How To Convert Fractions to Decimals
Summary
TLDRThis video tutorial demonstrates the process of converting fractions into decimals using long division. It begins with simple examples like 2/5 and 1/4, explaining each step in detail. The video then progresses to more complex fractions, such as 3/8 and 17/4, and discusses the concept of repeating decimals, especially when the denominator is 9. It provides clear examples to illustrate how to identify and handle repeating decimals, making the concept accessible to viewers.
Takeaways
- 📚 Converting a fraction to a decimal involves using long division.
- 🔢 Start by dividing the numerator by the denominator and adding a decimal point if necessary.
- 📉 For fractions like 2/5, the result is a finite decimal, which is 0.4 in this case.
- 📈 When converting 1/4, the process shows that the result is 0.25, a finite decimal.
- 🔍 For fractions with 8 in the denominator, like 3/8, the result is 0.375, another finite decimal.
- 🔄 Fractions with 9 in the denominator lead to repeating decimals, such as 1/9 which is 0.111... repeating.
- 🔢 Multiplying the numerator by a factor when the denominator has a 9, like 2/9, results in a repeating decimal that reflects this multiplication, e.g., 0.222... repeating.
- 📉 Fractions like 3/9 can be simplified to 1/3, and both have the same repeating decimal of 0.333... repeating.
- 🔄 Recognize patterns in repeating decimals for fractions with denominators that are multiples of 9, such as 23/99 which results in 0.232323... repeating.
- 📝 Practice converting fractions to decimals with different denominators to understand the process better, as demonstrated with examples like 3/8 and 17/4.
- 👍 The video concludes by reinforcing the knowledge of converting fractions to decimals and identifying repeating decimals.
Q & A
What is the main topic of the video?
-The main topic of the video is how to convert fractions into decimals using long division.
What is the first fraction the video uses as an example to convert into a decimal?
-The first fraction used as an example is 2/5.
How many times does 5 go into 2 when converting 2/5 into a decimal?
-5 goes into 2 zero times initially, but after adding a decimal point and a zero, 5 goes into 20 four times.
What is the decimal equivalent of 2/5?
-The decimal equivalent of 2/5 is 0.4.
What is the second fraction the video demonstrates converting into a decimal?
-The second fraction is 1/4.
How many times does 4 go into 10 when converting 1/4 into a decimal?
-4 goes into 10 two times.
What is the decimal equivalent of 1/4?
-The decimal equivalent of 1/4 is 0.25.
What happens when you get a remainder of zero in the long division process of converting fractions to decimals?
-When you get a remainder of zero, the number at the top is your final answer as a decimal.
What is the result of converting 3/8 into a decimal?
-3/8 converts to 0.375 as a decimal.
How does the video explain converting fractions with 9 in the denominator into decimals?
-The video explains that fractions with 9 in the denominator lead to repeating decimals, showing examples like 1/9 which results in a repeating 0.1.
What is the repeating decimal pattern for fractions with 9 in the denominator?
-The repeating decimal pattern for fractions with 9 in the denominator is the numerator repeated after the decimal point, such as 2/9 being 0.2 repeating.
What is the decimal equivalent of 17/4 according to the video?
-The decimal equivalent of 17/4 is 4.25.
How does the video describe the process of converting 328/999 into a decimal?
-The video describes converting 328/999 into a decimal as 0.328 repeating, with the pattern of 328 repeating indefinitely.
What is the significance of reducing fractions before converting them to decimals, as mentioned in the video?
-Reducing fractions before converting them to decimals simplifies the process and can help identify equivalent fractions that may have simpler repeating patterns, such as 3/9 being equivalent to 1/3.
Outlines
📚 Converting Fractions to Decimals with Long Division
This paragraph explains the process of converting fractions to decimals using long division. It begins with a simple example of converting 2/5 to 0.4, demonstrating how to add a decimal point and zero, and then continue the division until a remainder of zero is reached. The method is further illustrated with the fraction 1/4, which converts to 0.25. The video encourages viewers to practice with additional examples, such as 3/8 and 17/4, and explains the steps to arrive at their decimal equivalents, 0.375 and 4.25 respectively. The paragraph also touches on fractions with 9 in the denominator, which result in repeating decimals, using 1/9 as an example.
🔢 Understanding Repeating Decimals from Fractions with 9 in the Denominator
The second paragraph delves into fractions with 9 as the denominator and their conversion to repeating decimals. It uses 1/9 as an example to show how the division leads to a repeating pattern of 0.1. The concept is expanded to include other fractions with 9 in the denominator, such as 2/9 and 3/9, which simplify to 0.2 repeating and 0.3 repeating, respectively. The paragraph also discusses the equivalence of certain fractions, like 3/9 and 1/3, and their decimal representation. It further explores the pattern with fractions like 4/9, 5/9, and 6/9, which convert to 0.4, 0.5, and 0.6 repeating decimals. The paragraph concludes with examples of larger fractions, such as 23/99 and 328/999, which result in 0.23 and 0.328 repeating decimals, reinforcing the viewer's understanding of repeating decimals.
Mindmap
Keywords
💡Fraction
💡Decimal
💡Long Division
💡Numerator
💡Denominator
💡Repeating Decimal
💡Conversion
💡Remainder
💡Decimal Point
💡Equivalent
Highlights
Introduction to converting fractions into decimals using long division.
Demonstration of converting 2/5 into a decimal, resulting in 0.4.
Explanation of the long division process for converting fractions.
