More About Decimal Numbers

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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Think 12345 x 100 12345 x 100





1234500. 1.2345 x 100 = 1

=


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Think 12345 x 1000 12345 x 1000 = 1





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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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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