Round each to the nearest tenth: $$15.847$$ rounds to $$15.8$$ (hundredths digit 4 < 5), $$15.851$$ rounds to $$15.9$$ (hundredths digit 5 ≥ 5), and $$15.855$$ rounds to $$15.9$$ (hundredths digit 5 ≥ 5). So $$15.851$$ and $$15.855$$ both round to $$15.9$$, making exactly two results identical. Choice A incorrectly assumes all round the same way. Choice C misidentifies which numbers round identically. Choice D assumes each rounds differently.

First, round $$12.4951$$ to the nearest thousandth: look at the ten-thousandths place (1), which is < 5, so round down to $$12.495$$. Then round $$12.495$$ to the nearest whole number: look at the tenths place (4), which is < 5, so round down to $$12$$. Choice B incorrectly rounds up to 13. Choice C stops after the first rounding step. Choice D shows an intermediate step that wasn't requested.

First, round $$8.7654$$ to the nearest hundredth: look at the thousandths place (5), which is ≥ 5, so round up to $$8.77$$. Then round $$8.77$$ to the nearest tenth: look at the hundredths place (7), which is ≥ 5, so round up to $$8.8$$. Choice B incorrectly rounds the original number directly to tenths. Choice C stops after the first rounding step. Choice D incorrectly rounds down in the first step.

When you see a rounding problem that asks about place values, you need to complete the rounding first, then identify where each digit sits in the final answer.

Let's round $$7.38495$$ to exactly two decimal places. Look at the third decimal place (the thousandths place), which contains the digit $$4$$. Since $$4 < 5$$, you round down, keeping the first two decimal places unchanged: $$7.38$$.

Now identify where the digit $$8$$ appears in $$7.38$$. The place values from left to right are: ones ($$7$$), tenths ($$3$$), hundredths ($$8$$). The digit $$8$$ is in the hundredths place.

Let's examine why the other choices are wrong. Choice A claims the digit $$8$$ represents the tenths place, but the tenths place contains $$3$$, not $$8$$. Choice B suggests $$8$$ is in the ones place, but $$7$$ occupies the ones place. Choice C states $$8$$ represents the thousandths place, but after rounding to two decimal places, there is no thousandths place in our answer—and even in the original number, the thousandths place contained $$4$$.

The correct answer is D: the digit $$8$$ represents the hundredths place value.

Study tip: Always complete any required operations (like rounding) before answering place value questions. Remember the decimal place pattern: tenths, hundredths, thousandths. Count carefully from the decimal point to avoid mix-ups between similar-sounding place names.

This question tests your understanding of rounding decimals, specifically rounding to the nearest tenth. When you see a problem asking you to round a number, you need to identify which place value you're rounding to and look at the digit immediately to the right of it.

To round $$12.8349$$ to the nearest tenth, you first locate the tenths place (the first digit after the decimal point), which is $$8$$. Then you look at the digit in the hundredths place (the second digit after the decimal), which is $$3$$. Since $$3$$ is less than $$5$$, you round down, keeping the tenths digit as $$8$$ and dropping everything after it. This gives you $$12.8$$ gallons.

Looking at the wrong answers: Choice A ($$13.0$$) would be rounding to the nearest whole number, not the nearest tenth. Choice B ($$12.9$$) incorrectly rounds up—this would only happen if the hundredths digit were $$5$$ or greater, but it's $$3$$. Choice D ($$12.83$$) rounds to the nearest hundredth instead of the nearest tenth, keeping too many decimal places.

The correct answer is C: $$12.8$$ gallons will be used for the price calculation.

Study tip: Remember the rounding rule: if the digit you're looking at is $$5$$ or greater, round up; if it's less than $$5$$, round down. Always identify exactly which place value you're rounding to before you start.

First, round $$98.6789$$ to the nearest tenth: look at the hundredths place (7), which is ≥ 5, so round up to $$98.7$$. Then the computer rounds $$98.7$$ to the nearest whole degree: look at the tenths place (7), which is ≥ 5, so round up to $$99$$. Choice A incorrectly rounds down in the second step. Choice C stops after the first rounding step. Choice D shows incorrect intermediate rounding.

Rounding decimals estimates values to make numbers more manageable, especially in timing or quick calculations. To round 0.964 to the nearest tenth, find the tenths place, which is the 9. Check the following digit, the hundredths place, which is 6. As 6 is 5 or higher, round up the tenths from 9 to 10, which carries over to make it 1.0. A misconception is that rounding up a 9 simply stays as 9, but it actually increases the previous place value. Rounding helps estimate numbers in scenarios like race timings, providing a simplified view. It promotes easier comparisons and mental arithmetic in daily activities.

When you need to round a decimal number to the nearest ten, you're looking at the ones digit to decide whether to round up or down. The key is identifying which digit tells you what to do.

Looking at $$45,678.9524$$, you need to focus on the ones place, which contains the digit $$8$$. Since you're rounding to the nearest ten, the ones digit determines your direction. When the ones digit is $$5$$ or greater, you round up to the next ten. When it's $$4$$ or less, you round down.

Since the ones digit is $$8$$, you round up. This means $$45,678.9524$$ becomes $$45,680$$ when rounded to the nearest ten. The $$78$$ in the tens and ones places becomes $$80$$, making answer C correct.

Let's examine why the other choices miss the mark. Answer A ($$45,670$$) would only be correct if you were rounding $$45,674$$ or less to the nearest ten - this represents rounding down when you should round up. Answer B ($$45,679$$) isn't even a multiple of ten, so it can't be correct when rounding to the nearest ten. Answer D ($$45,700$$) would be the result if you were rounding to the nearest hundred instead of the nearest ten, since the tens digit is $$7$$.

Remember this strategy: when rounding to any place value, always look at the digit immediately to the right of your target place. If it's $$5$$ or greater, round up; if it's $$4$$ or less, round down.

When you encounter a multi-step rounding problem, you need to complete each rounding step in sequence, using the result from the previous step as your starting point for the next round.

Let's work through this step by step. First, you need to round $$4.99951$$ to the nearest ten-thousandth (fourth decimal place). Look at the fifth decimal place: it's 1, which is less than 5, so you round down. This gives you $$4.9995$$ centimeters.

Now for the second step: round $$4.9995$$ to the nearest thousandth (third decimal place). Look at the fourth decimal place: it's 5, so you round up. The third decimal place is currently 9, so rounding up means you carry over to the second decimal place, making it 10, which becomes 0 and carries over again. This continues until you get $$5.000$$ centimeters.

Looking at the wrong answers: Choice A ($$4.9995$$) is the result after only the first rounding step, not the final answer. Choice B ($$4.999$$) incorrectly rounds down in the second step instead of up. Choice C ($$5.0000$$) shows four decimal places when the final rounding should give three decimal places for thousandths.

Choice D ($$5.000$$) correctly shows the final result with three decimal places, representing the measurement rounded to the nearest thousandth.

Remember: in multi-step rounding problems, never skip ahead to round the original number directly to the final precision. Always complete each rounding step in order, using the previous result as your starting point.

Rounding decimals is a core skill that helps estimate values by fine-tuning to specific decimal places. To round 14.678 to the nearest thousandth, identify the thousandths place, which is the 8. Then, check the next digit to the right, but since there is none (implying 0), consider it as 0. Since 0 is less than 5, keep the thousandths digit as 8, resulting in 14.678. A common misconception is to round up without a further digit, but you only adjust if the next digit warrants it. Rounding is essential for capacities like fish tanks in volume calculations. It ensures accurate yet concise representations for planning or science.