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10. Mrs. Spaulding ordered the following: 24 yards trimming at 85 cents; yard trimming at $3.00; 22 yards braid at 50 cents, and 11 yards cord at 8 cents.

11. Miss Jackson bought 167 yards of net at 50 cents; 37 yards muslin at 55 cents; 21 yards of dress goods at $1.25, and 23 yards sundour at $1.25.

12. Mrs. Adams purchased 41 yards black dress goods at $3.00; 88 yards black dress goods at $2.20; 32 yards velvet at $1.25, and 4 yards braid at 50 cents.

13. Mrs. Howard bought 31 yards silk at $1.25; i} yards silk at 55 cents; Ž yard silk messaline at $1.25, and s yard georgette crepe at $1.95.

14. Miss Byron purchased 53 yards silk meteor at $1.20;

yard silk at $1.25; Ž yard silk net at $1.75, and 14 yards silk at $1.10.

15. Miss Loring ordered the following bill of goods: 11 yards ribbon at 28 cents; 1 dozen handkerchiefs at $1.50; 41 yards silk at $1.00, and 41 yards braid at 15 cents.

16. Mrs. Gibson bought the following goods: 11 dozen handkerchiefs at $1.20; 3) pairs No. 7642 curtains at $7:00 per pair; 31 yards tapestry at $1.35, and 92 yards scrim at 25 cents.

17. Miss Norris bought 23 yards filet net at 75 cents; 13 yards ribbon at 38 cents; À yard leather at 75 cents, and 33 yards net at 55 cents.

18. Miss Howell bought the following: 47 yards marquisette at 30 cents; 41 yards edging at 5 cents, and 38 yards net at 40 cents.

19. Mrs. Drake ordered the following bill of goods: 301 yards cretonne at 25 cents; 9 feet pole at 4 cents per foot; 12 yards organdie at $1.00, and 63 yards fringe at 7 cents.

20. Mrs. Chatfield purchased 41 yards net at 75 cents; 63 yards Swiss at 15 cents, and é yard cretonne at 60 cents.

21. Mrs. Arnold purchased i} yards dimity at 30 cents; 31 yards mull at 40 cents, and 102 yards cord at 8 cents.

22. Miss Penfield purchased 24 yards of braid at 10 cents and 44 yards cretonne at 60 cents.

23. Mrs. Madison bought 41 yards Jap toweling at 10 cents; 24 yards silkoline at 15 cents; 11 yards oil cloth at 25 cents, and 137 feet of rod at 5 cents per foot.

24. Miss Nelson purchased 11 yards Venetian lining at 50 cents; 4) yards satin at $1.00; 13 yards felt at 60 cents, and 31 yards satin at $1.35.

26. Miss Harding ordered 17 yards flouncing at $1.15; 2; yards lining at 50 cents; 11 yards lamb's wool at 85 cents, and 25 yards satin at 85 cents.

26. Mrs. Miller purchased the following: 13 dozen handkerchiefs at $1.20; 41 yards of net at 75 cents, 11 yards of ribbon at 28 cents and 92 yards of scrim at 25 cents.

27. Mrs. Dunn bought 54 yards of Jap toweling at 10 cents; 31 yards silkoline at 15 cents; 23 yards oilcloth at 20 cents, and 2 yards of silk at $2.00.

28. Mrs. Schaffer ordered the following bill: 61 yards fringe at 7 cents; 2. yards of braid at 10 cents; 44 yards cretonne at 60 cents, and 12 of a dozen buttons at 40 cents.

29. Mrs. Martin purchased 14 yards of silk at 35 cents; i yard silk brocade at $1.50; of a yard of taffeta at $1.75, and 1 of a yard silk at 55 cents.

The prices for these problems were taken from sales slips for 1916. Additional material may be provided by getting present prices and solving the problems with those prices.

Exercise 1. Decimal Fractions

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You are already familiar with United States money. You have added, subtracted, multiplied and divided various sums of money.

1. How many dimes make a dollar?

2. How many cents make a dime? How many cents are there in a dollar?

3. How many mills make a cent? How many mills are there in a dollar?

4. Read this amount: $2.485. The point which separates dollars from cents is known as the decimal point. The first figure (4) to the right of the decimal point in the above sum of money stands for 4 dimes.

5. Four dimes are equal to what part of a dollar? The second figure (8) to the right of the decimal point in the above sum stands for 8 cents.

6. Eight cents are equal to what part of a dollar? The third figure (5) to the right of the decimal point in that sum stands for 5 mills.

7. Five mills are equal to what part of a dollar?

8. Which is shorter to write: 2 dollars, 4 dimes, 8 cenis and 5 mills or $2.485?

In the above questions we found that 4 dimes - 4 of a dollar, 8 cents=1&y of a dollar and 5 mills=1067 of a dollar. All

5 1000 of these fractions of a dollar have 10 or some multiple of 10 as their denominator.

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A fraction whose denominator is ten or a product of tens (as 10; 100; 1000; 10,000 etc.) is called a decimal fraction.

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and Tooo

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We have already studied fractions in the form o, 18

under the name of common fractions. A common fraction, however, may have any number for its denominator. Decimal fractions, on the other hand, can only have 10 or a product of two or more tens for their denominators.

The common fraction *=the decimal fraction .4.

How, then, is a decimal fraction represented so that it appears different than a common fraction? This is done in United States money by using a decimal point and giving certain places to the right of the decimal point certain values.

We have already seen that 4 dimes (represented by the first place at the right of the decimal point) is 4 of a dollar. In a decimal, then, the first place at the right of the decimal point is tenth's place.

.1 means one tenth. The figure 8 in the second place at the right of the decimal point represents 8 cents or 18 of a dollar. Then, the second place at the right of the decimal point is hundredth's place.

.01 means one hundredth. The figure 5 in the third place at the right of the decimal point represents 5 mills or 100 of a dollar. Therefore, the

a third place at the right of the decimal point is thousandth's place.

.001 means one thousandth. Which is shorter to write: Todo or .001?

Here we see that, as a matter of convenience in writing, the denominators of decimal fractions are not written as in common fractions, but the denominator is indicated by the number of places to the right of the decimal point.

Decimals were invented by the Scottish mathematician Napier (1550 1617). At first people were much prejudiced against them, but now riprybody recognizes their convenience.

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The other names applied to the various decimal places are shown in the following illustration:

hundred thousands
ten thousands
thousands
hundreds
decimal point
hundred-thousandths
hundredths
ten-thousandths
thousandths
tenths
teng
millionths
units

111,111.111,111

This number is read: one hundred eleven thousand one hundred eleven and one hundred eleven thousand one hundred eleven millionths.

We see that the whole number is separated from the decimal fraction by the decimal point in writing and by the word and in reading. Also notice that the name of the last decimal place (millionths) is the name given to the decimal.

1. How does the 1 in tenth's place compare in value with the 1 in units' place?

2. How does the 1 in hundredth's place compare in value with the 1 in tenths' place?

3. Compare .2 with .02; .05 with .005; .001 with .1; .02 with .0002; 10 with .1.

4. Begin at the 1 in hundred-thousands place and go to the right. How do the values of the l's change? Begin at the 1 in millionth's place and go the left. How do the values of the 1's change?

It will be a great convenience to you in reading decimals if you learn the number of places designated by each name. 1 place is read tenths; 2 places, hundredths; 3 places, thousandths; 4 places, ten-thousandths; 5 places, hundred-thousandths; and 6 places, millionths.

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