Solve Scientific Notation Problems

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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.

The superscript 3 indicates that 7 was multiplied by itself three times.

We call this “seven to the third power” or “seven cubed”.

Scientific Notation-------------------------Motivation for Exponent Rules-------------------------Multiplication of Value with Same Base-------------------------Division of Values with the Same Base-------------------------An Exponent of Zero-------------------------Expression Raised to a Power-------------------------Powers of Products-------------------------Summary of Laws of Exponents-------------------------Multiplication with Scientific Notation-------------------------Addition with Scientific Notation Adding and subtracting with scientific notation may require more care, because the rule for adding and subtracting exponential expressions is that the expressions must havelike terms.

Remember that to be like terms, two expressions must have exactly the same base numbers to exactly the same powers.

The trailing zeroes are not significant because there is no decimal place so the significant digits are 2389.

Next, we want to move the decimal until it is located just after (to the right of) the first significant digit, so .

Step 1: Put the decimal after the first significant digit.

Step 2: Indicate how many places the decimal moved by the power of 10.

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