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1. How do we multiply a whole number by a power of 10? 36 × 10 Add on as many 0's as appear in the power. Examples. 2. 36 × 10 = 36 × 100 = 36 × 1000 = 360 3600 36,000 Add on one 0. Add on two 0's. Add on three 0's. How do we multiply a decimal by a power of 10? 7.32 × 10 Move the decimal point right as many digits as there are zeros in the power. Examples. 7.32 × 10= 73.2 7.32 × 100= 732 7.32 × 1000= 7,320 Move the decimal point one place right. Move the point two digits right: 732. However, since all the digits fall to the left of the decimal point, the whole number, 732, which we write without a decimal point. Move the point three digits right. To do this, we must add on a 0. Again, the answer is a whole number. Problem. If 5 pounds of sugar cost $2.79, how much will 50 pounds cost? Answer. Since 50 pounds are ten times 5 pounds, they will cost ten times more. Move the decimal point one place right: $27.90. Since money has two decimal digits, we added on a 0. (Lesson 3, Question 8) 3. How do we divide a decimal by a power of 10? 63.4 ÷ 10 Move the decimal point left as many digits as there are 0's in the power. If there are not enough digits, ad Examples. 63.4 ÷ 10= 6.34 Move the point one place left. 63.4 ÷ 100= .634 Move the point two digits left. 63.4 ÷ 1000= .0634 Move the point three digits left. do this, add on a 0. These example illustrate that, whenever we multiply or divide by a power of 10, the digits do not change We simply move the decimal point or add on 0's. Finally, we must see how to divide a whole number by a power of 10. Now in Lesson 1 we saw that when a whole number ends in 0's, we simply take off 0's. (Lesson 1, Question 11) 265,000 ÷ 100 = 2,650 But when a whole number does not end in 0's -- as 265 -- then there are no 0's to chop off We will see that we must place a decimal point to separate digits on the right. 4. How do we divide a whole number by a power of 10? 265 ÷ 10 Starting from the right of the whole number, separate as many decimal digits as there are 0's in the powe not enough digits, add on 0's. Examples. 265 ÷ 10 = 26.5 Starting from the right of 265, separate one decimal digit. 265 ÷ 100 = 2.65 Separate two decimal digits. 265 ÷ 1000 = .265 Separate three decimal digits. Again, as in Lesson 1, consider this array: As we move down the list -- as we push the digits one place left -- the number has been multiplied by 10, because each next place is worth 10 times more. (As we move from 2.658 to 26.58, we go from 2 ones to 2 tens.) It appears, though, as if the decimal point has shifted one place right, or, with whole numbers, that a 0 has been added on. As we move up the list -- as we push the digits to the right -- each number has been divided by 10. And so we can easily multiply or divide by a power of 10 because of the written system itself. Each place belongs to the next power of 10