Rounding and Estimation: Practice

The hundredths place holds the $1$ in $5.71\underline{4}2$, so the deciding digit is the thousandths digit, which is $4$.

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

Keep two decimal places and drop the rest, giving $5.71$.

The hundredths digit is $8$, so look at the thousandths digit, which is $6$.

$6 \ge 5 \;\Rightarrow\; \text{round up}$

Raise the hundredths from $8$ to $9$ and keep two decimal places, giving $0.09$.

The tenths place holds the $4$, so the deciding digit is the hundredths digit, which is $9$.

$9 \ge 5 \;\Rightarrow\; \text{round up}$

Raise the tenths from $4$ to $5$ and keep one decimal place, giving $12.5$. The digits past the hundredths do not matter.

Round each number to the nearest hundred first: $612$ rounds to $600$ and $289$ rounds to $300$.

$612 - 289 \approx 600 - 300 = 300$

The exact difference is $323$, so the estimate of $300$ is close.

Round each factor to the nearest ten first: $48$ rounds to $50$ and $21$ rounds to $20$.

$48 \times 21 \approx 50 \times 20 = 1000$

The exact product is $1008$, so the estimate of $1000$ is right on target.

The tenths place holds the $8$, so the deciding digit is the hundredths digit, which is $5$.

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

Raise the tenths from $8$ to $9$ and keep one decimal place, giving $6.9$.

Round the dividend to an easy nearby number: $812$ rounds to $800$, which divides evenly by $4$.

$812 \div 4 \approx 800 \div 4 = 200$

The exact quotient is $203$, so the estimate of $200$ is close.

The value $2.5$ sits exactly halfway between $2$ and $3$, so neither neighbor is strictly nearer.

$2.5 \approx 3$

The round-half-up convention sends an exact half to the upper neighbor, so $2.5$ rounds to $3$.

The tenths digit is $9$, and the next digit, the hundredths $6$, is $5$ or more, so round up. Raising $9$ tenths by one gives ten tenths, which carries.

$9.96 \approx 10.0$

The ten tenths roll over into the ones place, turning $9.9$ into $10.0$.

Round each factor to the nearest whole number first: $6.83$ rounds to $7$ and $4.1$ rounds to $4$.

$6.83 \times 4.1 \approx 7 \times 4 = 28$

The exact product is $28.003$, so the estimate of $28$ is close.

Round each number to the nearest hundred first: $789$ rounds to $800$ and $213$ rounds to $200$.

$789 - 213 \approx 800 - 200 = 600$

The exact difference is $576$, so the estimate of $600$ is a reasonable quick check.

The hundredths place holds the $3$ in $7.83\underline{5}$, so the deciding digit is the thousandths digit, which is exactly $5$.

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

By round-half-up the exact half goes up, so raise the hundredths from $3$ to $4$, giving $7.84$.