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Q: How can patterns be used to determine products of a number and a power of ten?
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How can patterns be used to determine products of a number and a power of 10?

2 X 104 is a 2 followed by four zeros. 5 x 109 is a 5 followed by nine zeros. 1 x 100 is a 1 followed by no zeros (1). When you multiply any number by 10n, you move the decimal point n places to the right. 8,000 x 103 = 8,000,000. So when you divide by a power of ten, you just move the decimal point to the left. Multiplying by 10n is the same as dividing by 10-n, and vice versa.


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In scientific notation, a number is expressed as a decimal multiplied by a power of 10. To determine if a number is big or small, look at the power of 10. If the power is positive, the number is big, and if the power is negative, the number is small. The higher the magnitude of the power, the larger or smaller the number.


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