~Basic Math~Decimals~

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.html


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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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~Basic Math~Decimals~