Charles Davies.

School arithmetic. Analytical and practical online

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11. What is the value of of of 6 bushels of grain ?

12. Reduce Sgals. 2qts. to the fraction of a hogshead.

13. Reduce 2fur. 36rd 2yd. to the fraction of a mile.

14. What part of a is 5s. *Id. ?

15. What part of a pound Troy is lOoz. 13pwt. Sgr. ?

16. llcwt. Qqr. 12/6. 7 02. l%dr. is what part of a ton?

17. What part is 2pk. qt. of Ibu. Spk. ?

18. 24/6. 6oz. is what part of Zqr. 12/6. I2oz. ?

19. Reduce 3wk. Id. 9/i. 36?n. to the fraction of a month

20. Reduce 2E. 32rrf. 8z/<7. to the fraction of an acre.

21. Reduce 12s. $d. \\far. to the fraction of a guinea.

22. What is the value of T y&, apothecaries' weight ?

23. What part of an Ell English is 3qr. 3?ia. l\in. ?

24. What is the value of $hhd. ?

25. What is the value gf f of 3 barrels of beer ?

26. What is the value of T V of a cwt. ?

27. Reduce 3 15' 18|" to the fraction of a sign.

28. Reduce 3 inches to the fraction of a hand.

29. What is the value of -fa of a hogshead of wine ?

30. What is the value of 7 of an acre of land ?



ADDITION AND SUBTRACTION.
196. To add or subtract denominate fractions.
1. Add of a to of a shilling.

| of a = of 2^=*$- of a shilling.
Then, 4J* + f ^W+lf =W*= * = 14s 2 ^



196. Give the rule for adding and subtracting denominate fractions.



DENOMINATE FRACTIONS. 177

Or, the |- of a shilling may be reduced to the fraction of a > :
thus,

I f ^V=Tth> of a &=& of a :
then, S+A = H+A=H of a >

which being reduced, gives 14s. %d. Ans.

2. Add f of a year, | of a week, and | of a day.

f of a year=f of -^p days=31w&. 2da.
J of a week=J of 7 days - - 2da. Shr.
I of a day = - - - - = - - - 3/tr.
Ans. Slwk. Ida. llhr.

3. From \ of a take J of a shilling.

J of a shilling^ of -5^ of a =-fa of a .
Then, ' i AF=^-A=-ofa^=9- 8 ^

4. From 1 j#>. Troy weigfit, take ^oz.

Ib. oz. pwt. gr.

lJ/6.= of Jjao2=21oz. = l 9

Joz.=^ of-y- ofygrr. = 80gfr. = 038

J?is. 1 8 16 16

RULE. Reduce the given fractions to the same unit, and
then add or subtract as in simple fractions, after ivhich reduce
to integers of a lower denomination :

Or : Reduce the fractions separately to integers of lower de-
nominations, and then add or subtract as in denominate num"
bers.

EXAMPLES.

5. Add 1J miles, T ^ furlongs, and 30 rods.

6. Add of a yard, J of a foot, and $ of a mile.

7. Add | of a cwt., * of a Ib., 13oz., J of a curt, and 6/6.

8. From J of a day take f of a second.

9. From | of a rod take f of an inch.

10. From *fc of a hogshead take f of a quart.

11. From $oz. take %pwl.

12. From 4fcw. take 4 T y&.

12



178 DUODECIMALS.

13. Mr. Merchant bought of farmer Jones 22J bushels of
wheat at one time, 19^ bushels at another, and 33f at an-
other : how much did he buy in all ?

14. Add % of a ton and -fa of a cwt.

15. Mr. Warren pursued a bear for three successive days ;
the first day he travelled 28-f- miles ; the second 33 T ^ miles ;
the third 29-^j- miles, when he overtook him : how far had he
travelled ?

16. Add 5f days and 52 T %- minutes.

17. Add $cwt., S%lb., and 3 T y&.

18. A tailor bought 3 pieces of cloth, containing respect-
ively, 18| yards, 21| Ells Flemish, and 16f Ells English :
how many yards in all ?

19. Bought 3 kinds of cloth ; the first contained \ of 3 of
f of yards ; the second, of f of 5 yards ; and the third, \
of f of | yards : how much in them all ?

20. Add \\cwt. 17f/&. and 7foz.

21. From f of an oz. take of &pwt.

22. Take } of a day and J of of j of an hour from
3 1 weeks.

23. A man is 6| miles from home, and travels 4wi. Ifur.
24?*d., when he is overtaken by a storm : how far is he then
from home ?

