Final answer:
To re-express a number with ten's factors, adjust the prefactor and exponent in scientific notation. By multiplying the prefactor by 10 and decreasing the exponent by one, the expression's form is changed while its value remains constant. This simplifies numeric expressions and aids in metric conversions.
Step-by-step explanation:
To re-express a number using ten's factors, we can adjust the prefactor and the exponent in scientific notation. For instance, multiplying a prefactor by 10 while decreasing the exponent by one keeps the value of the expression the same but changes its form. For example, you could rewrite 2 × 10±7 as 2 × 10 × 10±6 and then further simplify to 20 × 10±6. Similarly, by recognizing that 24 is divisible by 8, you can manipulate the expression 2 × 10±23 as 24 × 10±12 and then divide by 8 to get 3 × 10±5. This demonstrates that multiplication and division by powers of 10 can significantly simplify numerical calculations, which is particularly useful for expressions involving more than 100 units or dealing with conversion in metric systems and scientific measurements.