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8/13/2019 More About Decimal Numbers
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MORE ABOUT DECI
NUMBERS
IES Escultor Snchez Mes
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Introduction to Decimal Nu
A number written in decimal notaparts:
Whole # part
The decimal point
Decimal part
The position of the digit in the dec
number determines the digits val
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Place Value Chart
.
ones
tens
hundreds
thousands
tenths
hundredths
thousandths
Whole number part Decimal p
Decimal point
100101102103 10-1 10-2 10-3
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Writing a Decimal NumbWords
Write the whole number part
The decimal point is written and
Write the decimal part as if it were a w
number Write the place value of the last non-z
Ex: Write 6.32 in words
Six and thirty-two hundr
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Ex: Write 0.276 in wo
Zero and two hundred seve
thousandths
Or two hundred seventy-six thous
Ex: Write 10.0304 in w
Ten and three hundred fourTen-thousa
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Writing Decimal NumbeStandard Form
Write the whole number part
Replace and with a decimal poi
Write the decimal part so that the
zero digit is in the identified decimvalue
Note: if there is no and, then th
has no whole number part.
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Ex: Write in standard form
and three hundred four tthousandths
8 . 3 0 40
Ex: Write in standard form hundred sixty-two thousan
Note: no and no whole p
0 . 7 6 2
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Converting Decimal to Fra
To convert a decimal number tofraction, read the decimal numbcorrectly. Simplify, if necessary
Ex: Write 0.4 as a fraction
0.4 is read four tenths
100
5
Ex: Write 0.05 as a fraction
0.05 is read five hundredth
1
4
20
1=
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Converting Fractions to DeNumbers (base 10 denom
When the fraction has a power ofdenominator, we read the fractionto write it as a decimal number
Ex: Write as a decimal number10
3
The fraction is read three tenths
Note: no and no whole part
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Ex: Write as a decimal number100
27
The fraction is read twenty-seven huNote: no and no whole part
0 . 2 7
Ex: Write as a decimal number 1000
33
5
The mixed number is read five and ththousandths
5 . 3 30
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Converting fractions to decimals,
take the numerator and divide bythe denominator.
If the fraction is a mixed number,
put the whole number before thedecimal.
Rewrite as long division.n
d
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Rounding Decimal Num
Rounding decimal numbers is simrounding whole numbers:
Look at the digit to the right of theplace value to be rounded.
If the digit to the right is > 5, thenthe digit in the given place value out all the digits to the right (hit)
If the digit to the right is < 5, then
digit in the given place value and all the digits to the right (stay).
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Ex: Round 7.359 to the ne
tenths place
Identify the place to be rounded to: T
Look one place to the right. What numbCompare the number to 5: 5 > 5 hit
3 + 1 = 4 in the tenths place, zero out th
7.359 rounded to the nearest tenths p
7.400 = 7.4
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Ex: Round 22.68259 to the
hundredths place
Identify the place to be rounded to: H
Look one place to the right. What numbCompare the number to 5: 2 < 5 sta
Keep the 8 and zero out the rest
22.68259 rounded to the nearest hund
place is 22.68000 = 22.68
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Ex: Round 1.639 to the ne
whole number
Identify the place to be rounded to: o
Look one place to the right. What numbCompare the number to 5: 6 > 5 hit
1 + 1 = 2 in the ones place, zero out the
1.639 rounded to the whole number is
2.000 = 2
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Multiply by Powers of
When multiplying by 10, 100, 100
Move the decimal in the number tright as many times as there are
2.345 times 10, move the decimaplace to the right, 23.45
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Ex: Multiply 1.2345 x 10
Think 12345 x 10 12345 x 10
1.2345 has 4 decimal place
10 has 0 decimal places
Therefore the product of 1.2345 and
have 4 + 0 = 4 decimal places
123450. 1.2345 x 10 = 12
= 12
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Ex: Multiply 1.2345 x 100
Think 12345 x 100 12345 x 100
1.2345 has 4 decimal place
100 has 0 decimal places
Therefore the product of 1.2345 and
have 4 + 0 = 4 decimal places
1234500. 1.2345 x 100 = 1
=
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Ex: Multiply 1.2345 x 1000
Think 12345 x 1000 12345 x 1000 = 1
1.2345 has 4 decimal place
1000 has 0 decimal places
Therefore the product of 1.2345 and
have 4 + 0 = 4 decimal places
12345000. 1.2345 x 1000 = 1
= 1
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So what have we seen?
1.2345 x 10 = 12.345
1.2345 x 100 = 123.45
1.2345 x 1000 = 1234.5
1 zero move point 1 place to
2 zeros mo
point 2 places
3 zeros mo
point 3 places
To multiply a decimal number by a powemove the decimal point to the right the snumber of places as there are zeros.
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Ex: Multiply 34.31 x 1000
How many zeros are there in 1000
Move the decimal point in 34.31
to the right 3 times
34.310. 34.31 x 1000 = 34
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Ex: Multiply 21 x 100
How many zeros are there in 100?
Move the decimal point in 21
to the right 2 times
21 . 0 . 21 x 100 = 21000
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Divide by Powers of
When dividing by 10, 100, 1000,
Move the decimal in the number
as many times as there are zeros
76.89 divided 10, move the decim
place to the left, 7.689
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So what have we seen?
12345.6 10 = 1234.56
12345.6 100 = 123.456
1 zero move point 1 place to
2 zeros mo
point 2 places
To divide a decimal number by a power o
move the decimal point to the left the samof places as there are zeros.
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