Learning Place Value of Decimals: Why Isn't there a "Oneths" Place?

Phyl CampbellStarred Page By Phyl Campbell, 14th Jan 2014 | Follow this author | RSS Feed | Short URL http://nut.bz/3pl_hzru/
Posted in Wikinut>Family>Education

Place value, especially of decimals, can be complicated and difficult to explain. Hopefully a walk with me on my journey teaching the concept to my son will help you explain it to your children or help you understand it better yourself.

I am home-schooling my fifth grader for the first time, using a public online school curriculum. I hope this will be the first of many practical articles about this experience.

Why Isn't There a "Oneths" Place?

When we study place value of whole numbers, it is fairly straightforward. Ones, tens, hundreds, thousands, ten thousands, one hundred thousands, millions, and so forth are easy to explain to students of all ages. However, even adults get tripped up with fractions and decimals, probably because the lesson they remember (regardless of what was taught) is that "well, that's just the way it is." But math isn't English spelling, where words are pronounced differently depending on their country of origin. Math, on the contrary, is quite logical. There is a rhyme and reason for every part of every number. Some would argue that every nuance must not be understood, but for people who fear math, the missing nuances cause that fear. Exposing those nuances is like flipping on the light -- exposing the pile of laundry for the monster that appeared to be coming out from under the bed. Once the logic behind the math in understood, it isn't so scary. Anyone and everyone CAN do it if they understand what they are seeing and can relate to it.

So back to the basic question: why isn't there a oneths place? And the answer is simple – one, or really any number, divided by one, is the same as it started out. Any whole number divided by itself is one, which is a whole number. Any fraction divided by itself becomes one, a whole number. So the "oneths" place does exist – it's simply the whole number "one," and we call it the "ones" place.

Tenths place

After the decimal point, the next place value is the tenths place. I ask students to tell me what coin could be used to talk about tenths place. Most students can tell me "a dime," but some students will say "change," "cents," "dimes or quarters," or similar responses. It is not the student's fault that I worded the question badly. Although the dime is the coin that BEST answers the question, as ten dimes make a dollar and the dollar represents the whole number, having two nickels just as easily yields .10, as does 10 pennies. A patient teacher must continue to question, asking "which coin, with no help from any other coin and no change left over, could equal 1/10th of a dollar?" Or, "what one coin could show $0.10?" Or, "make a dollar using exactly 10 coins of equal value." These questions will help the learner to understand tenths in the most simplified way. Tenths can also be expressed as the fraction 1/10, or #/10, where # is any whole number. Real world examples of tenths may include a correct number of problems out of 10, like a pop quiz or homework assignment grade. Measurements may also include tenths – though this happens less often in the US, where the metric system is under-utilized.

If decimals are not getting my point across, I will draw a circle and bisect it 5 times (See resources for a more accurate pie chart of tenths). Math you can eat is a lot less scary than math that you can't eat, so when I'm bisecting circles I'm talking to the student about slices of pizza, cake, or pie.

Hundredths place

This is where my son got really confused. A penny is one cent, he reasoned, so pennies should be in the "oneth" place. However, just like a dime is one tenth of a dollar, a penny is one hundredth of a dollar. One "oneth" of a dollar is a dollar, and it's easier to just say a buck.

Aside: Clock Math as a Study in Circle Fractions

If the student is not already familiar, I'd also use this time slot to fit in clock math – a clock is a pie cut into 12 5-minute sections, but can also be thought of as 6 10-minute sections, 4 15-minute sections, and so on. And if a clock can be cut into 12, 6, and 4 sections of 5, 10, and 15 minutes, then it's time to show the student that the clock could just as easily be broken into 5, 10, and 15 sections of 12, 6, and 4 minutes each. Any way the clock or pie is sliced, there are still 24 hours that are each 60 minutes long, and foods well made are tasty to those that enjoy them.

Clocks and pies are rarely cut into 10 pieces, since it is difficult to bisect a circle evenly an odd number of times after the first one (in other words, it's easy to cut a pie in half; but more difficult to cut 3 equal slices – although three pieces would make a lovely peace sign -- or any odd number of cuts after that. It's much easier to cut the pie in half vertically, then into quarters, then bisect each of those the number of times one wishes to do so.) Despite the ease in free-handing, though, enter a search for circle graphs, pie graphs, and the number of pieces you want, and you will be able to find images with even slices. I have one referenced below.

