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7/27/2019 ~Basic Math~Decimals~
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7/27/2019 ~Basic Math~Decimals~
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What is Decimals?
The word "Decimal" really means "based on
10" (From Latin decima: a tenth part).
We sometimes say "decimal" when we mean
anything to do with our numbering system,
but a "Decimal Number" usually means there
is a Decimal Point.
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And that is a Decimal Number!
"three hundred twenty seven and four tenths"
Example:
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Application of Decimals
RM100 + RM30 + RM7 + RM0.80 + RM0.02
= RM137.82
If we are using money, it would looklike this:
If we are not using money, it would
look like this:
100 + 30 + 7 + .8 + .02 = 137.82
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When else do we use decimals?
Weight = 3.5 kg
Height = 1.61 m
Temperature = 43.7C
Measuring distances = 149.8 km
Can you think of any other?
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Ordering Decimals
Units Decimal
point
Tenths Hundredths Thousandths
0 . 4 0 2
0 . 4 2 0
0 . 3 7 5
1 . 2 0 0
0 . 8 5 0
Order the following decimals:0.402, 0.42, 0.375, 1.2, 0.850
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Example: Add 1.452 to 1.3
Line the decimals up: 1.452+ 1.3
"Pad" with zeros: 1.452
+ 1.300
Add: 1.452+ 1.300
2.752
That's all there is to it - just remember to line up the decimals, then add normally!
Adding Decimals
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Example: Subtract 0.03 from 1.1
Line the decimals up: 1.1- 0.03
"Pad" with zeros: 1.10- 0.03
Subtract: 1.10- 0.031.07
Subtracting decimals is easy if you keep your work neat!
Subtracting Decimals
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Example: Multiply 0.03 by 1.1
start with: 0.03 1.1
multiply without decimal points: 3 11= 33
0.03 has 2 decimal places,and 1.1 has 1 decimal place,so the answer has 3 decimal places: 0.033
Multiply without the decimal point, then re-insert it in the correct spot!
Multiplying Decimals
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Example: Divide 9.1 by 7
Ignore the decimal point and use Long Division:
13
7 )91
72121
0
Put the decimal point in the answer directly above thedecimal point in the dividend:
1.37 )9.1
The answer is 1.3
Dividing Decimals
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But what if you want to divide by a Decimal Number?
The trick is to convert the number you are dividing by
to a whole number first, by shifting the decimal point
of both numbers to the right:
Now you are dividing by a whole number, and can
continue as normal.
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Convert Decimals to Fractions
Step 1: Write down the decimal divided by 1.
0.75
1
Step 2: Multiply both top and bottom by 10 for every
number after the decimal point. (For example, if there aretwo numbers after the decimal, then use 100, if there are
three then use 1000, etc.)
x100
0.75 751 100
Example 1: Express 0.75 as a fraction
Step 3: Simplify (or reduce) the fraction
75 = 3
100 4
Note: 75/100 is called a decimal fraction and 3/4 is called a common fraction !
http://www.mathsisfun.com/simplifying-fractions.htmlhttp://www.mathsisfun.com/simplifying-fractions.html7/27/2019 ~Basic Math~Decimals~
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Convert Decimal to Percent
To convert from decimal to percentage, justmultiply the decimal by 100, but remember toput the "%" sign so people know it is per 100.
The easiest way to multiply by 100 is to movethe decimal point 2 places to the right:
move the decimal point 2 places to the right, and add the "%" sign!
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EXERCISES
Rearrange the decimals in ascending and descending order.
1) 0.0010, 0.1101, 0.0110, 0.1001, 0.0011, 0.01
~answers~
Ascending order:
0.0010, 0.0011, 0.01, 0.0110, 0.1001, 0.1101
Descending order:
0.1101, 0.1001, 0.0110, 0.01, 0.0011, 0.0010
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2) 0.3133, 0.3123, 0.1311, 0.0132, 0.2310, 0.2013
~answers~
Ascending order:0.0132, 0.1311, 0.2013, 0.2310, 0.3123, 0.3133
Descending order:
0.3133, 0.3123, 0.2310, 0.2013, 0.1311, 0.0132
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1) 12.32 and 0.439
2) 7.33085 and 0.01075
EXERCISESAdd and subtract the following decimals.
Add : 12.759
Subtract : 11.881
Add : 7.33085
Subtract : 7.30935
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EXERCISESMultiply and divide the following decimals.
1) 7.15 and 5
2) 66.6 and 12
Multiply : 35.75
Divide : 1.43
Multiply : 799.2
Divide : 5.55
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