24. A man sold -J^ of his farm at one time, ^ at another,
and ^7 at another : what part had he left ?

25. From 1 J of a take | of a shilling.

26. From loz. take %pwt.

27. From 8%cwt. take 4 T y6.

28. From 3|Z6. Troy weight, take \pz.

29. From 1^ rods take ^ of an inch.

30. From $f g) take ^ 3 .

DUODECIMALS.

197. If the unit 1 foot be divided into 12 equal parts, each
part is called an inch or prime, and marked '. If an inch be
divided into 12 equal parts, each part is called a second, and
marked ". If a second be divided, in like manner, into 12



DUODECIMALS. 179

equal parts, each part is called a third, and marked "' ; and
so on for divisions still smaller.

This division of the foot gives

1' inch or prime - - , - - - = -^ of a foot.

I" second is ^ of & - - - = y^ of a foot.

1'" third is T V of & of A' - = TT^ of a foot -



NOTE. The marks ', ", '", &c., which denote the fractional
units, are called indices,

TABLE.

12'" make 1" second.

12" " 1' inch or prime.

12' " 1 foot.

Hence : Duodecimals are denominate fractions, in which
the primary unit is 1 foot, and 12 the scale of division.

NOTE. Duodecimals are chiefly used in measuring surfaces and
solids.

ADDITION AND SUBTRACTION.

198. The units of duodecimals are reduced, added, and
subtracted, like those of other denominate numbers. The
scale is always 12.

EXAMPLES.

1. In 185', how many feet ?

2. In 250", how many feet and inches ?

3. In 4367'", how many feet?

4. What is the sum of 3/35. 6' 3" 2'" and 2ft. I' 10" 11'"?

5. What is the sum of 8/3L 9' 7" and 6/fc. 7' 3" 4"' ?

6. What is the difference between 9/fc. 3' 5" 6'" and 7/35.
3' 6" 7'"?

7. What is the difference between 40/35. 6' 6" and 29/fc. 7'" ?

8. What is the difference between 12ft. 7' 9" 6'" and 4/2.
9' 7" 9'"?

197. If 1 foot be divided into twelve equal parts, what is each part
called ? If the inch be so divided, what is each part called ? What are
duodecimals ? For what are duodecimals chiefly used ?

198. How do you add and subtract duodecimals ? What is the scale ?



180 DUODECIMALS.

MULTIPLICATION.

199. Begin with the highest unit of the multiplier and the
lowest of the multiplicand, and recollect,

1st. That 1 foot x 1 foot=l square foot (Art. 110).
2d. That a part of a foot x a part of a foot = some part of a
square foot.

NOTE. Observe that the unit is changed, by multiplication,
from a linear to a superficial unit.

Multiply 6ft. T 8" by 2/fc. 9'.

OPERATION.

ANALYSIS. Since a prime is ^ of a ft.

foot and a second T^T, g y g"

2 x 8" =-i i A of a square foot ; which re- 9 Q /
duced to 12ths, is 1' and 4" : that is,



1 twelfth, and 4 twelfths of -fe of a 2 X 8"= 1' 4"

square foot. 2x7'= 1 2'

2x7' =14 twelfths=l/. 2' 2 X 6 =12

2x6 =12 square feet, 9' x g" 6"

9 x 8"= T ^|-8 of a square foot=6" 9' x 7' 5' 3"

9'xT=fA-=5' 3" 9' X 6 = 4 6'
9 x6'=f|=46' p rod 18 3' r

RULE. I. Write the multiplier under the multiplicand,
so that units of the same order shall fall in the same
column.

II. Begin with the highest unit of the multiplier and
the lowest of the multiplicand, and make the index of each
product equal to the sum of the indices of the factors.

III. Eeduce each product, in succession, to the next higher
denomination, when possible.

NOTE. The index of the unit of any product is equal to the
of the indices of the factors.



EXAMPLES.

1 . How many solid feet in a stick of timber which is 25
feet 6 inches long, 2 feet 7 inches broad, and 3 feet 3 inches
thick ?

199. Explain the method of multiplying duodecimals. Give the
rule.



DUODECIMALS. 181

OPERATION.
.#

Beginning with the 2 feet, we say 2 25 6' length,
times 6' are 12'=1 square foot : then, 2 27' breadth.

times 25 are 50, and 1 to carry are 51 f

square feet. 51

Next, 7 times 6' are 42", =3' and 6" : 3' 6'

then 7' times 25=175'=14 7': hence, the ^4 j'
surface is 65 10' 6", and by multiplying

by the thickness, we find the solid contents 65 1" o
to be 214 1' 1" 6'" cubic feet. 3 X thickness.

