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multiplying_and_dividing_scientific_notation.html
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multiplying_and_dividing_scientific_notation.html
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<!DOCTYPE html>
<html data-require="math math-format">
<head>
<meta charset="UTF-8" />
<title>Multiplying and dividing scientific notation</title>
<script src="../khan-exercise.js"></script>
</head>
<body>
<div class="exercise">
<div class="vars">
<var id="DENOMINATOR">randRange( 1, 9 ) * Math.pow( 10, randRange( -5, 5 ) )</var>
<var id="QUOTIENT">randRange( 1, 99 ) * Math.pow( 10, randRange( -5, 5 ) )</var>
<var id="NUMERATOR">DENOMINATOR * QUOTIENT</var>
</div>
<div class="problems">
<div id="divide">
<p class="question">
Express this quotient in scientific notation:
<code>\Large{\frac{<var>scientific( 3, NUMERATOR )</var>}
{<var>scientific( 1, DENOMINATOR )</var>}}</code>
</p>
<div class="solution" data-type="multiple">
<span class="sol base"><var>scientificMantissa( 2, QUOTIENT )</var></span>
<code> \times 10 </code>
<sup class="sol exp" style="width: 20px;"><var>scientificExponent( QUOTIENT )</var></sup>
</div>
<div class="hints">
<p>Start by collecting like terms together.</p>
<p>
<code>= \Large{\frac{<var>scientificMantissa( 3, NUMERATOR )</var>}
{<var>scientificMantissa( 1, DENOMINATOR )</var>}}
\times\Large{\frac{10^{<var>scientificExponent( NUMERATOR )</var>}}
{10^{<var>scientificExponent( DENOMINATOR )</var>}}}</code>
</p>
<p>Then divide each term seperately. When dividing exponents with the same base, subtract their powers.</p>
<p>
<code>= <var>roundTo( 2, scientificMantissa( 3, NUMERATOR ) / scientificMantissa( 1, DENOMINATOR ) ).toFixed( 2 )</var>
\times 10^{<var>scientificExponent( NUMERATOR )</var>\,-\,<var>scientificExponent( DENOMINATOR )</var>}</code>
</p>
<p>
<code>= <var>roundTo( 2, scientificMantissa( 3, NUMERATOR ) / scientificMantissa( 1, DENOMINATOR ) ).toFixed( 2 )</var>
\times 10^{<var>scientificExponent( NUMERATOR ) - scientificExponent( DENOMINATOR )</var>}</code>
</p>
<div data-if="scientificExponent( QUOTIENT ) != scientificExponent( NUMERATOR ) - scientificExponent( DENOMINATOR )" data-unwrap>
<p>
To write the answer correctly in scientific notation, the first number needs to be between <code>1</code> and <code>10</code>.
In this case, we need to move the decimal one position to the right without changing the value of our answer.
</p>
<p>
<code>\qquad</code>We can use the fact that
<code><var>roundTo( 2, scientificMantissa( 3, NUMERATOR ) / scientificMantissa( 1, DENOMINATOR ) ).toFixed( 2 )</var></code> is the same as
<code><var>scientificMantissa( 2, QUOTIENT )</var> \div 10</code>, or
<code class="hint_blue"><var>scientificMantissa( 2, QUOTIENT )</var> \times 10^{-1}</code>.
</p>
<p><code>
= \color{<var>BLUE</var>}{<var>scientificMantissa( 2, QUOTIENT )</var> \times 10^{-1}}
\times 10^{<var>scientificExponent( NUMERATOR ) - scientificExponent( DENOMINATOR )</var>}
</code></p>
<p><code>= <var>scientific( 2, QUOTIENT )</var></code></p></div>
</div>
</div>
<div id="multiply">
<p class="question">
Express this product in scientific notation:
<code>(<var>scientific( 2, QUOTIENT )</var>)\times (<var>scientific( 2, DENOMINATOR )</var>)</code></p>
<div class="solution" data-type="multiple">
<span class="sol base"><var>scientificMantissa( 3, NUMERATOR )</var></span>
<code> \times 10 </code>
<sup class="sol exp" style="width: 20px;"><var>scientificExponent( NUMERATOR )</var></sup>
</div>
<div class="hints">
<p>Start by collecting like terms together.</p>
<p>
<code>= (<var>scientificMantissa( 2, QUOTIENT )</var>\times <var>scientificMantissa( 2, DENOMINATOR )</var>)
\times (10^{<var>scientificExponent( QUOTIENT )</var>}\times 10^{<var>scientificExponent( DENOMINATOR )</var>})</code>
</p>
<p>When multiplying exponents with the same base, add the powers together.</p>
<p>
<code>= <var>roundTo( 1, scientificMantissa( 2, QUOTIENT ) * scientificMantissa( 1, DENOMINATOR ) ).toFixed( 1 )</var>
\times 10^{<var>scientificExponent( QUOTIENT )</var>\,+\,<var>scientificExponent( DENOMINATOR )</var>}</code>
</p>
<p>
<code>= <var>roundTo( 1, scientificMantissa( 2, QUOTIENT ) * scientificMantissa( 1, DENOMINATOR ) ).toFixed( 1 )</var>
\times 10^{<var>scientificExponent( QUOTIENT ) + scientificExponent( DENOMINATOR )</var>}</code>
</p>
<div data-if="scientificExponent( NUMERATOR ) != scientificExponent( QUOTIENT ) + scientificExponent( DENOMINATOR )" data-unwrap>
<p>
To write the answer correctly in scientific notation, the first number needs to be between <code>1</code> and <code>10</code>.
In this case, we need to move the decimal one position to the left without changing the value of our answer.
</p>
<p>
<code>\qquad</code>We can use the fact that
<code><var>roundTo( 1, scientificMantissa( 2, QUOTIENT ) * scientificMantissa( 1, DENOMINATOR ) ).toFixed( 1 )</var></code> is the same as
<code class="hint_blue"><var>scientificMantissa( 3, NUMERATOR )</var> \times 10</code>.
</p>
<p><code>
= \color{<var>BLUE</var>}{<var>scientificMantissa( 3, NUMERATOR )</var> \times 10}
\times 10^{<var>scientificExponent( QUOTIENT ) + scientificExponent( DENOMINATOR )</var>}
</code></p>
<p><code>= <var>scientific( 3, NUMERATOR )</var></code></p></div>
</div>
</div>
</div>
</div>
</body>
</html>