Conversion of 1/4 into a decimal, yielding 0.25.
Step-by-step guide on using long division for 3/8, resulting in 0.375.
Conversion of 17/4 into a decimal, resulting in 4.25.
Discussion on fractions with 9 in the denominator leading to repeating decimals.
Conversion of 1/9 into a repeating decimal, 0.111... indefinitely.
Pattern recognition in converting fractions with denominators of 9.
Conversion of 2/9 and 3/9 into repeating decimals, 0.222... and 0.333... respectively.
Explanation of the equivalence between 3/9 and 1/3, both resulting in 0.333... repeating.
Conversion of 23/99 into a repeating decimal, 0.232323... indefinitely.
Conversion of 14/99 into a repeating decimal, 0.141414... indefinitely.
Conversion of 328/999 into a repeating decimal, 0.328328... indefinitely.
Conclusion summarizing the method of converting fractions to decimals and identifying repeating decimals.
Transcripts
in this video we're going to talk about
how to convert a fraction into a decimal
so let's start with a simple example two
over five how can we convert this
fraction into a decimal the best way to
do this is using long division how many
times does 5 go into two five goes into
two zero times so we need to add a
decimal point and a zero now we're gonna
treat 2.0 as if it's 20 how many times
does 5 go into 20 five goes into 20 four
times so 5 goes into 2.4 times if five
times four is twenty five times point
four is two and so if we subtract these
we get zero now once you get a remainder
of zero the number at the top is your
answer so what this means is that two
over five is equivalent to point four
and so that's how you can convert a
fraction into a decimal use the long
division now let's try another example
let's convert one over four into a
fraction so let's use long division
we're gonna put the numerator on the
inside so how many times this 4 go into
one four goes into one zero times so
once again we need to add a decimal
point and another zero now how many
times does 4 go into 10 four goes into
10 two times four times two is eight so
4 times point two is 0.8 and 10 minus 8
is 2 so one minus point eight is point
two now we need to add another zero
because 4 does it go into two and how
many times does 4 go into 20 four goes
into 20 five times
so once you get the remainder of zero
then what you have on top is your answer
so 1/4 is equivalent to 0.25 as a
decimal for the sake of practice go
ahead and try these two examples 3 over
8 and 17 over 4 convert each one into a
decimal so let's start with first one
now eight goes into three zero times so
let's add a decimal point how many times
does eight goes into thirty eight goes
into thirty three times 8 times 3 is 24
eight times four is thirty-two that's
too much because it exceeds 30 so eight
times point three must be two point four
thirty minus 24 is 6 so 3.0 minus two
point four is point six now we need to
add a zero how many times does 8 go into
16 well 8 times 8 is 64 so that exceeds
60 that's too much but 8 times 7 is 56
and so that works now 60-56 is for mr
now we need to add another zero and 8
goes into 40 five times 8 times 5 is 40
and so now we have a remainder of 0 so 3
over 8 is equal to 0.375 as a decimal so
that's it for the first example
now what about the next one what is 17
over 4 as a decimal well let's find out
so how many times does 4 go into 17 4
goes into 17 4 times 4 times 4 is 16 and
the difference between these two numbers
is 1 so 4 does it go into 1 so we need
to add a 0 now how many times does 4 go
into 10 4 goes into 10 two times 10
equally - should be 1.0 but we're gonna
treat it as if it's 10 4 times 2 is 8 so
4 times point zero is pointing so we
have a difference of point 2 and 4 goes
into 20 5 times 4 times 5 is 20 and so
the remainder is zero so therefore we
can say that 17 divided by 4 is 4 point
2 5 and that's it for this one
now let's talk about fractions that
contain 9 in the denominator these types
of fractions lead to repeating decimals
1 over 9 is basically 0.1 repeated and
so that's point 1 1 1 1 1 1 11 forever
and if you do long division on 1 over 9
you'll see that the 1 will keep
repeating for instance 9 does it go into
1 so 9 goes into 1 zero times so we
gotta add in zero and a decimal point 9
goes into 10 one time 9 times 1 is not
and so this gives us a difference of 0.1
I mean 1 minus point 9 is point 1 9 goes
into 10 one time again and 9 times 1 is
9 and notice that this will keep
repeating and then nine goes into this
10 in one time and then the pattern will
just continue so 1 over 9 is basically
point one repeating now what do you
think 2 over 9 is equal to well it's
gonna be this number times 2 so it's
gonna be point 2 repeated 3 over 9 is
basically point three repeating now 3
over 9 can be reduced to 1 over 3 if you
divide the 3 and the 9 by 3 so both 3
over 9 and 1 over 3 they're equivalent
fractions they both equal point 3
repeated and so you can see a pattern
here four over nine is point four
repeated five over nine is point five
repeating 6 over nine which is the same
as 2 over 3 if you divide the top and
the bottom number by 3 this is equal to
point six repeated
now what if we have two nines let's say
23 over 99 what is that equal to 23 over
99 that's gonna be point 23 repeating
and so for instance 14 over 99 is
basically 0.14 repeating so this is
point 2 3 2 3 2 3 and so forth and this
is point 1 4 1 4 1 4 and so forth now
what do you think 328 over 9 9 9 is
equal to so this is going to be 0.32 8
repeating which is Street
I forgot the decimal point 0.32 8 and
then 3 to 8 3 to 8 and so forth so
that's all I got for this video now you
know how to convert a fraction into a
decimal and you know how to identify if
it's gonna be a repeating decimal so
thanks for watching
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