[Music] welcome to math with Mr J in this video I'm going to go through a mini course on converting between fractions decimals and percents we will go through decimals to fractions and decimals to percents then fractions to decimals and fractions to percents then percents to fractions and percents to decimals everything is put into chapters and timestamped so feel free to jump around let's start with converting decimals to fractions and jump into our examples here starting with number one where we have 0.9 9/10 now when we convert a decimal to a fraction we need to take a look at the place the decimal ends so does it end in the tenths hundredths thousands 10,000 or whatever the case may be we use that place to determine the denominator of the fraction and then whatever number we have on the right side of the decimal so the decimal digit or digits will be the numerator for example number one we have a nine that's going to be our numerator now that decimal ends in the 10th place so our denominator is going to be 10 so 9 over 10 910 now once we have the fraction we can and look to simplify if possible 9/10 is in simplest form the only common factor between 9 and 10 is 1 so again this fraction is in simplest form now if we look at the decimal we can read that as 9/10 and then looking at the fraction we can read that as 9/10 these are equal one is just a decimal the other a fraction let's move on to number two where we have 0 .09 so 9 hundredths this looks similar to number one we have a 9 on the right side of the decimal but that decimal ends in the hundredths place so our denominator is going to be 100 so 9 over 100 9 hundredths the only common factor between 9 and 100 is 1 so this is in simplest form moving on to number three we have 0.2 210s two is going to be our numerator and this decimal ends in the 10's place so 10 is going to be our denominator so 2 over 10 210s now this fraction is correct 2/10 is correct but we can simplify here we have a greatest common factor of two that we can divide the numerator and denominator by 2 ID two is 1 and then 10 / two is five so we get 1 over 5 1 15 the only common factor between 1 and five is 1 so this is in simplest form now so 210 as a decimal equals 2 over 10 210 as a fraction and we were able to simplify that fraction to 1 15 let's move on to number four where we have 0.75 75 hundredths here we have 75 to the right of the decimal and this decimal ends in the hundredths place so 75 is our numerator and then 100 is our denominator 75 over 100 75 hundredths and this is correct but we can simplify here we have a greatest common factor of 20 25 that we can divide the numerator and denominator by 75 / 25 gives us 3 and then 100 / 25 gives us four so we get 3 over 4 34s the only common factor between three and four is 1 so this is now in simplest form moving on to number five we have 0 014 14,000 we have 14 to the right of the decimal and this ends in the thousand's place so 14 is our numerator and then 1,000 is our denominator so 14 over 1,00 14,000 and this is correct but we can simplify we have a greatest common factor of two that we can divide the numerator and denominator by 14 / 2 is 7 1,000 / 2 is 500 so 7 over 500 here is 7 500s the only common factor between 7 and 500 is 1 so this is in simplest form and then lastly let's move on to number 6 where we have 3.36 3 and 36 hundredths so for this one we have a whole number which don't let that throw us off all we need to do is focus on the decimal and do the same thing we did for all of the other examples so we can start by writing our whole number three and then we worry about the decimal so we have 36 to the right of the decimal and it ends in the hundredths so 36 is our numerator and then one 100 is our denominator so we get 3 and 36 over 100 3 and 36 hundredths so whenever we have a whole number like that we just rewrite the whole number and then we can focus on the decimal being converted to a fraction now 36 H hundredths can be simplified we have a greatest common factor of four that we can divide the numerator and denominator by so we rewrite our whole number and then focus on that fraction 36 / 4 is 9 and then 100 / 4 is 25 so we get 3 and then 9 over 25 3 and 9 25ths the only common factor between 9 and 25 is 1 so this is in simplest form so there's how to convert decimals to fractions let's move on to to decimals to percents here's our section on converting decimals to percents let's jump into our examples starting with number one where we have 0.52 52 hundredths now when going from a decimal to a percent all we need to do is multiply by 100 multiply the decimal by 100 and that will give us the percent and remember a quick way to multiply by 100 is to to move the decimal twice to the right so for number one let's multiply by 100 by moving the decimal once twice to the right this gives us 52 percent now we don't need that decimal at the end after the two when we write our percent since this is a whole number here we can leave that off