Example 1. Price goods per lb. so as to gain 10 per cent. if bought at £1. 5s. 9d. per cwt.

Example 2. 715 qrs. of wheat are bought for £1260: what must be the price per qr. so as to gain 12 p.c.?

Price these goods to gain the quoted p.c.

1. 7 tons 5 cwts. costing £20. 12s. 6d.-per lb. to gain 10 p.c.

2.

5 sacks of flour costing £16. 8s. 4d.-per lb. to gain 5 p.c. 3. 814 things costing £35. 7s. 6d.—per art. to gain 12 p.c.

4. 65 centals of cotton costing £85. 11s. 4d.-per lb. to gain

25 p.c.

5. 840 gallons of oil costing £38. 5s. 9d.-per gall. to gain 20 p.c.

SECTION VI.

METHODS OF PREDICTION.

THESE are based on De Morgan's rules (pp. 18-25), and his methods of multiplication and division are always to be employed in connection with them.

1. Form axb.

Observe the number of integers or decimal ciphers in each multiplier.

==

the

The places which must be taken in each number of places required correct the number of integers or decimal ciphers in the other + 1.

Reverse one, placing the significant digits one to

the left of those in the other.

Example 1. 25-1875346 × 3·1871586 to 2 places.

Example 2. 12-83475 ×·00038765 to 4 places.

2. Form a ÷ b.

Observe the number of integers or decimal ciphers in the divisor and dividend.

Hence decide by inspection the number of integers or decimal ciphers in the quotient.

The number of places which must be taken in the divisor = number of places required correct number of quotient integers or ciphers number of divisor integers or ciphers + 1.

The number of places which may have to be taken in the dividend = number of places required correct + number of quotient integers or ciphers number of dividend integers or ciphers +1.

Employ the significant figures so determined.

Example 1. 373-8651÷ 8514.37 to 4 places.

Example 2. £73965. 19s. 81d.÷8901 to 3 places.

Observe the number of integers or decimal ciphers in any multiplier and decide by inspection the number in the product of the other two.

The number of places which must be correct in this product = number of places required correct + number of integers or ciphers in the multiplier +1.

The number of places which must be taken in the multiplier = number of places required correct + number of integers or ciphers in the product + 1.

PRODUCTS AND QUOTIENTS.

Example. £.03125 × 2·20462125 × 25·19 to 2 places.

143

4. Form ax

Observe the number of integers or decimal ciphers in either multiplier and decide by inspection the number in the remaining quotient.

The number of places which must be correct in this quotient = number of places required correct + number of integers or ciphers in the multiplier +1.

The number of places which must be taken in the multiplier = number of places required correct + number of integers or ciphers in the quotient + 1.

Example. £31-14260416 × 12∙18÷73 to 3 places.

Observe the number of integers or decimal ciphers in the divisor.

Decide by inspection the number in the dividend and hence also in the quotient.

The number of places which may have to be correct in the dividend = number of places required correct + number of quotient integers or ciphers number of dividend integers or ciphers +1.

=

The number of places which must be taken in the divisor number of places required correct number of quotient integers or ciphers number of divisor integers or ciphers + 1.

Example. £311-4260416 × 12-18-÷-73 to 3 places.

Observe the number of integers or decimal ciphers in the dividend.

Decide by inspection the number in the divisor and hence also the number in the quotient.

The number of places which must be correct in the divisor = number of places required correct + number of quotient integers or ciphers number of divisor integers or ciphers +1.

The number of places which may have to be taken in the dividend = number of places required correct + number of quotient integers or ciphers number of dividend integers or ciphers + 1.

Example. 1.47÷2·20462125÷20-41 to 4 places.