# Rounding decimal places

**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.

**Step 4: State the answer.**

$$3.621 = 3.62$$

**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 $$8$$**.**

**Step 4: State the answer.**

$$\textrm{1.8 kg}$$

**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 $$4$$**.**

**Step 4: State the answer.**

$$\textrm{3.24 kg}$$

**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 $$3$$

**Step 4: State the answer.**

$$\textrm{1.2 cm}$$ 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 $$6$$**.**

**Step 4: State the answer.**

$$\textrm{8.96 m}$$.