# Rounding decimal places

Last updated: September 17, 2021

## How to round decimal places

Rounding off decimal places is needed for estimation. Be it purchasing something from a store or determining the daily temperatures of a region, estimation is used everywhere. Estimations provide approximate values as determining the exact value of a quantity becomes difficult at times.

### E1.9A: Make estimates of numbers and give approximation to specified numbers and decimal places round off answers to reasonable accuracy in the context of a given problem.

The procedure of rounding off decimal numbers depend upon the decimal places. If a number has to be rounded off to $$1$$ decimal point, then the answer depends upon the digit at the hundredths place. If the digit is greater than $$5$$ then increase the tenths place digit by $$1$$ or otherwise no change in the digit. If a number has to be rounded off to $$2$$ decimal points, then the answer depends upon the digit at the thousandths place. Same procedure follows for the thousandths place value.

## Worked examples

Example 1: Round off $$7.68$$ to $$1$$ decimal place.

First it is clear that the answer depends upon the hundredths place value. Check if the number is greater than five or not. Here, $$8 > 5$$. Increase the digit at the tenths place and write the answer. So, the answer is $$7.7$$

Example 2: Round off the value $$3.621$$ to nearest hundredths.

Step 1: Find the number to round off.

Since rounding off it to nearest hundredths, select $$1$$

Step 2: Check if the number is greater than five or not.

$$1 < 5$$

Step 3: Change the number.

The number to the left of $$1$$ remains as is.

$$3.621 = 3.62$$

### E1.9B: Make estimates of quantities and give approximation to specified numbers and decimal places round off answers to reasonable accuracy in the context of a given problem.

The estimation method followed for numbers is followed for quantities as well.

## Worked examples

Example 1: Round off $$\textrm{1.76 kg}$$ of rice to $$1$$ decimal place.

Step 1: Find the number to round off.

The number to round off is $$6$$.

Step 2: Check if the number is greater than five or not.

$$6 > 5$$

Step 3: Change the number.

Choose the next number $$8$$.

$$\textrm{1.8 kg}$$

Example 2: Round off the value $$\textrm{2.342 kg}$$ to $$2$$ decimal places.

Step 1: Find the number to round off.

The number to round off is $$2$$.

Step 2: Check the number is greater than five or not.

$$2 < 5$$

Step 3: Change the number.

No change in the number $$4$$.

$$\textrm{3.24 kg}$$

### E1.9C: Make estimates of lengths numbers and give approximation to specified numbers and decimal places round off answers to reasonable accuracy in the context of a given problem.

The estimation method followed for numbers is followed for lengths as well.

## Worked examples

Example 1: Round off $$\textrm{1.25 cm}$$ of rod to $$1$$ decimal places.

Step 1: Find the number to round off.

The number to round off is $$2$$.

Step 2: Check if the number is greater than five or not.

$$5 = 5$$

Step 3: Change the number.

It can take both values, $$2$$ or $$3$$

$$\textrm{1.2 cm}$$ or $$\textrm{1.3 cm}$$

Example 2: Round off the value $$\textrm{8.956 m}$$ to 2 decimal places.

Step 1: Find the number to round off.

The number to round off is $$6$$.

Step 2: Check the number is greater than five or not.

$$6 > 5$$

Step 3: Change the number.

Choose the next number $$6$$.

$$\textrm{8.96 m}$$.