Thanks for visiting the European number format version of the decimals and percents worksheets page at Math-Drills.Com where you will find A4 paper, commas for decimals and points for thousands separators. Decimals worksheets with European number formats including comparing and sorting decimals, and adding, subtracting, multiplying and dividing decimals. To start, you will find the general use printables below to be helpful in teaching the concepts of decimals and place value. More information on them is included just under the sub-title.
Further down the page, rounding, comparing and ordering decimals worksheets allow students to gain more comfort with decimals before they move on to performing operations with decimals. There are many operations with decimals worksheets throughout the page. It would be a really good idea for students to have a strong knowledge of addition, subtraction, multiplication and division before attempting these questions. At the end of the page, you will find decimal numbers used in order of operations questions.
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The thousandths grid is a useful tool in representing operations with decimals. Each small rectangle represents a thousandth. Each square represents a hundredth. Each row or column represents a tenth. The entire grid represents one whole. The hundredths grid can be used to model percents or decimals. The decimal place value chart is a tool used with students who are first learning place value related to decimals or for those students who have difficulty with place value when working with decimals.
For students who have difficulty with expanded form, try familiarizing them with the decimal place value chart first, and let them use it to help them write numbers in expanded form. There are many ways to write numbers in expanded form. 1,23 could be written as 1 + 0,2 + 0,03 OR 1 + 2/10 + 3/100 OR 1 × 100 + 2 × 10-1 + 3 × 10-2 OR any of the previous two written with parentheses/brackets OR 1 + 2 × 1/10 + 3 × 1/100 with or without parentheses, etc. Despite what the answer key shows, please teach any or all of the ways depending on your students' learning needs.
Rounding decimals is similar to rounding whole numbers; you have to know your place value! When learning about rounding, it is also useful to learn about truncating since it may help students to round properly. A simple strategy for rounding involves truncating, using the digits after the truncation to determine whether the new terminating digit remains the same or gets incremented, then taking action by incrementing if necessary and throwing away the rest. Here is a simple example: Round 4,567 to the nearest tenth. First, truncate the number after the tenths place 4,5|67. Next, look at the truncated part (67). Is it more than half way to 99 (i.e. 50 or more)? It is, so the decision will be to increment. Lastly, increment the tenths value by 1 to get 4,6. Of course, the situation gets a little more complicated if the terminating digit is a 9. In that case, some regrouping might be necessary. For example: Round 6,959 to the nearest tenth. Truncate: 6,9|59. Decide to increment since 59 is more than half way to 99. Incrementing results in the necessity to regroup the tenths into an extra one whole, so the result is 7,0. Watch that students do not write 6,10. You will want to correct them right away in that case. One last note: if there are three truncated digits then the question becomes is the number more than half way to 999. Likewise, for one digit; is the number more than half way to 9. And so on...
We should also mention that in some scientific and mathematical "circles," rounding is slightly different "on a 5". For example, most people would round up on a 5 such as: 6,5 --> 7; 3,555 --> 3,56; 0,60500 --> 0,61; etc. A different way to round on a 5, however, is to round to the nearest even number, so 5,5 would be rounded up to 6, but 8,5 would be rounded down to 8. The main reason for this is to not skew the results of a large number of rounding events. If you always round up on a 5, on average, you will have slightly higher results than you should. Because most before college students round up on a 5, that is what we have done in the worksheets that follow.
The comparing and ordering decimals worksheets can be used to help students recognize ordinality in decimal numbers. The comparing decimals worksheets have students compare pairs of numbers and the ordering decimals worksheets have students compare a list of numbers by sorting them.
Try the following mental addition strategy for decimals. Begin by ignoring the decimals in the addition question. Add the numbers as if they were whole numbers. For example, 3,25 + 4,98 could be viewed as 325 + 498 = 823. Use an estimate to decide where to place the decimal. In the example, 3,25 + 4,98 is approximately 3 + 5 = 8, so the decimal in the sum must go between the 8 and the 2 (i.e. 8,23)
Have you thought about using base ten blocks for decimal subtraction? Just redefine the blocks, so the big block is a one, the flat is a tenth, the rod is a hundredth and the little cube is a thousandth. Model and subtract decimals using base ten blocks, so students can "see" how decimals really work.
In the next set of questions, the quotient does not always work out well and may have repeating decimals. The answer key shows a rounded quotient in these cases.