Exercises: rounding decimal numbers

$0.23$

You have to round to one decimal place. Mentally divide the number into two pieces:

$0{.}2 \;\; 3$

Consider the first digit of the second part. This is the first digit to be omitted.

$0{.}2 {\color{red} 3}$

The digit under consideration is a 3. So it is rounded down. This means that the second part is cut off without changing the first.

$0.2$

$0{.}78$

You have to round to one decimal place. Mentally divide the number into two pieces:

$0{.}7 8$

Consider the first digit of the second part. This is the first digit to be omitted.

$0{.}7 {\color{red}8}$

The digit under consideration is an 8. So it is rounded up. This means that the second part is omitted and the last digit is increased by 1. The 7 becomes the 8.

$0{.}8$

$3{.}716$

You have to round to one decimal place. Mentally divide the number into two pieces:

$3{.}7 16$

Consider the first digit of the second part. This is the first digit to be omitted.

$3{.}7 \color{Red}16$

The digit under consideration is a 1. So it is rounded down. This means that the second part is cut off without changing the first.

$3{.}7$

$10{.}008548548484$

You have to round to one decimal place. Mentally divide the number into two pieces:

$10{.}0 08548548484$

Consider the first digit of the second part. This is the first digit to be omitted.

$10{.}0 \color{red}08548548484$

The digit under consideration is a 0. So it is rounded down. This means that the second part is cut off without changing the first.

$10{.}0$

$99{.}999$

You have to round to one decimal place. Mentally divide the number into two pieces:

$99{.}9 99$

Consider the first digit of the second part. This is the first digit to be omitted.

$99{.}9 \color{red}99$

The digit under consideration is an 8. So it is rounded up. This means that the second part is omitted and the last digit is increased by 1. Since it is a 9, you have to adjust several digits.

$100{.}0$

As you can see, "increasing" the 9 at the tenths place also results in an adjustment of the ones, tens, and hundreds.

The number is to be rounded to three decimal places. To do this, divide the number into two parts:

1. the part that ranges from the left until the place to which you should round

2. the part containing all other digits on the right of it

$1.789\mid2$

Now consider the first digit of the second part: It is a 2, so you round down.

$1.789$

The number is to be rounded to three decimal places. To do this, divide the number into two parts:

1. the part that ranges from the left until the place to which you should round

2. the part containing all other digits on the right of it

$13.271\mid5$

Now consider the first digit of the second part: It is a 5, so you round up.

$13.272$

The number is to be rounded to three decimal places. To do this, divide the number into two parts:

1. the part that ranges from the left until the place to which you should round

2. the part containing all other digits on the right of it

$34.576\mid834523$

Now consider the first digit of the second part: It is a 8, so you round up.

$34.577$

The number is to be rounded to three decimal places. To do this, divide the number into two parts:

1. the part that ranges from the left until the place to which you should round

2. the part containing all other digits on the right of it

$8.872\mid487$

Now consider the first digit of the second part: It is a 4, so you round down.

$8.872$

The number is to be rounded to three decimal places. To do this, divide the number into two parts:

1. the part that ranges from the left until the place to which you should round

2. the part containing all other digits on the right of it

$5.619\mid8$

Now consider the first digit of the second part: It is a 9, so you round up. Be careful: Since you round up a 9, you have to adjust also the digits to the left of it (from 1 to 2).

$5.620$

The number is to be rounded to three decimal places. To do this, divide the number into two parts:

1. the part that ranges from the left until the place to which you should round

2. the part containing all other digits on the right of it

$98.999\mid8$

Now consider the first digit of the second part: It is a 9, so you round up. Be careful: Since you round up a 9, you have to adjust also the digits to the left of it (from 899 to 900).

$99.000$

Use the written method of addition to obtain a decimal number.

$7:9 =$

Calculate the first three digits so that you can later round to two decimal places.

$7:9=0.777\dots$

Now you round the last digit away (up) and you obtain:

$\frac{7}{9}\approx0.78$

Use the written method of addition to obtain a decimal number.

$11 : 125 =$

Calculate the first three digits so that you can later round to two decimal places.

$11:125=0.088$

Now you round the last digit away (up) and you obtain:

$\frac{11}{125}\approx0.09$

Use the written method of addition to obtain a decimal number.

$8 : 23 =$

Calculate the first three digits so that you can later round to two decimal places.

$8:23=0.347\dots$

Now you round the last digit away (up) and you obtain:

$\frac{8}{23}\approx0.35$

Use the written method of addition to obtain a decimal number.

$\frac{9}{100}=$

When you divide a number by 100, you can directly move the decimal point of the number two places (that is, the number of zeros after one) to the left.

$=0.09$

This number does not have to be rounded, since it has already only two decimal places.

$\frac{3}{7}=$

Perform a written division. Since you want to round the result to three digits, you have to compute (at least) four digits.

$=0.4285\dots$

Now, round to three digits (up).

$\approx0.429$

$\frac{8}{13}=$

Perform a written division. Since you want to round the result to three digits, you have to compute (at least) four digits.

$=0.6153\dots$

Now, round to three digits (down).

$\approx0.615$

$\frac{5}{3}=$

Perform a written division. Since you want to round the result to three digits, you have to compute (at least) four digits.

$=1.6666\dots$

Now, round to three digits (up).

$\approx1.667$

$\frac{2}{7}=$

Perform a written division. Since you want to round the result to three digits, you have to compute (at least) four digits.

$=0.2857\dots$

Now, round to three digits (up).

$=0.286$

$\frac3{11}=$

Perform a written division. Since you want to round the result to three digits, you have to compute (at least) four digits.

$=0.2727\dots$

Now, round to three digits (up).

$\approx0.273$

$\frac{13}{11}=$

Perform a written division. Since you want to round the result to three digits, you have to compute (at least) four digits.

$=1.1818\dots$

Now, round to three digits (up).

$\approx1.182$