More on Rounding

Here are some more examples of rounding.

• Round $6.187$ to the nearest whole number.
  Answer: From the number line we can see that $6.187$ is much closer to $7$ than to $6$. So the answer is $7$.

  

  Alternatively, the answer is either $6$ or $7$. To decide which, we look at the digit after the decimal point. It is the $8$ in $6.{\color{#08F}8}17$. As $8$ is greater than $5$, we increase the $6$ (the $6$ in ${\color{#08F}6}.817$) so it becomes $7$. The answer is $7$.

• Round $6.817$ to $1$ decimal place.
  Answer: From the number line above we can see that $6.817$ is closer to $6.8$ than to $6.9$, so the answer is $6.8$.

• Round $-6.817$ to the nearest whole number.
  Answer: This is much the same as rounding $6.817$ to the nearest integer. The answer is $-7$ because $-6.817$ is closer to $-7$ than to $-6$.

• Round $13.42$ to the nearest whole number.
  Answer: It is $13$ because $13.42$ is closer to $13$ than to $14$.
  Alternatively, the answer is either $13$ or $14$. To decide which we look at the digit afterr the decimal point. It is the $4$ in $13.{\color{#08F}4}2$. As $4$ is less than $5$, we leave the $3$ (the $3$ in $1{\color{#08F}3}.43$) unchanged. The answer is $13$.

• Round $-13.42$ to the nearest whole number.
  Answer: It is $-13$ because $-13.42$ is closer to $-13$ than to $-14$.

• Round $0.9765625$ to (a) $1$ decimal place, (b) $4$ decimal places, (c) $6$ decimal places.
  Answer:(a) $0.9765625$ is between $0.9$ and $1.0$. It is closest to $1.0$, as can be seen from the number line. So $1.0$ is the answer.

  

  Or, we can look at the digit after the $9$ (the $9$ in $0.{\color{#08F}9}765625$), which is $7$. As $7$ is greater than $5$, we increase the $9$. this means that we go up from $0.9$ to $1.0$.
  (b) The answer iws either $0.9765$ or $0.9766$, but which one? As $0.9765625$ is closest to $0.9766$, $0.9766$ is the answer.
  Or, find the digit in the $4$th decimal place, this is $5$ (the $5$ in $0.976{\color{#08F}5}625$). Now find the digit following this, which is $6$ (the $6$ in$0.9765{\color{#08F}6}25$) . As $6$ is greater than $5$, we increase $5$ by $1$ to get $0.9766$.
  (c) The answer is $0.976562$ or $0.976563$. These are the same distance from $0.9765625$ so either can be considered correct. If we want to round to make the last digit even, then we take $0.976562$ as the answer. Or, find the digit in the $6$th decimal place, this is $2$ (the $2$ in $0.97656{\color{#08F}2}5$). The $2$ is followed by $5$, and there is nothing after the $5$. So we can take either $0.976562$ or $0.976563$ as the answer. If we want to round up or down to make the last digit of the answer even we take $0.976562$ as the answer.

More practice for you