Decimal fractions - Lesson 1

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Decimal fractions - Lesson 1
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<h1>Introduction to decimal fractions:</h1>
<h1><img src="https://imgoat.com/uploads/2cc227532d/91760.png" width="348" height="243"/></h1>
<p><a href="https://savedyouaspot.files.wordpress.com/2016/02/fractions.jpg">Source</a></p>
<h3>Decimal fraction:</h3>
<blockquote>A fraction where the denominator (the bottom number) is a power of ten (such as 10, 100, 1000, etc).<br>
You can write decimal fractions with a decimal point (and no denominator), which make it easier to do calculations like addition and multiplication on fractions</blockquote>
<p><a href="https://www.google.co.za/url?sa=t&amp;rct=j&amp;q=&amp;esrc=s&amp;source=web&amp;cd=2&amp;ved=0ahUKEwi5s5aMv9nZAhXiLsAKHaGuCa4QFgg1MAE&amp;url=https%3A%2F%2Fwww.mathsisfun.com%2Fdefinitions%2Fdecimal-fraction.html&amp;usg=AOvVaw0vYbYtZnH7HRQEFgJEvc1i">Source</a></p>
<p><br></p>
<h1>Place value and value of a digit:</h1>
<p>There is a big difference between the place value and the value of a number. &nbsp;Learners get confused between the two.</p>
<p><br></p>
<p>&nbsp;<img src="https://imgoat.com/uploads/2cc227532d/91727.png" width="686" height="170"/></p>
<h2>Using the example above:</h2>
<h3>The place value of:</h3>
<ul>
  <li>9 is Ten thousands</li>
  <li>5 is Thousands</li>
  <li>3 is Hundreds</li>
  <li>7 is Tens</li>
  <li>8 is Units</li>
  <li>1 is tenths</li>
  <li>4 is hundredths</li>
  <li>2 is thousandths</li>
</ul>
<h3>Place value is at which place the number is at.</h3>
<h2>The value of the:</h2>
<ul>
  <li>9 is 90 000 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;or &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;9 Tth</li>
  <li>5 is 5000 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;or &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;5 Th</li>
  <li>3 is 300 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; or &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;3 &nbsp;H</li>
  <li>7 is 70 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;or &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;7 T</li>
  <li>8 is 8 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;or &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;8 U</li>
  <li>1 is 1/10 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;or &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;0,01</li>
  <li>4 is 4/100 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;&nbsp;or &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;0,04</li>
  <li>2 is 2/1000 &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;or &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;0,001 &nbsp;&nbsp;&nbsp;</li>
</ul>
<h3>The value of a digit is how much it is.</h3>
<p><br></p>
<h3>Let your learners do the following:</h3>
<p><strong>Write down the place value and the value of the digit in color as a decimal fraction:</strong></p>
<p><img src="https://imgoat.com/uploads/2cc227532d/91728.png" width="164" height="65"/>&nbsp;&nbsp;&nbsp;&nbsp;</p>
<p>The<strong> place value</strong> of the digit is thousandths</p>
<p>The <strong>value</strong> of the digit is 0,002</p>
<p><br></p>
<p><img src="https://imgoat.com/uploads/2cc227532d/91736.png" width="128" height="53"/></p>
<p><strong>Place value</strong> of the digit is tenths</p>
<p><strong>Value</strong> of the digit is 0,6</p>
<p><br></p>
<p><img src="https://imgoat.com/uploads/2cc227532d/91737.png" width="196" height="59"/></p>
<p><strong>Place value</strong> of the digit is tenths</p>
<p><strong>Value</strong> of the digit is 0,04</p>
<p><br></p>
<h3>Writing a fraction as a decimal number:</h3>
<p>When writing a fraction as a decimal number, always change your denominator to <strong>10,100,1000 </strong>. Remember, when you multiply with a number at the bottom, you have to multiply with the same number at the top too!!</p>
<p><br></p>
<p><br></p>
<p><img src="https://imgoat.com/uploads/2cc227532d/91740.png" width="248" height="101"/>&nbsp;&nbsp;</p>
<ul>
  <li>In this example, the denominator can change to 10.</li>
  <li>We multiply with 2 at the top and bottom</li>
  <li>The answer is now over a fraction part of 10 and as a decimal it will be 6 tenths.</li>
  <li>Written as a decimal fraction it will be 0,6</li>
  <li>Teach your learners that if the fraction is over 10, 10 has one zero, so this means 1 place behind (on the right) of the comma.</li>
  <li>There are no wholes in front of the fraction, so the whole will be 0.</li>
  <li>Only the fraction will be written as a decimal.</li>
</ul>
<p><br></p>
<p><img src="https://imgoat.com/uploads/2cc227532d/91741.png" width="358" height="109"/></p>
<ul>
  <li>This denominator can not change to 10 or 100 but to 1000.</li>
  <li>We multiply with 125 at the top and at the bottom.</li>
  <li>Here are no wholes in this fraction, which means only the fraction will be written as a decimal.</li>
  <li>1000 has 3 zero's. &nbsp;This means that there must be three numbers behind the comma.</li>
  <li>Written as a decimal fraction, this answer will be 0,875</li>
</ul>
<p><br></p>
<p>Taking the next 2 examples, let's look at the difference between the two:</p>
<p><img src="https://imgoat.com/uploads/2cc227532d/91742.png" width="280" height="86"/>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<img src="https://imgoat.com/uploads/2cc227532d/91743.png" width="374" height="85"/></p>
<p>For the example on the left, the denominator changes to 100. &nbsp;We multiply with 25 at the top and bottom to get our answer. &nbsp;The fraction is over 100, which have two zero's. &nbsp;This means that we have two places behind the comma. &nbsp;Written as a decimal it will be 0,75.</p>
<p><br></p>
<p>The second example can also be taken to 100. &nbsp;The difference here is that there is a whole in front of the fraction. &nbsp;In the example you will see that we leave the whole as it is, we only change the fraction. The denominator can change to 100, we multiply with 2 at the top and bottom to get our answer. &nbsp;The fraction is over 100, which means that there are 2 zero's and that we have two places behind the comma. &nbsp;</p>
<p><br></p>
<p>A common mistake learners make, is that they write the decimal fraction as 0,60. &nbsp;There are 2 places behind the comma, but learners have to go back and see that the fraction they wrote is 60 and not 6.</p>
<p>The correct answer for this decimal fraction will be 1,06 as 06 must be the two places behind the comma and the 1 in front of the comma is the whole.</p>
<p><br></p>
<h1>Conclusion</h1>
<ul>
  <li>Learners have to know the difference between the value and place value of digits.</li>
  <li>Practice these decimal fractions as much as you can. &nbsp;</li>
  <li>This is just the introduction to decimal fractions, teach your learners these basics of decimal fractions before we go on to the next lesson.</li>
</ul>
<p><img src="https://imgoat.com/uploads/2cc227532d/91759.gif" width="562" height="141"/></p>
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