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Decimals

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Theresa McGeragle

on 23 January 2013

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Transcript of Decimals

Decimals Rounding Decimals Numbers In The Media And now you know all about
UNIT 4: decimals You can round decimals to the nearest tenth, hundredth, thousandth, and whole much like you round whole numbers to nearest ten, hundred, and thousand. Exploring Thousandths A thousandth is the decimal you get when you divide a whole by 1000. Ex) The worlds population in 2012 is about 7.25 billion! Write this number in standard form.
different ways to represent fractions/decimals
relate fractions to decimals
round decimals
estimate and add, subtract, divide and multiply decimals
know and understand decimals up to thousandths 1. Write the number in expanded form: 7 + .25 billion.
2. .25 billion is a quarter of a billion.
3.One billion is 1000 millions and a quarter of 1000 is 250.
4. Add the quarter billion to 7 billion.
5. 7 000 000 000 + 250 000 000 = 7 250 000 000
The world population is about 7 250 000 000! Round the number to the nearest ten, hundred or thousand, million or billion depending on how accurate you want your number. 43678000 rounded to its nearest ten thousand is 43 670 000. Reports in the media often contain large numbers in decimals. It is important to know what these decimals mean and how to write them. Ex) Pretend you are a reporter and you need to report the number 43 678 000 in a decimal. Take all the digits except the zeros and put a . ( decimal ) in between the first place value and second. The decimal for 43 678 000 is 43.67 Comparing and Ordering Decimals We can compare decimals much like we compare whole numbers. Ex) Order the numbers in this graph from greatest to least. Height jumped by students .1 m .88 m .84 m .82 m .86m mark Lucas Kevin Joe Mark= .879 Lucas= .84 Joe= .897 Kevin= .82 The 2 (hundredths column) in .82 is smaller than all the other hundredths columns. The 4 in Lucas's (hundredths column) is smaller then Marks and Joe's hundredth column jump. The 7 (hundredth column) in .879 is only smaller than joes jumps hundredth column. Joes jump is biggest. TIP! Even though 8675 is bigger than 868, .8675 is smaller than .868 since decimals are only bits (fractions) of a whole number. Adding zeros after a decimal does not affect the value of the decimal at all. .6727466927 = 672746692700000000000000000000000000000000 Estimating Sums and Differences Ex) Round 5.727 to its nearest hundredth.
You can use a number line by seeing where the digit after the place value you want to round to places on a line from 1 - 10. 5.725 The two in 5.727 is its hundredth column and 7 is one place value smaller than that.
Place 7 on a number line from 1 - 10. 1 2 3 4 5 6 7 8 9 10 7 is closer to 10 than 1 so you round up and change the hundredths column ( 2 ) to a three and erase the 7. TIP! If the number is exactly halfway on the number line ( number 5 ) you always round up. Their are a few ways you can estimate to see if your answer is reasonable. You can round both the decimals you are adding are subtracting to the nearest whole number. Estimate 2.345 + 1.99. Use the strategy you have from the rounding lesson to see if the tenth is closer to 10 or 1. 2.345 = rounded = 2
1.99 = rounded = 2 Add 2+2=4. 4 is your estimate. You can also round one of the decimals to the nearest whole.
Estimate 2.345 + 1.99 2.345 = rounded = 2 2 + 1.99 =3.99 Your estimate is 3.99! If you are looking for an even more accurate estimate you can round to the nearest tenth or hundredth. Estimate 2.345 + 1.99 by rounding them to their nearest tenth. 2.345s hundredth column is closer to 0 than 10 and 1.99s hundredth column is closer too 10 than one so round both 2.345s tenth column down ad 1.99s up. 2.345 rounded is 2.3
1.99 rounded is 2 2.3 + 1 = 3.3 is your estimate! Adding and Subtracting Decimals Adding and subtracting decimals is important since many stats and facts are recorded in decimals and we need to know how to compare these numbers
You can add decimals much like adding whole numbers. Ex) Timmy and Mark have been running a 42.2 km marathon. Mark has run 21.654 km and Timmy has run 16.783 km. How many km have they run combined? 1. Add 21.654 + 16.783 just like you would add
