Final answer:
You can use mental math to multiply 5.4 by powers of 10 by moving the decimal point. For 5.4 * 10^3, move the decimal three places right to get 5400. For 5.4 * 0.01, move the decimal two places left to get 0.054.
Step-by-step explanation:
To explain how you can use mental math to find the products of 5.4 * 10^3 and 5.4 * 0.01, you can apply the concept of multiplying by powers of 10. For 5.4 * 10^3, you recognize that 10^3 is the same as 10 multiplied by itself three times, which equals 1000. Therefore, to compute 5.4 * 10^3 mentally, you can simply move the decimal point in 5.4 three places to the right, resulting in 5400.
Similarly, for 5.4 * 0.01, you recognize that 0.01 is equivalent to 1/100, which is the same as 10^-2. So, multiplying 5.4 by 0.01 is simply moving the decimal point in 5.4 two places to the left, giving you 0.054. These methods rely on understanding how multiplying by 10, 100, 1000 (10^n) affects the placement of the decimal point in a number.