197 7' 6"

16 5' 7" 6"''
214 1'1"6'"

2. Multiply 9/2. 4m. by 8/2. 3m.

3. Multiply 9#. 2m. by fyfc 6m.

4. Multiply 24/2. 10m. by 6/2. 8m.

5. Multiply 70/2. 9m. by 12/2. 3m.

6. How many cords and cord feet in a pile of wood 24 feet
long, 4 feet wide, and 3 feet 6 inches high ?

7. How many square feet are there in a board 17 feet 6
inches in length, and 1 foot 7 inches in width ?

8. What number of cubic feet are there in a granite pillar
3 feet 9 inches in width, 2 feet 3 inches in thickness, and 12
feet 6 inches in length ?

9. There is a certain pile of wood, measuring 24 feet in
length, 16 feet 9 inches high, and 12 feet 6 inches in
width. How many cords are there in the pile ?

10. How many square yards in the walls of a room, 14
feet 8 inches long, 11 feet 6 inches wide, and 7 feet 11 inches
high ?

11. If a load of wood be 8 feet long, 3 feet 9 inches wide,
and 6 feet 6 inches high, how much does it contain ?

12. How many cubic yards of earth were dug from a cellar
which measured 42 feet 10 inches long, 12 feet 6 inches wide,
and 8 feet deep ?

13. What will it cost to plaster a room 20 feet 6' long, 15
feet wide, 9 feet 6' high, at 18 cents per square yard?

14. How many feet of boards 1 inch thick can be cut from
a plank 18/2. 9m. long, l/t. Sin. wide, and 3m. thick, if there
is no waste in sawing ?



182 DECIMAL FRACTIONS.

DECIMAL FRACTIONS.

200. There are two kinds of Fractions : Common Frar
tions and Decimal Fractions.

A Common Fraction is one in which the unit is divided
into any number of equal parts.

A Decimal fraction is one in which the unit is divided ac-
cording to the scale of tens.

201. If the unit 1 be divided into 10 equal parts, the parts
are called tenths.

If the unit 1 be divided into one hundred equal parts, the
parts are called hundredths.

If the unit 1 be divided into one thousand equal parts, the
parts are called thousandths, and we have similar expressions
for the parts, when the unit is further divided according to the
scale of tens. *

These fractions may be written thus :

Four-tenths, - - - *fo.

Six-tenths, - - T V

Forty-five hundredths,

125 thousandths,

1047 ten thousandths, -

From which we see, that in each case the denominator
indicates the fractional unit ; that is, determines whether it is
one-tenth, one-hundredth, one-thousandth, &c.

202. The denominators of decimal fractions are seldom
written. The fractions are usually expressed by means of
a period, placed at the left of the numerator.

Thus ^5- is written - . 4



200. How many kinds of fractions are there? What are they?
What is a common fraction ? What is a decimal fraction ?

201. When the unit 1 Is divided into 10 equal parts, what is each
part called ? What is each part called when it is divided into 100 equal
parts? When into 10000? Into 10,000, &c. ? How are decimal frac-
tions formed ? What gives denomination to the fraction !



DECIMAL FRACTIONS. 183

This method of writing decimal fractions is" a mere lan-
guage, and is used to avoid writing the denominators. The
denominator, however, of every decimal fraction is always
understood :

It is the unit 1 with as many ciphers annexed as there
are places of figures in the decimal.

The place next to the decimal point, is called the place
of tenths, and its unit is 1 tenth. The next place, to the
right, is the place of hundredths, and its unit is 1 hundreth ;
the next is the place of thousandths, and its unit is 1 thous-
andth ; and similarly for places still to the right.

DECIMAL NUMERATION TABLE.



d
S

T3

2

| oJ

'o a 2 'O'fsS
'g , Sg^
rS "3 a -*' ^ 2

a a



.4 is read 4 tenths,

.54 - - 54 hundredths.

.064 - - 64 thousandths.

.6754 - - 6154 ten thousandths,

.01234 - - 1234 hundred thousandths

.007654 - - 7654 mfflionths.

.0043604 - - 43604 ten millionths.

NOTE. Decimal fractions are numerated from left to right ;
thus, tenths, hundredths, thousandths, &c.

