Rounding and Estimation: Practice

The tenths digit decides it, and here it is $3$.

$3 < 5 \;\Rightarrow\; \text{round down}$

The number has not reached the midpoint $0.5$, so it rounds down to $0$.

The deciding digit is the tenths digit, which is $7$.

$3.7 \approx 4$

Since $7 \ge 5$, the number is past the midpoint $3.5$ and rounds up to $4$.

Rounding to the nearest hundred, the deciding digit is the tens digit, which is $5$.

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

By the round-half-up convention the exact half goes up, so $250$ rounds to $300$.

The tenths digit decides it, and here it is $2$.

$2 < 5 \;\Rightarrow\; \text{round down}$

The number has not reached the midpoint $4.5$, so it rounds down to $4$.

The ones digit decides which way to round, and here it is $4$.

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

Keep the tens digit, giving $60$.

Rounding to the nearest tenth, the deciding digit is the hundredths digit, which is $7$.

$7 \ge 5 \;\Rightarrow\; \text{round up}$

Raise the tenths digit from $4$ to $5$ and drop the rest, giving $3.5$.

The value $5.5$ sits exactly halfway between $5$ and $6$, so this is the tie case.

$5.5 \approx 6$

The round-half-up convention sends an exact half up, so $5.5$ rounds to $6$.

The deciding digit is the tens digit, which is $7$.

$7 \ge 5 \;\Rightarrow\; \text{round up}$

Raise the hundreds digit from $3$ to $4$ and zero the rest, giving $400$.

The tenths digit decides it, and here it is $1$.

$1 < 5 \;\Rightarrow\; \text{round down}$

The number has not reached the midpoint $2.5$, so it rounds down to $2$.

The value $0.5$ is exactly halfway between $0$ and $1$, which is the tie case.

$0.5 \approx 1$

By the round-half-up convention an exact half goes up, so $0.5$ rounds to $1$.

The tenths digit decides it, and here it is $4$.

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

The number has not reached the midpoint $7.5$, so it rounds down to $7$.

Round each number to the nearest ten first: $31$ rounds to $30$ and $58$ rounds to $60$.

$31 + 58 \approx 30 + 60 = 90$

The exact sum is $89$, so the estimate of $90$ is a reasonable quick check.