Final answer:
To estimate 3 3/7 divided by 6, convert the mixed number to an improper fraction (24/7), then multiply by the reciprocal of 6 (1/6), giving 24/42, which simplifies to 4/7. Since 4/7 is slightly over 1/2, our estimate is just over 1/2. Remember to round calculator results according to the significant figures of the original data.
Step-by-step explanation:
Estimating the division of a mixed number by a whole number involves converting the mixed number into an improper fraction, then performing division, and finally rounding to an appropriate level of precision. Since calculators give exact results, humans need to apply rounding rules based on significant figures and the context of the problem. Let's walk through the estimation process for 3 3/7 divided by 6.
First, convert the mixed number 3 3/7 into an improper fraction: 3 * 7 + 3 = 24/7. Then, divide 24/7 by 6, which is the same as multiplying by its reciprocal, 1/6. The result is (24/7) * (1/6). Simplify this by multiplying the numerators and denominators: 24 * 1 = 24 and 7 * 6 = 42, giving us 24/42. This further simplifies to 4/7 after dividing both numerator and denominator by 6.
Now, to estimate, you can see that 4/7 is a little more than half, because 3.5/7 would be exactly half. So our estimate for 3 3/7 divided by 6 is a bit over 1/2. Keep in mind that when performing calculations with a calculator, you must consider significant figures and round appropriately as the calculator presents an overly precise answer. For instance, when dividing numbers like 12.2 by 1.7, one must round the calculator's answer to reflect the precision of the original data.