DECIMAL SYSTEM - WordPress.com...Decimals are part numbers. The dot separates the whole numbers from...

DECIMAL SYSTEM

Almudena Casares Fernándezwww.matematicasalmudena.com

Decimals are part numbers. The dot separates

the whole numbers from the part numbers and

it is called the decimal point.

32.156

Whole number Part numberDecimal

point

www.matematicasalmudena.com Almudena Casares Fernández

Name the whole number and the part number

with the value of the last digit.


34.267 = 3 Tens+ 4 Ones + 2 Tenths + 6 Hundredths + 7 Thousandths

You read in “math way”:

Thirty-four and two hundred and sixty seven thousandths

VIDEO:http://www.youtube.com/watch?v=qQ4YaNkA7_4

Decimal point


http://www.youtube.com/watch?v=qQ4YaNkA7_4

30.2

426.51

2.4

32.1627

102.45

27.12

0.13

45.953

0.125


Putting zeros on the end of decimals doesn’t change them.

4.5 = 4.50

To order them, look carefully at the value of each digit. First compare the whole number parts, then the digits in the tenths place, then the digits in the hundredths place, and so on.

Between two decimals there are infinite decimals.


The YES or NO game. Display these randomly chosen

numbers on the board. Pick one of them but don't tell the

students which one. They must guess which number you have

chosen by asking you questions, to which you will only answer

yes or no. They could ask questions like, is your number

greater than... or, does your number have more than 4

tenths? Each time a question is asked a student can come to

the board and click on the numbers that have been

eliminated. You could play this game regularly and use the

timer function to encourage the class to ask better questions

and beat their previous time to find the number you were

thinking of.


http://www.mathspad.co.uk/teach/tools/orderingDecimalsTool.swf

1. Exact decimals: An exact or terminating

decimal is one which does not go on forever,

so you can write down all its digits.

2.4

3.999

5.28


2. Recurring decimals: A recurring decimal is a decimal

number which goes on forever, but where some of the digits

are repeated over and over again. That is called a repeating

digit or recurring part.

o Pure recurring decimals: The recurring part begins just

after the decimal point.

o Mixed recurring decimals: There is a non -repeating part

and after it, the recurring part begins.

2.44444 2.4; 0.454545 =0.45

2.43333 2.43; 0.79050505 =0.7905


3. No exact and no recurring decimals: They go on

forever, but they don’t have any recurring part.

3.141592...

7.01001000100001....

Find out the first twenty

decimal digits of Pi.


Rounding to the nearest value:

1st) See what you are rounding to.

2nd) Look at the digit to the right of it.

3rd) If it’s smaller than 5, your digit stays the

same. If it’s 5 or more, your digit goes up one.

4th) After you round the number, eliminate all

other digits to the right.

3.25 (rounded to the nearest tenth) 3.3


The error is the difference between the value of an approximtion, and the true value.

PLAY AND LEARNhttp://www.ixl.com/math/grade-5/round-decimalshttp://www.sheppardsoftware.com/mathgames/decimals/scooterQuestDecRound.htm

3.58 3.6 error 3.6-3.58 0.02

Try it out!


http://www.ixl.com/math/grade-5/round-decimals

http://www.sheppardsoftware.com/mathgames/decimals/scooterQuestDecRound.htm

Key: Line up the decimal points.


Key: Multiply as if they were whole numbers and

after that, put decimal point counting all

decimal digits in all factors.


To multiply decimals by 10, 100, 1000 … move

decimal point one, two, three … places to the

right.

3.226 100

4.5 10

62.32 1000

7.8 100


Case 1) Natural number divided by a natural number

Long division does not always work out to a whole

number.

Key: Add zeros to the dividend after writing a decimal

point in the quotient.


Case 2) The dividend is a decimal number and the

divisor is a whole number

Key: Divide as usual until you find the decimal point at

the dividend. Then write a decimal point at the

quotient and continue the division.


Case 3) The divisor is a decimal number.

Property: The quotient will not change if we multiply

the dividend and the divisor by the same number; or if

we divide the dividend and the divisor by the same

number.

Key: Make the divisor into a whole number by

multiplying it by 10, 100, 1000, … and then divide as a

division of whole numbers.


To divide decimals by 10, 100, 1000,… move

decimal point one, two, three … places to the

left.

322.6:100

4.5:10

62.32:1000

78:100


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