Multiplying by powers of tenFollow the following shortcut when multiplying by powers of ten Whole numbers multiplied by powers of 10 When multiplying a whole number by a power of ten, just count how many zero you have and attached that to the whole number Examples: 1) 56 × 10 There is only one zero, so 56 × 10 = 560 2) 45 × 10,000 There are 4 zeros, so 45 × 10000 = 450000 3) 18 × 10,000,000 There are 7 zeros, so 18 × 10,000,000 = 180,000,000 Decimals multiplied by powers of 10 When multipying a decimal by a positive power of ten (positive exponent), move the decimal point one place to the right for each zero you see after the 1 Examples: 1) 0.56 × 10 There is only one zero, so move the decimal point one place to the right. 0.56 × 10 = 5.6 2) 0.56 × 100 There are 2 zeros, so move the decimal point two places to the right 0.56 × 100 = 56 3) 0.056 × 1000 There are three zeros, so move the decimal point 3 places to the right. 0.056 × 1000 = 56 4) 0.056 × 100,000 0.056 × 100,000 = 0.056 × 1000 × 100 = 56 × 100 = 5600 When multipying a decimal by a negative power of ten (negative exponent), move the decimal point one place to the left for each zero you see before the 1 Note that 0.1 = 10^{1}, 0.01 = 10^{2}, 0.001 = 10^{3}, and so forth.... We call 10^{1}, 10^{2}, and 10^{3} negative powers of 10 because the exponents are negative Examples: 1) 56 × 0.1 There is only one zero, so move the decimal point one place to the left. 56 × 0.1 = 5.6 2) 560 × 0.01 There are 2 zeros, so move the decimal point two places to the left 560 × 0.01 = 5.6 2) 560 × 0.001 There are 3 zeros, so move the decimal point two places to the left 560 × 0.001 = 0.560 3) 0.56 × 0.1 There is only one zero, so move the decimal point one place to the left. 0.56 × 0.1 = 0.056 4) 0.56 × 0.01 There are 2 zeros, so move the decimal point two places to the left 0.56 × 0.01 = 0.0056 Any questions about multiplying by powers of ten? Let me know... 




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