202. Are the denominators of decimal fractions generally written ?
How are the fractions expressed? Is the denominator understood?.
What is it ? What is the place next the decimal point called ? What
is its unit ? What is the next place called ? What is its unit ? What
is the third place called ? What is its unit ? Which way are decimals
numerated ?



184 DECIMAL FRACTIONS.

203. Wfite and numerate the following decimals :

Four tenths, .4

Four hundredths, - .0 4

Four thousandths, .004

Four ten thousandths, - .0004

Four hundred thousandths, .00004

Four millionths, - .000004

Four ten millionths, .0000004.

Here we see, that the same figure expresses different deci-
mal units, according to the place which it occupies : therefore,

The value of the unit, in the different places, in passing
from the left to the right, diminishes according to the scale
of tens.

Hence, ten of the units in any place, are equal to one unit in
the place next to the left ; that is, ten thousandths make one
hundredth, ten hundredths make one-tenth, and ten-tenths,
the unit 1.

This scale of increase, from the right hand towards the
left, is the same as that in whole numbers ; therefore,

Whole numbers and decimal fractions may be united by
placing the decimal point between them : thus,

Whole numbers. Decimals.



I

I






836 3'0 641. 0478976

A number composed partly of a whole number and partly
of a decimal, is called a mixed number.



DECIMAL FRACTIONS. 185



RULE FOR WRITING DECIMALS.

Write the decimal as if it were a whole number, prefix-
ing as many ciphers as are necessary to make it of the
required denomination.

RULE FOR READING DECIMALS.

Read the decimal as though it were a whole number,
adding the denomination indicated by the lowest decimal
unit.

EXAMPLES.

Write the following numbers, decimally :
(1.) (2.) (3.) (4.) (5.)

3 16 17 32 165



10 , 1000 10000 100 10000
(6.) (7.) (8.) (9.) (10.)



Write the following numbers in figures, and then numerate
them.

1. Forty-one, and three-tenths.

2. Sixteen, and three millionths.

3. Five, and nine hundredths.

4. Sixty-five, and fifteen thousandths.

5. Eighty, and three millionths.

6. Two, and three hundred millionths.

7. Four hundred, and ninety-two thousandths.

8. Three thousand, and twenty-one ten thousandths.

9. Forty-seven, and twenty-one hundred thousandths.

10. Fifteen hundred, and three millionths.

11. Thirty-nine, and six hundred and forty thousandths.

12. Three thousand, eight hundred and forty millionths.
1 3. Six hundred and fifty thousandths.

203. Docs the value of the unit of a figure depend upon the place
which it occupies V How does the value change from the left towards
the right ? What do ten units of any one place make ? How do the
units of the place increase from the right towards the left ? How may
whole numbers be joined with decimals? What is such a number
called? Give the rule for writing decimal fractions. Give the rule
for reading decimal fractions.



186 UNITED STATES MONEY.

UNITED STATES MONEY.

204. The denominations of United States Money correspond
to the decimal division, if we regard 1 dollar as the unit.

For, the dimes are tenths of the dollar, the cents are hun-
dredths of the dollar, and the mills, being tenths of the cent,
are thousandths of the dollar.

EXAMPLES.

1. Express $39 and 39 cents and 7 mills, decimally.

2. Express $12 and 3 mills, decimally.

3. Express $147 and 4 cents, decimally.

4. Express $148 4 mills, decimally.

5. Express $4 6 mills, decimally.

6. Express $9 6 cents 9 mills, decimally.

7. Express $10 13 cents 2 mills, decimally.

ANNEXING AND PREFIXING CIPHERS.

205. Annexing a cipher is placing it on the right of a
number.

If a cipher is annexed to a decimal it makes one more deci-
mal place, and therefore, a cipher must also be annexed to the
denominator (Art. 202).

The numerator and denominator will therefore have been
multiplied by the same number, and consequently the value
of the fraction will not be changed (Art. 161) : hence,

Annexing ciphers to a decimal fraction does not alter its
value.

We may take as an example, .3 T 3 7 .

If we annex a cipher, to the numerator, we must, at the
same time, annex one to the denominator, which gives,

204. If the denominations of Federal Money be expressed decimally
what is the unit ? What part of a dollar is 1 dime ? What part of a
dime is a eent ? What part of a cent is a mill ? What part of a dollar
is 1 cent ? 1 mill ?

