# Division by 10, 100 and 1000:

To divide a decimal number by 10, 100, or 1000, shift the digits in the decimal number to the left by as many places as there are zeros over 1, to get the quotient.

Consider 31.5 ÷ 10.

31.5 ÷ 10 = 315/10 xx 1/10 = 315/100 = 3.15

Similarly, 315 ÷ 100 = 315/10 xx 1/100 = 315/1000 = 0.315.

Let us see if we can find a pattern for dividing numbers by 10, 100, or 1000. This may help us in dividing numbers by 10, 100, or 1000 in a shorter way.

31.5 ÷ 10 = 3.15

31.5 ÷ 100 = 0.315

31.5 ÷ 1000 = 0.0315.

Take 31.5 ÷ 10 = 3.15. In 31.5 and 3.15, the digits are the same i.e., 3, 1, and 5 but the decimal point has shifted in the quotient. The decimal point has shifted to the left by one place. Note that 10 has one zero over 1.

Consider now 31.5 ÷ 100 = 0.315. In 31.5 and 0.315, the digits are the same, i.e., 3, 1, and 5 but the decimal point has shifted in the quotient. It has shifted to the left by two places. Note that 100 has two zeros over 1.

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Division of Decimal Numbers by 10,100 & 1000 [00:14:16]
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