so for number one our decimal 5200s equal 52% let's move on to number two where we have 0.01 so 100th let's multiply by 100 by moving the decimal once twice to the right so it comes after the one now which gives us 1% 100th equals 1% let's move on to number three where we have 0.9 9/10 and I'm going to rewrite this decimal underneath because we're going to need a little more room for this one so let's multiply by 100 by moving the decimal once twice to the right so we have a gap there now we need to fill that Gap that place with a zero so our percent here is 90% 9/10 equals 90% % lastly let's move on to number four where we have 0.436 436,000 let's multiply by 100 once twice to the right so the decimal goes in between the three and the six so we have 43.6% 436,000 equal 43.6 6% and that's it that's how to convert decimals to percent let's move on to fractions to decimals here's our section on converting fractions to decimals we will go through four examples for numbers one and two we will work through them by hand so without a calculator and then numbers three and four we will work through those by discussing what we need to plug into a calculator let's let's jump into number one where we have 1/8 now when we convert a fraction to a decimal we can divide the numerator the top number of the fraction by the denominator the bottom number of the fraction so for number one we need to do 1 / 8 so let's set this up 1 / 8 now as far as 1 / 8 how many whole groups of 8 in one one how many eights in one well we can't do that so we need to use a decimal and then a zero in order to work through the division remember Zer to the right of a decimal or decimal digits do not change the value of the number so we're able to do this now once we have that decimal and the zero we can bring the decimal straight up into the quotient the answer and I'm I'm going to extend the division bar as well now we can think of this as 10 / 8 so how many whole groups of eight in 10 how many eights in 10 well one so we need to put the one above the zero now make sure that one is above the zero not the one we used that zero in the tenths place and thought of this as 10 so the one needs to go above that zero in order to keep everything lined up correctly now we multiply 1 * 8 8 subtract 10 - 8 is 2 now we don't have a clean cut zero there at the bottom so what we can do we can use another zero that we can bring down to continue on now we have 20 20 / 8 so how many whole groups of eight in 20 well two that gets us to 16 2 * 8 16 subtract 20 - 16 is 4 so we still don't have that clean cut zero there at the bottom so let's use another zero that we can bring down so now we have 40 40 divided 8 how many whole groups of 8 in 40 well five and that hits 40 exactly 5 * 8 is 40 so subtract 40 - 40 is 0 so now we have that clean cut zero there at the bottom we went all the way over within our division problem and we have that zero at the bottom so we are done we get .125 125,000 1/8 equal 0.125 so 125,000 now you'll notice when I rewrote that decimal I started with a and then the decimal this is common when writing decimals because it and see the decimal we don't want the decimal to get overlooked so something to keep in mind let's move on to number two where we have 5 12ths so we need to do 5 / 12 so let's set this up we have 5 / 12 so 5 / 12 how many whole groups of 12 in five well we can't do that so we need a decimal and a zero in order to work through this bring the decimal straight up we can extend this division bar here and we can think of this as 50 / 12 so how many whole groups of 12 in 50 well four that gets us to 48 now make sure that four is above the Zero 4 * 12 48 subtract 50 - 48 is 2 so we need to continue on let's use another zero that we can bring down and now we have 20 so 20 / 12 how many whole groups of 12 in 20 well 1 that gets us to 12 so 1 * 12 is 12 subtract 20 - 12 is 8 let's use another zero that we can bring down and now we have 80 so 80 / 12 how how many whole groups of 12 in 80 well six that gets us to 72 so 6 here 6 * 12 72 subtract 80 - 72 is 8 let's use another zero and keep going here so we have 80 again how many whole groups of 12 in 80 well 6 6 * 12 72 subtract we get eight now I'm going to stop there because that pattern is going to continue on forever so we end up with a repeating decimal here we get 0 41 and then those sixes repeat they will never end so again a repeating decimal here now we have different options as far as how we want to write out this decimal the first option 5 12ths equal 0 416 and then we put a bar above the six so we can put a bar above the repeating digit or digits if we have multiple digits that repeat the bar is a way for us to write out repeating decimals and in this example the bar above the six tells us that the six repeats or we can round and we can round to whatever place we would like but for this example let's round to the 10's place and the hundredths place let's start with the 10's place so 5 12ths is approximately