305. When is a cipher annexed to a number? Does the annexing
of ciphers to a decimal alter its value ? Why not ? What dp three
tenths become by annexing a cipher ? What by annexing two ciphers ?
Three ciphers? What do 8 tenths become by annexing a cipher? By
annexing two ciphers V By annexing three ciphers t



DECIMAL FRACTIONS. 187

,3 = -j^j- = .30 by annexing one cipher,
.3 = T 3 TM7ir -300 by annexing two ciphers.

if a decimal point be placed on the right of an integral
number, and ciphers be then annexed, the value will not be
changed : thus, 5 = 5.0 = 5.00 = 5.000, &c.

206. Prefixing a cipher is placing it on the left of a
number.

If ciphers are prefixed to the numerator of a decimal frac-
tion, the same number of ciphers must be annexed to the
denominator. Now, the numerator will remain unchanged
while the denominator will be increased ten times for every
cipher annexed ; and hence, the value of the fraction will be
diminished ten times for every cipher prefixed to the nume-
rator (Art. 160).

Prefixing ciphers to a decimal fraction diminishes its
value ten times for every cipher prefixed.

Take, for example, the fraction .2= T *j-.
.2 becomes -ffc = .02 by prefixing one cipher,
.2 becomes -fipfc = - 002 by prefixing two ciphers,
.2 becomes -ffiPfc = .0002 by prefixing three ciphers :

in which the fraction is diminished ten times for every cipher

prefixed.

ADDITION OF DECIMALS.

207. It must be remembered, that only units of the same
kind can be added together. Therefore, in setting down
decimal numbers for addition, figures expressing the same
unit must be placed in the same column.

200. When is a cipher prefixed to a number ? When prefixed to a
decimal, does it increase the numerator ? Does it increase the denomi-
nator? What effect then has it on the value of the fraction ? What
do .3 become by prefixing; a cipher? By prefixing two ciphers? By
prefixing three? What do .07 become by prefixing a cipher ? By pre-
fixing two ? By prefixing three ? By prefixing four ?

207. What parts of unity may be added together ? How do you set
down the numbers for addition? How will the decimal points fall ?
How do you then add ? How many decimal places do you point off m
the sum ?



188 ADDITION OF

The addition of decimals is then made in the same manner
is that of whole numbers.

I. Find the sum of 37.04, 704.3, and .0376.

OPERATION.

Place the decimal points in the same column : HA

this brings units of the same value in the same 704.3

column : then add as in whole numbers : hence, .0376

741.3776

RULE. I. Set down the numbers to be added so that
figures of the same unit value shall stand in the same
column.

II. Add as in simple numbers, and point off in the sum
from the right hand, as many places for decimals as are equal
to the greatest number of places in any of the numbers added.

PROOF. The same as in simple numbers.

EXAMPLES.

1. Add 4.035, 763.196, 445.3741, and 91.3754 together.

2. Add 365.103113, .76012, 1.34976, .3549, and 61.11
together.

3. 67.407 + 97.004+4 + .6 + .06 + .3.

4. .0007 + 1.0436 + .4 + .05 + .047.

5. .0049+47.0426 + 37.0410 + 360.0039.

6. What is the sum of 27, 14, 49, 126, 999, .469, and
.2614 ?

7. Add 15, 100, 67, 1, 5, 33, .467, and 24.6 together,

8. What is the sum of 99, 99, 31, .25, 60.102, .29, and
100.347?

9. Add together .7509, .0074, 69.8408, and .6109.

10. Required the sum of twenty-nine and 3 tenths, four
hundred and sixty-five, and two hundred and twenty-one
thousandths.

1 1 . Required the sum of two hundred dollars one dime
three cents and 9 mills, four hundred and forty dollars nine
mills, and one dollar one dime and one mill.

12. What is the sum of one-tenth, one hundredth, and one
thousandth ?



DECIMAL FRACTIONS. 189

13. What is the sum of 4, and 6 ten-thousandths ?

14. Required, in dollars and decimals, the sum of one dollar
one dime one cent one mill, six dollars three mills, four dol-
lars eight cents, nine dollars six mills, one hundred dollars six
dimes, nine dimes one mill, and eight dollars six cents.

15. What is the sum of 4 dollars 6 cents, 9 dollars 3 mills,
14 dollars 3 dimes 9 cents 1 mill, 104 dollars 9 dimes 9 cents
9 mills, 999 dollars 9 dimes 1 mill, 4 mills, 6 mills, and 1
mill?