whole numbers lined up by place value. 2 1. 6 5 4
+ 1 6. 7 8 3
--------------
3 8. 4 3 7 1 2. To check your answer you can estimate by rounding the two decimals to see if your answer was reasonable.
If the sums are about the same then your answer is reasonable. 22
+17
39 Timmy might drop out of the run do to health problems but Mark wants to continue. How many more km does Mark have to run before he finishes the 42.2 km marathon? 1. Subtract how far he has run from the total distance of the marathon to find the difference. 1 11 9 10
4 2. 2 0 0
- 2 1. 6 5 4
2 0. 5 4 6 \ \ \ \ Multiplying Decimals by 10, 100, 1000 and 10 000 - when you multiply by 10, 100,
1000, and 10000 you shift the
decimal in the number to the
right the same number of times
as their are zeros in the number. Cheat Sheet number divided number of shifts
to the right 10 100 1000 10000 1 2 3 4 Ex) Multiply 8.72 by 10, 100, 1000
and 10000. 8.72 x 10 = 87.2 8.72 x 100 = 872. 8.72 x 1000 = 8720. 8.72 x 10000 = 87200. Dividing Decimals by 10, 100, 1000 and 10 000 - when you divide decimals by 10, 100, 1000 and 10000 you shift the decimal point in the decimal to the left the same number of times as their are zeros in the number you are dividing by Cheat Sheet 10
100
1000
10000 1
2
3
4 number decimal shifts Ex) Divide 2.4 by 10, 100, 1000 and 10 000. 2.4 / 10 = . 2 4 decimal shift once to the left 2.4 / 100 = . 0 2 4 decimal shift twice to the left 2.4 / 1000 = . 0 0 2 4 decimal shift three times to the left decimal shift four times to the left 2.4 / 10000 = . 0 0 0 2 4 Multiplying Decimals by .1, .01, and .001. When you multiply decimals by .1, .01 and .001 you
decimal shift to the left once for .1, twice for .01, and
three times for .001. Ex) Multiply 481 x .1. You need to decimal shift the decimal in 481 once to the left since it is being multiplied by .1. 4 8.1 Multiply 481 x .001. You need to decimal shift the decimal in 481 three times to the left since it is being multiplied by .001. .4 8 1 481 x .1 = 48.1 481 x .001 = .481 Multiplying Decimals by a
1 digit Whole Number - You can multiply decimals by whole numbers much like you multiply whole numbers by whole numbers with a few exceptions Ex) Multiply 2.63 x 3. 1. Round 2.63 to 3. 3 x 3 = 6.
We now know the product will be smaller than 6. 2. Set up multiplication just like you do for whole numbers. 2.63
x 3 3. Multiply 3 x 3 ( hundredths column ) = 9. Put 9 under.
Continue with the rest of the digits. 2.63
x 3
9 4. Add all of the digits you have placed under. 2.63
x 3
9
18
+ 5
35 5. Use your estimate of 6. to help place your decimal on 35 ( the decimal point is after 6 so you would put the decimal after 3 in 35 because 3.5 is close to 6 ) Dividing Decimals by a 1 Digit Whole Number You can divide decimals by 1 digit whole numbers much like you divide whole numbers. long divide 8.4 by 4. 1. Set up long division. 4 8.4 2. Four goes into eight twice and
4 x 2 = 8.
8 - 8 = 0 2
4 8.4
- 8
0 3. Bring down the four.
Four goes into four once and
4 x 1 = 4.
4 - 4 = 0. 2 1
4 8.4
- 8
0 4
- 4
0 short divide 7.4 by 3 3 7.4 1. Set up short division 2. Three goes into seven twice with a remainder of one. Put a two under seven and a one in between 7 and 4. 3 7.4
2 1 3. Three goes into fourteen four times with a 2 remainder. Put a four under four and since their are no more numbers to divide place your remainder of 2 after four and add a zero to make 10. 3 7.4 0 0 0
2 4 9 9 9 4. Place a decimal point in between 2 and 1 to get you answer of 2.1. 5. Finally drag the decimal point down from in between 7.4 to in between 2 and 4 to get your answer of 2.4999. 1 1 1 1 .
4.If you continue your short division you will notice that u get a continuing 9 so write three nines to make sure it is continuing and put a dot above to show infinity. For more help on the unit decimals visit these links for fun decimal games: http://cemc2.math.uwaterloo.ca/mathfrog/english/kidz/addsubdec.shtml For example if you have a thousandth grid and you shade in 378 squares, you have .725. You can show thousandths in decimals or a fraction : Decimal fraction .725 or 725
1000
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