Multiplying by 10, 100, 1000, etc. Give the pupil a few examples to write and work like these: ILLUSTRATIONS: 3.2 × 10 = 32.0. 4.25 x 10 = 42.5. 63.42 × 10 = 634.2. 734.5 × 10 = 7345. He will soon see that in each product he has simply rewritten the multiplicand with the decimal point one place farther to the right. Give him examples like these: = 4.3 × 1000 4300.0. 7.156 × 1000 = 7156. 6.0402 × 1000 = 6040.2. 96.145 × 1000 = 96145. It is not long until he discovers that 1. To multiply a decimal by 10, Remove the decimal point one place to the right. 2. To multiply a decimal by 100, Remove the decimal point two places to the right. 3. To multiply a decimal by 1000, Remove the decimal point three places to the right. In General: To multiply a decimal by 10, or any power of 10, Remove the decimal point to the right in the multiplicand as many places as there are O's in the multiplier. Multiplying by Any Multiple of 10. Let the pupil write the work for a number of these: 2.7 × 300 = 810.0. 2.7 × 3000 = 8100.0. He will soon discover that To multiply a number by any multiple of 10, 1. Remove the decimal point in the multiplicand as many places to the right as there are O's in the multiplier. 2. Multiply the result by the number to the left of the O's in the multiplier. EXAMPLE: EXPLANATION: = 4.2 x 300 420 × 3 = 1260. There are two O's in the multiplier. Remove the decimal point two places to the right,the result is 420. Multiply by 3, the number before the O's in the mul tiplier, 420 × 3 = 1260. TALK: DIVISION OF DECIMALS. Briefly review multiplication and division of dollars and cents. $2.50 × 4 is what? (Pupil.) $10.00. $10.00 4 is what? (Pupil.) $2.50. The pupil knows that the dividend is equal to the product of the divisor by the quotient. He also knows that in multiplication of decimals the product has as many decimal places as both the multiplicand and multiplier. Hence, it follows that the dividend must have as many as both divisor and quotient. Have the pupil prove this. Remember: 1. Before beginning the division, the dividend must have at least as many decimal places as the divisor. 2. If the dividend lacks in the number of decimal places, annex O's until the number of places in both is the same. 3. Divide as in whole numbers, paying no attention to O's that may be on the left of the dividend or divisor. 4. After dividing, if the number of decimal places used in the dividend is the same as the number used in the divisor, the quotient is an integer. 5. After dividing, if the number of decimal places used in the dividend is greater than the number used in the divisor, the number of decimal places in the quotient must equal that The dividend has two decimal places. The divisor has none. Hence, the quotient must have two, that the number in divisor and quotient may equal those in the dividend. Give examples with no decimal point in the divisor. The pupil will discover that— When the divisor is a whole number, we write the decimal point in the quotient as soon as we come to it in the dividend. WHERE BOTH DIVIDEND AND DIVISOR HAVE AN EQUAL NUMBER OF DECIMAL PLACES. Give examples where the number of places in div idend and divisor are equal, as : 123 .25) 30.75 25 57 50 75 75 Here the pupil knows that since the divisor has as many decimal places as the dividend, there will be none in the quotient. He knows this from his work in multiplication. Hence, with such examples, he has no difficulty. Give practice examples to make sure of this. 2d Method-Making the Divisor a Some teachers write examples that seem difficult, in such a way that the decimal point is removed altogether from the divisor. They then point off as in the first examples given in division here. TO ILLUSTRATE: 42.346 1.24 = ? The pupil sees by inspection that if he multiplies the divisor above by 100, he removes the decimal point. Since he must treat the dividend in the same way to keep the value unchanged, we have 3d Method-The Check Plan. The result in the preceding case is also accomplished by counting to the right from the decimal point in the dividend, as many places as there are decimal places in the divisor, and inserting a check mark there to indicate when the decimal point is to be placed in the quotient. If the number of decimal places in the dividend is less than the number in the divisor, annex O's to |