16. If you sell one piece of cloth for $4,25, another for
$5,075, and another for $7,0025, how much do you get for
all?

17. What is the amount of $151,7, $70,602, $4,06, and
$807,2659 ?

18. A man received at one time $13,25 ; at another $8,4 ;
at anotlier $23,051j at another $6 ; and at another $0,75 :
how much did he receive in all ?

19. Find the sum of twenty-five hundredths, three hundred
and sixty-five thousandths, six tenths, and nine millionths.

20. What is the sum of twenty-three millions and ten, one
thousand, four hundred thousandths, twenty-seven, nineteen
millionths, seven and five tenths ?

21. What is the sum of six millionths, four ten-thousandths,
19 hundred thousandths, sixteen hundredths, and four tenths?

22. If a piece of cloth cost four dollars and six mills, eight
pounds of coffee twenty-six cents, and a piece of muslin three
dollars seven dimes and twelve mills, what will be the cost
of them all ?

23. If a yoke of oxen cost one hundred dollars nine dimes
and nine mills, a pair of horses two hundred and fifty dollars
five dimes and fifteen mills, and a sleigh sixty-five dollars
eleven dimes and thirty-nine mills, what will be their entire
cost?

24. Find the sum of the following numbers : Sixty-nine
thousand and sixty-nine thousandths, forty-seven hundred and
forty-seven thousandths, eighty-five and eighty-five hun-
dredths, six hundred and forty-nine and six hundred and
forty-nine ten-thousandths ?



100 SUBTRACTION OF



SUBTRACTION OF DECIMALS

208. Subtraction of Decimal Fractions is the operation of
finding the difference between two decimal numbers.

I. From 3.275 to take .0879.

NOTE. In this example a cipher is annexed OPSBATION.
to the minuend to make the number of decimal 3.2750
places equal to the number in the subtrahend. This 08 *7 Q

does not alter the value of the minuend (Art. 205)
hence, 3.1871

RULE. I. Write the less number under the greater, so that
figures of the same unit value shall stand in the same column.

II. Subtract as in simple numbers, and point off the deci-
mal places in the remainder, as in addition.

PROOF. Same as in simple numbers.

EXAMPLES.

1. From 3295 take .0879.

2. From 291.10001 take 41.375.

3. From 10.000001 take 111111.

4. From 396 take 8 ten-thousandths.

5. From 1 take one thousandth.

6. Fcom 6378 take one-tenth.

7. From 365.0075 take 3 millionths.

8. From 21.004 take 97 ten-thousandths.

9. From 260.4709 take 47 ten-millionths.

10. From 10.0302 take 19 millionths.

11. From 2.01 take 6 ten-thousandths.

12. From thirty-five thousands take thirty-fire thousandths.

13. From 4262.0246 take 23.41653.

14. From 346.523120 take 219.691245943.
' 15. From 64.075 take .195326.

16. What is the difference between 107 and .0007?

17. What is the difference between 1.5 and .3785 ?

18. From 96. 71 take 96.709.



208. What is subtraction of decimal fractions ? How do you set down
the numbers for subtraction ? How do you then subtract ? How many
decimal places do you point off in the remainder ?



DECIMAL FRACTIONS. 191

MULTIPLICATION OF DECIMAL FRACTIONS.

209. To multiply one decimal by another.
1. Multiply 3.05 by 4.102.

OPERATION.

ANALYSIS. If we change both factors to vul- s. 3 05

&r fractions, the product of the numerator will 4JJL2. 1 1Q9
be the same as that of the decimal numbers, and

the number of decimal places will be equal to the 610

number of ciphers in the two denominators: 305

hence, 12 . 20

12.51110

RULE. Multiply as in simple numbers, and point off" in
the product, from the right hand, as many figures for decimals
as there'are decimal places in both factors ; and if there be
not so many in the product, supply the deficiency by prefixing
ciphers.

EXAMPLES

1. Multiply 3. 049 by .012.

2. Multiply 365.491 by .001.

3. Multiply 496. 0135 by 1.496.

4. Multiply one and one milliouth by one thousandth.

5. Multiply one hundred and forty-seven millionths by one
millionth.

6. Multiply three hundred, and twenty-seven hundredth^
by 31.

7. Multiply 31.00467 by 10.03962.

8. What is the product of five-tenths by five-tenths ?

9. What is the product of five-tenths by five-thousandths ?

10. Multiply 596.04 by 0.00004.


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Online LibraryCharles DaviesSchool arithmetic. Analytical and practical → online text (page 13 of 24)