and I'm using the approximately symbol here since we are rounding it's not exact now as far as rounding we have a four in the 10's place with a one to the right in the hundredths so this rounds to 41s 5 12ths is a approximately 410 how about rounding to the hundredths place well 5 12ths is approximately we have a 1 in the hundredths and then a six in the thousandths so we round up here 5 12ths is approximately 42 hundredths so there are some options as far as working with repeating decimals let's move on to numbers three and and four here are numbers three and four let's jump into number three where we have 9 over 16 916 so we need to divide the numerator by the denominator so plug in 9 the numerator divided by 16 the denominator this gives us 0.56 2 5 so 5,625 10,000 so let's write this up here 916 equal 0.5625 again 5,625 10,000 now another possibility here is to round this to make it shorter so if we get long decimals or even repeating decimals we can round so for examp example number one we can round to the Ten's place hundredths place whatever place we want to let's do tenths and hundreds here so 916 is approximately and I'm using the approximately symbol here since we are rounding it's not exact let's start with the 10ths place we have a five in the 10ths with a six in the hundredths so we round up 916 is a pro approximately 610 now let's round to the hundredths so 916 is approximately well we have a 6 in the hundredths with a two in the thousands so this rounds to 56 hundredths 9/16 is approximately 56 hundredths so some different options there as far as how we can write this out let's move on to number four where we have 30 over 35 30 35ths so we need to divide the numerator by the denominator so plug in 30 divided by 35 that gives us 0.85 7 1 4 two those six digits repeat and go on forever in that pattern now it can be very hard to tell if a decimal repeats if we have multiple repeating digits and the calculator cuts the decimal off before we can tell if it repeats this is a good example of this because depending on your calculator you may not be able to tell if this decimal repeats based on the number of digits shown on your calculator now like I mentioned earlier what we can do if we have a long decimal or a a repeating decimal we can round but before we round here let's write this out as a repeating decimal 30 over 35 30 35ths equals 0.85 7 1 4 2 and we can put a bar above those digits to show that they repeat now our other option is to round so let's do that and we can round to whatever place we would like but let's do the tths and hundreds place again starting with the tenths place so we have 30 35ths is approximately well we have an 8 in the tths with a five to the right in the hundredths so this rounds up to 9 10ths so 30 35ths is approximately 9/10 now let's round to the hundredths so 30 35ths is approximately and then we have a five in the hundredths with a seven to the right in the thousandths so this rounds up as well 30 35ths is approximately 8600 so there you have it there's how to convert a fraction to a decimal let's move move on to fractions to percents now let's take a look at converting fractions to percents and just like last section we will go through four examples for numbers one and two we will work through them by hand so without a calculator and then numbers three and four we will work through those by discussing what we need to plug into a calculator now when converting fractions to percents we can do this by dividing and then multiplying we take the fraction and divide the numerator by the denominator the top divided by the bottom this will give us a decimal we then need to convert that decimal to a percent by multiplying it by 100 and remember a quick way to multiply by 100 is to move the decimal twice to the right so we go from a fraction to a decimal and then that decimal to a percent let's jump into our examples starting with number one where we have 34s well we need to start by dividing the numerator by the denominator 3 / 4 so let's come down here and set this up so 3 / 4 now as far as 3 ID 4 how many whole groups of four in three how many fours in three well we can't do that so we need a decimal after three and then a zero in order to start to work through this problem now remember zeros to the right of a decimal or decimal digits do not change the value of a number so we're able to do this now let's take the decimal and bring it straight up into where the quotient the answer will be now we can go through our division steps I'm going to extend this division bar here and now we can think of this as 30 / 4 how many whole groups of four how many fours in 30 well 7 that gets us to 28 now make sure that seven is above the zero not the three since we used that zero and thought of this as 30 / 7 now we multiply 7 * 4 is 28 subtract 30 - 28 8 is 2 now we don't have a clean cut zero at the bottom there so what we can do we can use another zero that we can bring down in order to continue the problem