# Decimal Rounding

# Decimal Rounding:

To do **decimal rounding**:

- Figure out the place value to be rounded to... (ex: tenths, hundredths, thousandths ...)
- Round the
**original number** by counting in increments of the place value specified, in a manner that the count surrounds the number being rounded.

(ex: for rounding 0.23 to tenths, count 0.1, 0.2, [0.23], 0.3, 0.4.)
- Decide what number in your counted list is closest to the original number.

(ex: 0.2 = 0.20, 0.3 = 0.30... decide if 0.23 is closer to 0.30 or 0.20)

To round, you have the ability to do the following ....

Given the following following statements, identify the **place value** we will round to ...

- Round 0.762 to the nearest tenth ... Tenth (10th)
- Round 0.821 to the nearest hundredth ... Hundredth (100th)
- Round 1.2543 to the nearest tenth... Tenth (10th)
- Round 53.1239 to the nearest thousandth... Thousandth (1000th)

Counting in increments of the place value ...

Given the following following statements, **Count around the given number by the specified place value** ...

- Round 0.768 to the nearest tenth ... 0.6, 0.7, 0.768 0.8, 0.9
- Round 0.821 to the nearest hundredth... 0.81, 0.82, 0.821 0.83, 0.84,
- Round 1.2743 to the nearest tenth... 1.1, 1.2, 1.2743 1.3, 1.4
- Round 53.1234 to the nearest thousandth... 53.122, 53.123, 53.1234 53.124, 53.125

The following is an example of Rounding to a decimal position.

Given a request to round 0.2344 to the nearest hundredth (100th).

- Identify the
**place value **you are rounding to ... Rounding to place value **100th**
**Count** past and **surround** the given number by counting by increments of the place value.
0.22, 0.23, **0.2344** 0.24, 0.25
- Decide which of the counted numbers is closest to the given number.Its closest to
**0.2344 is closest to 0.23** because 0.2344 is closer to 0.2340 than to 0.2350

Therefore, 0.2344 rounded to the the hundredths position is 0.23

The following is an example of Rounding to a decimal position.

Given a request to round 0.53721 to the nearest hundredth (100th).

- Identify the
**place value **you are rounding to ... Rounding to place value **100th**
**Count** past and **surround** the given number by counting by increments of the place value.
0.534, 0.535, ** 0.53591** 0.536, 0.537
- Decide which of the counted numbers is closest to the given number.Its closest to
**0.53591 is closest to 0.536** because 0.53591 is closer to 0.53600 than to 0.53500

Therefore, 0.53591 rounded to the the hundredths position is 0.536

The following is an example of Rounding to a decimal position.

Given a request to round 0.1275 to the nearest hundredth (100th).

- Identify the
**place value **you are rounding to ... Rounding to place value **100th**
**Count** past and **surround** the given number by counting by increments of the place value.
0.126, 0.127, ** 0.1275** 0.128, 0.129
- Decide which of the counted numbers is closest to the given number.Its closest to
**0.1275 is closest to 0.128** because 0.0.1275 is closer to 0.1280 than to 0.1270

Therefore, 0.1275 rounded to the the hundredths position is 0.128

# Check Your Understanding

What is the place value mentioned in the following request to round?

- Round to the nearest hundredths
- Round to the nearest thousandths
- Round to the nearest ten-thousandths

Can you count by increments of place values? Think an answer then look at an example of one
possible answer ...

- Count by ten-thousandths.
- Count by tenths.
- Count by thousandths.

Why are the following statements true??

- 0.7 is less than 0.71 and 0.71 is less than 0.8
- 0.82 is less than 0.821 and 0.821 is less than 0.83
- 0.1 is less than 0.15 and
0.15 is less than 0.2
- 0.78 is less than 0.78999 and 0.78999 is less than 0.79

Why are the following statements true??

- 0.7 and 0.8
surround .78
- 0.97 and 0.98 surround 0.972
- 0.854 and 0.855 surround 0.8545
- 1.4 and 1.5 surround 1.41

Why are the following statements true??

- 0.78 is closer to 0.8 than to 0.7
- 0.972 is closer to 0.97 than to 0.98
- 0.8545 is closer to 0.855 than to 0.854
- 1.41 is closer to 1.4 than to 1.5

Do some interactive practice

- Enter a number between 0 and 999.9999.
- Enter a place value to round to .... 10ths, 100ths, 1000ths
- Figure out what you believe the answer should be.
- Click the button "Check" and check your answer.

