How To Convert Fractions to Decimals

Summary

This 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

00:00

📚 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.

05:02

🔢 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.

Keywords

💡Fraction

A fraction represents a part of a whole and is expressed as a ratio of two integers, the numerator (top number) and the denominator (bottom number). In the video, fractions are the starting point for demonstrating the conversion process to decimals, with examples like 'two over five' and 'one over four'.

💡Decimal

A decimal is a way of expressing a fraction in a numerical form that extends the whole number with digits after a decimal point. The video's main theme revolves around converting fractions into decimal form, showing that 'two over five' converts to '0.4' and 'one over four' to '0.25'.

💡Long Division

Long division is a method used to divide numbers where the divisor is larger than one. It is the primary technique used in the video to convert fractions into decimals, such as dividing the numerator by the denominator and adjusting for decimal places when necessary.

💡Numerator

The numerator is the top number in a fraction that indicates the number of parts being considered. In the script, the numerator is used in the long division process, like 'two' in 'two over five', to determine the decimal equivalent.

💡Denominator

The denominator is the bottom number in a fraction that represents the total number of equal parts the whole is divided into. The denominator, such as 'five' in 'two over five', dictates the number of times the numerator can be divided into before reaching a decimal.

💡Repeating Decimal

A repeating decimal is a decimal that has a digit or a sequence of digits that repeat infinitely. The video explains that fractions with 9 in the denominator, like 'one over nine', result in repeating decimals, which are illustrated as '0.111...'.

💡Conversion

Conversion in the context of the video refers to the process of changing a fraction into a decimal. The script demonstrates several conversions, such as converting '3 over 8' to '0.375' and '17 over 4' to '4.25'.

💡Remainder

In the process of long division, the remainder is what is left over after division. The script mentions that once the remainder is zero, the current number at the top is the decimal equivalent of the fraction, as seen when converting 'one over four' to '0.25'.

💡Decimal Point

The decimal point is used to separate the whole number part from the fractional part of a decimal. The video script describes adding a decimal point and a zero to the numerator when the long division does not divide evenly, as in the case of 'one over four' becoming '0.2'.

💡Equivalent

Equivalent in this context means that two quantities have the same value or result in the same outcome. The video shows that fractions and decimals can be equivalent, such as 'two over five' being equivalent to '0.4'.

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