Aside: Skip Counting is Learning to Multiply

I'm not sure why it is that counting by ones, twos, fives, and tens is easier for most people than counting by threes, sixes, sevens, or eights, but as a general rule this is true. Logically, it would have to do with using fingers and body parts as counters, but I think it would have been just as easy to make an abacus that counted off in sixes if mankind had chosen to do so. The nines multiplication tables are now taught to most children using either the finger manipulation method or the "digits add up to nine" method (see resources if you're not familiar with this).

However, something being a general rule does not mean that the rule cannot be adjusted or broken. Most people have (or can imagine having) 10 fingers. In counting by ones, each finger stands for one, which allows a person to count to 10. In counting by twos, each finger stands for two, which allows one to count to 20. Counting by 5s allows those fingers to reach 50. But there's no reason why the same method can't be used and practiced to help learners skip count to 30 by 3s, 40 by 4s, 60 by 6s, and so forth. While older learners (8 and up) should start learning to memorize times tables without training aids, those who need a hand should practice skip counting and using their fingers as guides to keep track of what has been counted.

But back to decimals. Here's a review, and thousandths place has been added:

Thousandths place

Thousandths place is usually rounded off in terms of dollars and cents, but students will see thousandths place at fueling stations, in rounding repeated numbers like 2/3, and sometimes in percentage grades – fractions that don't become decimals easily (with only two places after the decimal). In money terms, 1,000 times .001 = $1.00. As a fraction, thousandths place is written as 1/1000 or #/1000.

Aside: Amount and Value

If your learner is still getting stuck on decimal place value, it may help to remind him or her about the difference between amount and value. For example, show that $0.10 is one dime while $.01 is one penny. Each has the amount of one coin. However, each coin has different value. If someone has $.19, then he or she might have one dime (or two nickels) and nine pennies. While he or she might have more coins representing the nine cents, the nine cents does not have more value than the dime (or two nickels). No one explains that better than the poet Shel Silverstein, in his poem, Smart:

End of Lesson

Thanks for sticking with me until the end. I really hope this lesson has been helpful to you. I didn't think math was very easy when I was growing up, but the more I have taught, the better my understanding. I hope you'll find the same to be true for you.

Check out my other teaching articles:
Why does that letter make that sound?
Help for getting kids ready in the mornings
Adjusting craft and card table legs for taller people

Resources

A printable worksheet I used with my son:
http://www.helpingwithmath.com/printables/tables_charts/cha0301place_value_thousandths01.htm

A pie graph I used because it had tenths.
http://www.moveitmaththesource.com/realfractions/elementaryscho13.html

http://www.youtube.com/watch?v=xBTGKiVgWcA
(Video about 9 times table)

http://www.youtube.com/watch?v=xNEvk1-Y6zQ (Shel Silverstein Video)

I made the graph I used as a photo in the "thousandths" section. Other photos came from morgueFile.com

Tags

Decimals, Fractions, Hundredths, Math, Place Value, Skip Counting, Tenths, Thousands

Meet the author

author avatar Phyl Campbell
I am "Author, Mother, Dreamer." I am also teacher, friend, Dr. Pepper addict, night-owl. Visit my website -- phylcampbell.com -- or the "Phyl Campbell Author Page" on Facebook.

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Comments

author avatar Phyl Campbell
15th Jan 2014 (#)

Thanks, Mark, for the quick mod and star merit. My head is still a little fried from all the math! ;)

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author avatar Fern Mc Costigan
15th Jan 2014 (#)

Excellent and interesting post!

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author avatar Phyl Campbell
15th Jan 2014 (#)

Thanks, Fern!

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author avatar Connie McKinney
15th Jan 2014 (#)

Great post, Phyl. I like the drawing of the circle to explain fractions. Math is pretty straight forward unlike English. It's still not my best subject.
Anyway, good luck with the math lessons. It sounds like you're doing a good job at homeschooling so far. I think you can get a lot of articles out of this one.
Sharing now.