# Decimal Rounding:

To do **decimal rounding**:

- Figure out the place value to be rounded to... (ex: tenths, hundredths, thousandths ...)
- Round the
**original number**by counting in increments of the place value specified, in a manner that the count surrounds the number being rounded.

(ex: for rounding 0.23 to tenths, count 0.1, 0.2, [0.23], 0.3, 0.4.) - Decide what number in your counted list is closest to the original number.

(ex: 0.2 = 0.20, 0.3 = 0.30... decide if 0.23 is closer to 0.30 or 0.20)

To round, you have the ability to do the following ....

Given the following following statements, identify the **place value** we will round to ...

- Round 0.762 to the nearest tenth ... Tenth (10th)
- Round 0.821 to the nearest hundredth ... Hundredth (100th)
- Round 1.2543 to the nearest tenth... Tenth (10th)
- Round 53.1239 to the nearest thousandth... Thousandth (1000th)

Counting in increments of the place value ...

Given the following following statements, **Count around the given number by the specified place value** ...

- Round 0.768 to the nearest tenth ... 0.6, 0.7, 0.768 0.8, 0.9
- Round 0.821 to the nearest hundredth... 0.81, 0.82, 0.821 0.83, 0.84,
- Round 1.2743 to the nearest tenth... 1.1, 1.2, 1.2743 1.3, 1.4
- Round 53.1234 to the nearest thousandth... 53.122, 53.123, 53.1234 53.124, 53.125

The following is an example of Rounding to a decimal position.

Given a request to round 0.2344 to the nearest hundredth (100th).

- Identify the
**place value**you are rounding to ... Rounding to place value**100th** **Count**past and**surround**the given number by counting by increments of the place value. 0.22, 0.23,**0.2344**0.24, 0.25- Decide which of the counted numbers is closest to the given number.Its closest to
**0.2344 is closest to 0.23**because 0.2344 is closer to 0.2340 than to 0.2350

Therefore, 0.2344 rounded to the the hundredths position is 0.23

The following is an example of Rounding to a decimal position.

Given a request to round 0.53721 to the nearest hundredth (100th).

- Identify the
**place value**you are rounding to ... Rounding to place value**100th** **Count**past and**surround**the given number by counting by increments of the place value. 0.534, 0.535,**0.53591**0.536, 0.537- Decide which of the counted numbers is closest to the given number.Its closest to
**0.53591 is closest to 0.536**because 0.53591 is closer to 0.53600 than to 0.53500

Therefore, 0.53591 rounded to the the hundredths position is 0.536

The following is an example of Rounding to a decimal position.

Given a request to round 0.1275 to the nearest hundredth (100th).

- Identify the
**place value**you are rounding to ... Rounding to place value**100th** **Count**past and**surround**the given number by counting by increments of the place value. 0.126, 0.127,**0.1275**0.128, 0.129- Decide which of the counted numbers is closest to the given number.Its closest to
**0.1275 is closest to 0.128**because 0.0.1275 is closer to 0.1280 than to 0.1270

Therefore, 0.1275 rounded to the the hundredths position is 0.128

# Check Your Understanding

What is the place value mentioned in the following request to round?

- Round to the nearest hundredths
- Round to the nearest thousandths
- Round to the nearest ten-thousandths

Can you count by increments of place values? Think an answer then look at an example of one possible answer ...

- Count by ten-thousandths.
- Count by tenths.
- Count by thousandths.

Why are the following statements true??

- 0.7 is less than 0.71 and 0.71 is less than 0.8
- 0.82 is less than 0.821 and 0.821 is less than 0.83
- 0.1 is less than 0.15 and 0.15 is less than 0.2
- 0.78 is less than 0.78999 and 0.78999 is less than 0.79

Why are the following statements true??

- 0.7 and 0.8 surround .78
- 0.97 and 0.98 surround 0.972
- 0.854 and 0.855 surround 0.8545
- 1.4 and 1.5 surround 1.41

Why are the following statements true??

- 0.78 is closer to 0.8 than to 0.7
- 0.972 is closer to 0.97 than to 0.98
- 0.8545 is closer to 0.855 than to 0.854
- 1.41 is closer to 1.4 than to 1.5

Do some interactive practice

- Enter a number between 0 and 999.9999.
- Enter a place value to round to .... 10ths, 100ths, 1000ths
- Figure out what you believe the answer should be.
- Click the button "Check" and check your answer.