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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
www.matematicasalmudena.com Almudena Casares Fernández
Name the whole number and the part number
with the value of the last digit.
www.matematicasalmudena.com Almudena Casares Fernández
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
www.matematicasalmudena.com Almudena Casares Fernández
30.2
426.51
2.4
32.1627
102.45
27.12
0.13
45.953
0.125
www.matematicasalmudena.com Almudena Casares Fernández
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.
www.matematicasalmudena.com Almudena Casares Fernández
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.
www.matematicasalmudena.com Almudena Casares Fernández
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
www.matematicasalmudena.com Almudena Casares Fernández
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
www.matematicasalmudena.com Almudena Casares Fernández
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.
www.matematicasalmudena.com Almudena Casares Fernández
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
www.matematicasalmudena.com Almudena Casares Fernández
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!
www.matematicasalmudena.com Almudena Casares Fernández
Key: Line up the decimal points.
www.matematicasalmudena.com Almudena Casares Fernández
Key: Multiply as if they were whole numbers and
after that, put decimal point counting all
decimal digits in all factors.
www.matematicasalmudena.com Almudena Casares Fernández
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
www.matematicasalmudena.com Almudena Casares Fernández
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.
www.matematicasalmudena.com Almudena Casares Fernández
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.
www.matematicasalmudena.com Almudena Casares Fernández
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.
www.matematicasalmudena.com Almudena Casares Fernández
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
www.matematicasalmudena.com Almudena Casares Fernández
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