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author avatar Phyl Campbell
15th Jan 2014 (#)

Thanks for the vote of confidence, Connie! Normally the lessons are delivered via an online coach, but this one wasn't for some reason. Probably because it is covered in an earlier grade. But if someone is in the same boat as me, maybe it will help, and so much the better. Thanks!

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author avatar Ptrikha
15th Jan 2014 (#)

A great article on basic maths. The usage of clocks and Pies is great. I would like to share something here. In cricket, each over bowled by a bowler consists of 6 balls. So a keen interest in cricket made my multiplication and division by 6 quite great. Now, If someone asks me what is 264/6. I do not have to wait even a second, and would tell 44. Why?
Because 50 overs in cricket mean 300 balls, and 264 balls mean 6 overs, or 36 balls less. So that makes them 44 overs. Difficult to explain to someone who does not follow cricket. Yet may be Peter Giblett and Johnnydod can follow.
And I am also going to share this work of yours on Zurker.

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author avatar Phyl Campbell
15th Jan 2014 (#)

Thanks so much Ptrikha! I can follow what you are saying, though I don't follow Cricket. I appreciate the share on Zurker -- thanks!

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author avatar Ptrikha
16th Jan 2014 (#)

You are welcome :)

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author avatar cnwriter..carolina
15th Jan 2014 (#)

absolutely marvellous this Phyl...numbers are so important..did you watch the movie Pi?

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author avatar cnwriter..carolina
15th Jan 2014 (#)

I shared...

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author avatar MarilynDavisatTIERS
16th Jan 2014 (#)

Good evening, Phyl;great Article. I do not do math. Seriously, I asked after learning division if I could stop attending any more math lectures; I was only in the 3rd grade. Alas they did not understand what I knew about myself and made me participate. If I had you for a teacher, perhaps my checkbook would not have been such a mess....thank goodness for Quick Books :) ~Marilyn

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author avatar Phyl Campbell
16th Jan 2014 (#)

Oh, what a compliment, Marilyn! You are too sweet! Thanks!

Carolina -- There are a couple of movies Pi, 3.14, Life of Pi -- I read the last but did not see any. The last "math" flick I watched was "Proof," and I loved it. Then again, Philip Seymour Hoffman is always interesting to watch... I'm glad you liked it.

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author avatar cnwriter..carolina
26th Jan 2014 (#)

Pi is the one...

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author avatar vpaulose
17th Jan 2014 (#)

Great info. Very nice. Hope to see more. Thank you dear brother Phyl.

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author avatar Peter B. Giblett
17th Jan 2014 (#)

I read his at first and it was not a good time because I was not feeling well, a few days later I have now perked up and am now more able to read, understand and enjoy. Thank you - Good explanation.

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author avatar Phyl Campbell
17th Jan 2014 (#)

Thank you, deal vpaulose. However, as a woman, I'm not sure calling me "brother" is appropriate. I assume from your profile picture that you are male. If I am mistaken, then my sincere apologies. My profile picture is a drawing someone did of me when I was much younger and better looking. ;)

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author avatar cnwriter..carolina
26th Jan 2014 (#)

but your beauty shines from within not only on your face but in your words and comments...

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author avatar Phyl Campbell
17th Jan 2014 (#)

Peter -- I'm sorry you were not feeling well before. I am glad that your comment suggest you are on the mend. Thank you for your comment. I am certainly glad if you enjoyed it.

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author avatar Kingwell
19th Jan 2014 (#)

I really like this. I too found math difficult at school. Loved the video!

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author avatar Phyl Campbell
19th Jan 2014 (#)

Thanks Kingwell! Everytime someone starts to talk about math that is somewhat over my head, I think of this poem. So glad you enjoyed the video!

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author avatar Sivaramakrishnan A
20th Jan 2014 (#)

I was good in certain areas of maths. The foundation should be strong and then we can build further easily. Thanks Phyl for in depth analysis to make it look a cake walk! siva

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author avatar Phyl Campbell
20th Jan 2014 (#)

Thanks, Siva!! I like cake. ;)

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author avatar Legend
26th Jan 2014 (#)

grea share!

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author avatar Phyl Campbell
26th Jan 2014 (#)

Thanks, Legend!

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