so now we have 20 20 / 4 which is 5 so let's put our five up here then multiply 5 * 4 20 subtract 20 - 20 is 0 so we went all the way over within our division problem and we have that clean cut zero at the bottom so we are done 75 so I'm going to come to the side here and rewrite our decimal and I'm starting with a zero and then a decimal this is typical when writing decimals because that's going to help us recognize we have a decimal here it's going to help us see the decimal so 0 75 so 3/4s in decimal form is 0.7 75 let's multiply by 100 to convert it to a percent and a quick way to do that again move the decimal twice to the right so once twice so the decimal is now here this gives us 75% and we don't need that decimal at the end since we have a whole number here we can leave that off so 34s equals 75 5% let's move on to number two where we have 7 15s so we need to do 7 / 15 the numerator divided by the denominator so 7 / 15 now 7 divid 15 how many whole groups of 15 in seven how many 15s in seven well we can't do that so let's use a decimal and a zero in order to work through this problem I'm going to extend the division bar here and bring the decimal straight up now we can think of this as 70 ID 15 so how many whole groups of 15 in 70 well four that gets us to 60 now we multiply 4 * 15 is 60 subtract 70 - 60 gives us 10 so we don't have that clean cut zero we can continue on so let's use another zero that we can bring down so now we have 100 100 / 15 how many whole groups of 15 in 100 well six that gets us to 90 so let's put our six then multiply 6 * 15 is 90 subtract 100 - 90 is 10 so we still don't have that cleancut zero let's use another zero that we can bring down so we have 100 again 100 / 15 how many whole groups of 15 in 100 well 6 6 * 15 is 90 subtract we get 10 again and you may notice that we have a pattern here and this is going to give us a repeating decimal it's never going to end we can add as many zeros as we'd like and bring them down and we're not going to get to that clean cut zero and we end up with 100 again so we have 100 ID 15 how many whole groups of 15 in 100 well 6 6 * 15 is 90 subtract 100 - 90 gives us 10 again and again those sixes are going to continue forever so what we can do here I'm going to write the decimal off to the side so we have 0.4 6666 and these continue on we have a repeating decimal so we have a few different options here but before we get to that we have our decimal so we need to multiply by 100 let's move the decimal once twice to the right so we end up with 46 six repeating percent so how do we write this the first way we can write 71 15s equals 46.6 and then use a bar over the six to show that that digit repeats percent the next way to write this percent is to round and for this example we're going to round to the 10th place so at the bottom here we see we have a six in the tths with a six to the right in the hundredths place this tells us to round up so if we round to the nearest 10th we have 7 15s is approximately and I'm using the approximately symbol here since we are rounding it's not exact 46 7 per so rounding to the nearest 10th you can also round to the nearest 100th or whatever place you would like and then the last option I'm going to mention is rounding to the nearest whole percent and that's going to be the ones place so if we look at the bottom here we have a six in the ones place with a six to the right in the 10ths so is this closer to 46% or 47% well that's 6 in the 10 10's Place tells us to round up this is closer to 47% so 71 15 is approximately 47% so a few different options there as far as working with that repeating decimal so when we come across repeating decimals we can still write them as a percent or even if we come across long decimals that don't repeat we're able to round those if we need to let's move on to numbers three and four here are numbers three and four let's jump into number three where we have 24 30ths well we need to start by dividing the numerator by the denominator so 24 / 30 so we plug in 24 divided by 30 that gives us 0.8 810 so that's 243s as a decimal now we need to convert that decimal to a percent by multiplying it by 100 and again we can do this by moving the decimal twice to the right so once twice to the right and we can fill this Gap this place with a zero this gives us 80% and we don't need that decimal at the end since we have a whole number here we can leave that off so 243s equal 80% let's move on to number four where we have 316 so we need to divide the numerator by the denominator so we need to plug in 3 / 16 that gives gives us 0.1875 so 1,875 10,000 so that's 316 as a decimal now we need to multiply by 100 to convert it to a percent let's do that by moving the decimal once twice to the right so the decimal goes in between the 8 and the Seven that gives us 18.75% so 316 equals 18.75% and I do want to mention we can round this to the nearest whole perent if needed and all we need to do here is round to the ones place so