WEBVTT
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Let’s look at some strategies for converting fractions to decimals.
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Here’re the three strategies we’re going to try.
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The first one is by using power of 10, the second one mental math, and the third one division.
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Let’s start converting fractions to decimals with power of 10.
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Seven-tenths, we can easily convert seven-tenths to a decimal if we remember what the decimal place values are.
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Here’s a place value chart.
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Starting after the decimal point, you get tenths, hundredths, and thousandths.
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The fraction we’re trying to convert has a denominator of 10.
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This means that our numerator of seven would go in the tenths place.
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Our fraction doesn’t have anything in the ones place, so we place a zero there, and then put the seven in the tenths place.
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The decimal form of seven-tenths is 0.7.
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Here’s another example, eight hundredths.
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Again, we’re looking at the power of 10s, thinking about place value, where should the eight go?
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We place the eight in the hundredths place.
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This fraction has no whole numbers.
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Eight hundredths in decimal form looks like this, 0.08.
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Converting fractions to decimals with power of 10 works any time that you have a fraction with the denominator that is a power of 10, whether that be a 10, 100, 1000, 10000.
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As long as it’s a power of 10, you can use this strategy to convert fractions to decimals.
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But unfortunately, we don’t always get to work with powers of 10 in the denominator.
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Sometimes, there’re other things.
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So what should we do when we have a denominator like this one?
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We’re gonna solve this one with mental math.
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First, you have to think about the place value system with decimals, ones, decimal, tenths, hundredths, thousandths.
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So we need to come up with a strategy to take our denominator and put it into one of these systems.
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How can we change this 20 to a tenth, hundredth, or thousandth?
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So maybe you think we can change this 20 to 10 by dividing by two.
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But that doesn’t work easily because three is not divisible by two.
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So you try again with the hundredths.
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Then you realize that if you multiply by five for the numerator and the denominator, you can come up with a fraction with a base of 100.
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Three twentieths equals fifteen hundredths.
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The final answer then looks like this, 0.15.
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But not everything is easily converted with powers of 10 or mental math.
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It would be really difficult for us to try to convert this three-eighths into a power of 10 using mental math.
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That’s when we need our third strategy.
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That’s why we need to know how to convert fractions to decimals with division.
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So we’ll go back to our example of three-eighths.
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We wanna convert three-eighths to decimal form.
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So we set up our problem to do division.
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We put three inside the box and the eight on the outside.
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We know that eight goes in the three zero times.
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And then we bring up our decimal.
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We then ask the question, how many times does eight go into 30?
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And that’s three times.
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When we subtract, we get six.
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We bring down another zero and need to ask the question, how many times does eight go into 60?
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Seven times, seven times eight is 56.
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60 minus 56 is four.
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Bring down a zero.
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How many times does eight go into 40?
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Five times, five times eight is 40.
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There is no remainder.
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And we have just discovered that the decimal form of three-eighths is 375 thousandths, 0.375.
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I want to quickly go back and look at the example we used for our mental math problem.
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Because maybe it was really hard for you to think about how to convert 20 to 100 in your head.
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And if that is ever the case, if you’re struggling to use mental math, division will always work.
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Let’s try it here.
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We’re going to divide three by 20.
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I know that 20 goes into three zero times.
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And 20 would then go into 30 one time.
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One times 20 is 20.
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30 minus 20 is 10.
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Bring down a zero.
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How many times does 20 go into 100?
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The answer is five times.
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Five times 20 is 100, and we have a remainder of zero.
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We found the same answer by using a different strategy, three twentieths is in fact fifteen hundredths, 0.15.
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Okay, so I know I said we’re going to look at three strategies.
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But I do have one more strategy we’re going to look at.
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This one is just a bonus strategy.
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Sometimes, the simplest and most practical way to convert fractions to decimals is just to use a calculator.
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A calculator is a helpful tool to help best divide more complex fractions and convert them into decimals.
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Each of these strategies will help you convert fractions to decimals.