KEY TO CARD No. 26.

NOTE.-The separatrix or point, is in the place of units when reading decimals, and instead of reading units, tens, hundreds, &c. towards the left as in whole numbers, we be gin with the point, calling it units, and read to the right.

EXAMPLES.

Call the point, units. .25 units, tens, hundreds : twentyfive hundredths. .5 units, tens: five tenths. .075 units, tens, hundreds, thousands: seventy-five thousandths.

LESSON 6.
DIGRESSION 1st.

What is the amount of .25 .5 .75 .875 and .95 of a pound?

RULE IN ADDITION.

.. Begin at the period or units, and place tens under tens, hundreds under hundreds, &c. towards the right; then add as in whole numbers carrying at every ten.

.40

40

LESSON 5.

What is the decimal of 2?

20)19.00(.95

180

. 100
100

.875 thousandths.

.95 hundredths.

3.325

Answer, £ 3.325

In words, Three pounds, and three hundred and twen

ty-five thousandths of a pound.

Or,

Ans. .95

Three tenths, two hun

KEY TO CARD No. 26.

dredths, and 5 thousandths || Proof of Lessons 6 and 7, by mental and practical calcula

to place the decimal point or .25 of a pound in Addition?

KEY TO CARD No. 27.

REMARKS.

In the first place we fix the point and annex three ciphers to the 1 thus, 1.000

Then say, how many times 12 in 100? 8 times and 4 remain. Bring down the other cipher makes 40. How many times 12 in 40? 3 times and 4 remain. Then annex a cipher to the remainder and mark it with an asterisk thus, 40*. Then proceed.

How many times 12 in 40? 3 times and 4 remain. Anhex another cipher to the remainder and mark it as before. Then how many times 12 in 40 again? 3 times and 4 remain; and in this manner 4 would remain continually without end.

We will therefore call this decimal a surd,† that is, a number which cannot be reduced to exactness.

Let this decimal be marked with the sign of more, thus, .08333+4

But whence came this 0 on the left side of the 8?

I will explain it: we had three places of decimals annexed to the 1; then we added two more marked with a star or asterisk; the whole make five decimal places in the dividend.

Now, the rule says, "If there be a deficiency of decimal places in the quotient, supply the defect by prefixing ciphers on the left."

Let us count the decimals in the quotient, beginning at the right: 3, 3, 3, 8: here are only four, but we ought to have five; because there are five decimal places in the dividend.

Then prefix a cipher on the left of 8 in the quotient, and place the separatrix or point on the left of the cipher.

To read this decimal, call the point units: then proceed to the right; "Tens, hundreds, thousands, tens of

+ A decimal that comes to a close without a remainder, as in Lesson 4, may be called a finite decimal.

KEY TO CARD No. 27.

thousands, hundreds of thousands."

66

Eight thousand

three hundred and thirty-three; One hundred thousandths." Answer in figures, .08333+4 of a pound, or in form of a

50

45

.5

This decimal is also a surd. The quotients of such fractions must be continued in proportion to the magnitude of the integer from which they proceed; that is to say, of a pound is a sum of greater value than of a farthing; and as decimals decrease towards the right, it is more needful to extend the decimals of a pound, than of an inferior denomination.

옳

Five places of decimals are commonly sufficient for minuteness in most cases of importance; but for the sake of curiosity in some peculiar calculations, the operator may extend decimals to what length he please. NOTE. The remainder of a surd must be added in proof.

Copy the following on your slates, having reference at the same time, to the Table on page 185.

.1

.12

.123

.1234

One, tenth.

Twelve, hundredths.

One hundred and twenty-three, Thousandths. One thousand two hundred and thirty-four, Ten thousandths.

.12345 Twelve thousand three hundred and forty-five, One hundred thousandths.

,123456 One hundred twenty-three thousand four hundred and fifty-six, Millionths.

KEY TO CARD No. 27.

Decimals may be read collectively or singly.

Collectively thus: One hundred twenty-three thousand four hundred and fifty-six, Millionths.

Singly thus: One tenth, two hundredths, three thousandths, four ten thousandths, five hundred thousandths, six millionths.

Count the decimal places in the greatest number of decimal figures of the sum to be added. Begin at the right of the sum total, and count as many towards the left for decimals.

2. Subtraction.

Let the decimal places in the remainder, be equal to the greatest number of decimals in either of the two numbers above singly considered.

3. Multiplication.

The number of decimal places in the product, must be equal to the whole of those in the two factors; and if figures are wanting in the product, prefix ciphers on the left, to supply the defect.