is this closer to 18% or 19% well we need to take a look at the ones place here and the 10's place to the right that seven tells us that we round up so 316 is approximately 19% so this is exact right here and then this is rounded to the nearest whole percent so that's something to keep in mind especially if we end up with a very long decimal or a repeating decimal we can always round if need be so there you have it there's how to convert a fraction to a percent let's move on to percents to fractions now let's take a look at converting percents to fractions starting with number one where we have 23% now remember percent means per 100 so we can think of this as for each 100 or out of 100 so all we need to do in order to go from a percent to a fraction is to take away the percent symbol and rewrite whatever we have with a denominator of 100 so put it over 100 once we have the fraction we can simplify if possible so for 23% we write this as 23 over 100 23 hundredths and that's it that's our fraction now this fraction cannot be simplified the only common factor between 23 and 100 is 1 so we are done again 23% equal 23 over 100 as a fraction 23 hundredths let's move on to number two where we have 10% so we need to drop that percent symbol and put this over 100 so 10 over 100 10 hundredths and that's 10% as a fraction but we can simplify here we have a greatest common factor of 10 that we can divide the numerator and denominator by in order to simplify so we need to divide the numerator by 10 and the denominator by 10 10 / by 10 gives us 1 and then 100 / 10 gives us 10 so we get over 10 1110th the only common factor between 1 and 10 is 1 so this is in simplest form we are done here 10% equal 10 over 100 10 hundredths but we were able to simplify that to 1 over 10 1110th let's move on to number three where we have 94% so let's write this as a fraction here we have 94 over 100 94 H hundredths and this is correct but we can simplify here we have a greatest common factor of two that we can divide the numerator and denominator by in order to simplify 94 / 2 that's 47 and then 100 ID 2 is 50 so we get 47 over 50 47 50ths the only common factor between 47 and 50 is 1 so we are done lastly let's move on to number four where we have 65% so we write this as a fraction as 65 over 100 65 hundredths and that is correct but we can simplify again here we have a greatest common factor of five that we can divide 65 by our numerator and 100 by our denominator 65 divid 5 gives us 13 and 100 ID 5 gives us 20 the only common factor between 13 and 20 is 1 so we are in simplest form 13 over 20 13 20ths so there you have it there's how to convert percents to fractions let's move on to our last section percents to decimals here's our section on percents to decimals let's jump into our examples starting with number one where we have 85% now when going from a percent to a decimal all we need to do is divide by 100 divide the percent by 100 and that will give us the decimal and remember a quick way to divide by 100 is to move the decimal twice to the left so for number one let's divide 85% by 100 for 85% the decimal comes after the five after the ones place so I'm going to rewrite this as 85 and then the decimal we can always write a decimal after a whole number if need be we typically don't write decimals or see them with a whole number though because they aren't needed so something to keep in mind so to divide by 100 here let's move the decimal once twice to the left that gives us 85 85 hundredths so 85% equals 0.8 5 now when I rewrote that decimal I started with a zero and then the decimal this is common when writing decimals because it helps us recognize and see the decimal we don't want the decimal to get overlooked let's move on to number two where we have 2% I'm going to rewrite this underneath with a decimal and now we need to divide by 100 so let's move the decimal once twice to the left and we need to fill this Gap this place with a zero so we get 02 2% equals 0.02 200 as a decimal let's move on to number three where we have 70% I'm going to rewrite this underneath with a decimal by 100 so move the decimal once twice to the left so we get 70 70% equal 0.70 70 hundreds as a decimal now one more thing I do want to mention about number three remember zeros to the right of decimal digits do not change the value of anything so really we can write this as 0.7 as well so 710 so we took that zero on the end off these decimals are equivalent so they are both correct so that's something to be aware of when working with decimals lastly let's move on to number four where we have 39.4% so let's divide this by 100 in order to convert it to a decimal so let's move the decimal once twice to the left and we end up with 394 so 39.4% equals 0.394 so 394,000 so there you have it there's how to convert percents to decimals and that's it that's our mini course on converting between fractions decimals and percents I hope that helped thanks so much for watching until next time peace