Rounding and Estimation: Additional Practice (Set 2)

Round each factor to an easy nearby number: $24.6$ rounds to $25$ and $0.48$ rounds to $0.5$.

$24.6 \times 0.48 \approx 25 \times 0.5 = 12.5$

The answer should be about $12.5$, so the calculator's $1.1808$ is ten times too small, signalling a misplaced decimal point. The correct product is $11.808$.

Rounding to the nearest thousand, the deciding digit is the hundreds digit, which is exactly $5$.

$5 \ge 5 \;\Rightarrow\; \text{round up}$

By round-half-up the exact half goes up: raise the thousands from $9$ to $10$, which carries, so $89{,}500$ rounds to $90{,}000$.

Round each value to one nonzero digit: $19$ rounds to $20$ and $4.95$ rounds to $5$.

$19 \times 4.95 \approx 20 \times 5 = 100$

The total is about $100$ dollars. The exact total is $94.05$ dollars, so the estimate of $100$ is close and quick.

Round each factor to an easy nearby number: $0.62$ rounds to $0.6$ and $48$ rounds to $50$.

$0.62 \times 48 \approx 0.6 \times 50 = 30$

The answer should be about $30$, so the calculator's $297.6$ is about ten times too large, signalling a misplaced decimal point. The correct product is $29.76$.

Round each number to the nearest whole number first. The tenths digit decides each: $8.6$ rounds to $9$, $8.4$ rounds to $8$, and $8.5$ is a tie that rounds up to $9$.

$9 + 8 + 9 = 26$

The sum of the rounded values is $26$. Note $8.5$ rounds up by the round-half-up convention.

First round $7.96$ to the nearest tenth. The hundredths digit is $6$, so round the tenths up; the $9$ tenths carry.

$7.96 \approx 8.0$

Now round $8.0$ to the nearest whole number. The tenths digit is $0$, so it stays at $8$. The two results are $8.0$ then $8$.

The tenths digit is $9$, and the deciding digit, the hundredths $7$, is $5$ or more, so round up. Raising $9$ tenths carries, and the ones and tens are also $9$, so the carry ripples up.

$199.97 \approx 200.0$

The ten tenths become one whole; $199.9$ rolls all the way up to $200.0$. Keep one decimal place.

Round each number to the nearest whole number: $4.8 \to 5$, $5.1 \to 5$, $6.2 \to 6$, and $4.9 \to 5$.

$5 + 5 + 6 + 5 = 21$

The estimate is $21$. The exact total is $21.0$, so rounding each to the nearest whole number was right on the mark here.

Rounding to the nearest tenth, only the single digit just to the right of the tenths place decides it, which is the hundredths digit $4$.

$4 < 5 \;\Rightarrow\; \text{round down}$

So $6.249$ rounds to $6.2$. The student's error was looking past the hundredths digit; the $9$ in the thousandths place cannot push the rounding up.

Round each number first: $418 \approx 400$, $192 \approx 200$, and $2.9 \approx 3$. Add the top, then divide.

$\frac{418 + 192}{2.9} \approx \frac{400 + 200}{3} = \frac{600}{3} = 200$

The estimate is about $200$. The exact value is near $210$, so the estimate is in the right ballpark.

Estimate the total before trusting the receipt: each book is about $13$ dollars (or round $12.50$ to $13$), and there are $7$.

$7 \times 12.50 \approx 7 \times 13 = 91$

The true total is $87.50$ dollars, close to the estimate. The rung-up $8.75$ is ten times too small, so the decimal point landed one place too far left.

First round $3.495$ to the nearest hundredth. The thousandths digit is $5$, so round the hundredths up.

$3.495 \approx 3.50$

Now round $3.50$ to the nearest tenth. The hundredths digit is $0$, so the tenths digit stays.

$3.50 \approx 3.5$

The final answer is $3.5$. Rounding step by step matters here: it is the two-step process the question asks for.