Final answer:
To find the number, we solve the equation 3x - 9.2 = 2114, resulting in x = 707.7333…, and discuss the importance of correctly multiplying/dividing by powers of 10 and proper rounding in mathematical operations.
Step-by-step explanation:
To solve for the number in the question '9.2 less than 3 times a number is the same as 2114,' we set up the equation 3x - 9.2 = 2114, where x represents the number we're trying to find. We add 9.2 to both sides of the equation to isolate the term with the variable, giving us 3x = 2123.2. Then, we divide both sides by 3, which gives us x = 707.7333…, and this can be rounded as required.
When multiplying and dividing by powers of 10, it's important to know how the operation affects the decimal point. For multiplication, the decimal point moves to the right for positive exponents and to the left for negative exponents. When dividing, the inverse occurs. For example, 1.9436 ÷ 1000 = 0.0019436 and this concept helps us understand why we move the decimal point.
Lastly, proper rounding is essential in mathematical operations. When adding or subtracting, the result should be rounded to the same number of decimal places as the least accurate number. For multiplication and division, the answer should have the same number of significant figures as the number with the fewest significant figures amongst the numbers you're calculating.