done the same way as addition, by getting the powers of ten to match; factoring out the power of ten that is the same, and subtracting the decimal values that come together when the power of ten is factored out.The exponent tells us we are dividing by ten twenty-three times, so this must be a very small number!Therefore, let’s move the decimal twenty-three places to the left.Scientific Notation is a handy way to write very large and very small numbers.Instead of having to use lots of digits, scientific notation allows shorter versions of the number to be written.


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