Scientific Notation

<h1>Text Preview</h1> <p>Last time, we learned about dividing monomials. Let’s take a short review.</p> <p>You are given a quotient of monomials.</p> <p>Select the correct simplified expression from the list. Then, click the “Submit” button.</p> <p>Now, let’s continue with today’s lesson.</p> <p>Here we have two large numbers: <font size="+2" face="Times New Roman">2,000,000</font> and <font size="+2" face="Times New Roman">150,000</font>.</p> <p>Suppose we wish to multiply them.</p> <p>The operation is rather cumbersome. We could easily lose track of the place value in the final answer.</p> <p>Let’s look at the first number. Suppose we rewrite it as the product of two numbers: <EQUATION></p> <p>We can rewrite the second term as a power of ten. It becomes <EQUATION></p> <p>Likewise, we can transform our second number into <EQUATION></p> <p>Now, multiplying the two numbers is easier. We use the product of powers rule to multiply the powers of ten.</p> <p>The answer is a number times a power of ten: <EQUATION></p> <p>We call an expression in this form <b>scientific notation</b>. </p> <p>The general form is: <EQUATION>. A number in scientific notation is a monomial because it is the product of two numbers.</p> <p>Let’s convert the number <font size="+2" face="Times New Roman">19200</font> to scientific notation.</p> <p>First, we move the decimal place so that only one digit is to the left.</p> <p>The resulting number, <font size="+2" face="Times New Roman">1.9200</font>, is the first term in the scientific notation expression.</p> <p>Next, we count the number of places that we moved the decimal place.</p> <p>In this case, we moved it four places to the left.</p> <p>What shall we have as the exponent of ten? Click the “Submit” button after entering your answer.</p> <p>We moved the decimal four places to the left. Therefore, we use four as the exponent of ten.</p> <p>We can drop the trailing zeroes. The result is the number in scientific notation: <EQUATION></p> <p>Here we have a number that is less than one: <font size="+2" face="Times New Roman">0.000023</font>. Let’s convert it to scientific notation.</p> <p>In this case, we move the decimal five places to the right. </p> <p>What shall we have as the exponent of ten? Click the “Submit” button after entering your answer.</p> <p>If we move the decimal to the right, then we set the value as negative.</p> <p>This gives us the number in scientific notation: <EQUATION></p> <p>Now, you try converting some numbers.</p> <p>You are given a number to convert.</p> <p>Enter the values for the terms in scientific notation. Then click the “Submit” button.</p> <p>Remember, if we move the decimal to the left, then the exponent will be positive.</p> <p>This will be the case when converting numbers greater than one.</p> <p>If we move it to the right, then the exponent of ten will be negative.</p> <p>This will be the case when converting numbers less than one.</p> <p>If we convert the number 1 to scientific notation, the exponent is zero. This is written as <EQUATION>.</p> <p id="TextCopyright">Copyright 2006 The Regents of the University of California and Monterey Institute for Technology and Education</p>