# Rounding Decimals

Sometimes we need to round decimals.

Rounding decimals is very similar (almost identical) to rounding whole numbers.

Also, we need to know place value of decimals.

**Example 1.** Round 236.45 to the nearest ten.

We proceed in the same way as with rounding whole numbers.

Find tens in 236.45: 2**3**6.45. It is 3.

Look at the digit immediately to the right of 3: it is 6.

Since 6 is greater or equal than 5 then we increase 3 by 1 (resulting in 4) and change all digits to the right of 3 to zeros.

So, 236.45 rounded to ten is 240.00.

Also, we can ignore trailing zeros after the decimal point: 240.00 becomes 240.

**Answer: 240.**

Next example.

**Example 2.** Round 234.56 to the nearest one.

Find ones in 234.56: 23**4**.56. It is 4.

Look at the digit immediately to the right of 4: it is 5.

Since 5 is greater or equal than 5 then we increase 4 by 1 (resulting in 5) and change all digits to the right of 4 to zeros.

So, 2345.56 rounded to ones is 235.00, which is 235.

**Answer: 235.**

Next example shows how to round to nearest tenth.

**Example 3**. Round 936.54 to the nearest tenth.

Find tenths in 936.54: 936.**5**4. It is 5.

Look at the digit immediately to the right of 5: it is 7.

Since 4 is less than 5 then we leave 4 and change all digits to the right of 4 to zeros.

So, 936.54 rounded to tenth is 936.50, which is 936.5.

**Answer: 936.5.**

Next example shows how to round to thousandth.

**Example 4**. Round 0.6794 to the nearest thousandth.

Find thousandths in 0.6794: 8.6794. It is 9.

Look at the digit immediately to the right of 9: it is 4.

Since 4 is less than 5 then we leave 4 and change all digits to the right of 9 to zeros.

So, 0.6794 rounded to thousandth is 0.6790, which is 0.679.

**Answer: 0.679.**

Next two examples are harder than previous, because we need to touch other digits as well.

**Example 5**. Round 5267.98 to the tenth.

Find tenths in 5267.98: 5267.**9**8. It is 9.

Look at the digit immediately to the right of 9: it is 8.

Since 8 is greater or equal than 5 then we increase 9 by 1 (resulting in 10) and change all digits to the right of 9 to zeros.

But wait. We obtained 10 which is two-digit number. But we need only one digit.

No problem. We leave 0 on place of 9 and add remaining 1 to the digit immediately to the left of 9: 7+1=8.

So, 5267.98 rounded to tenth is 5268.00 which is 5268.

**Answer: 5268.**

Final example.

**Example 6.** Round 5137.998. to the nearest hundredth.

Find hundredths in 5137.998: 5137.9**9**8. It is 9.

Look at the digit immediately to the right of 9: it is 8.

Since 8 is greater or equal than 5 then we increase 9 by 1 (resulting in 10) and change all digits to the right of 9 to zeros.

Again we obtained 10 which is two-digit number. But we need only one digit.

We leave 0 on place of 9 and add remaining 1 to the digit immediately to the left of 9: 9+1=10.

Again we obtained 10. We do the same thing once more: leave 0 and 1 to the digit immediately to the left: 7+1=8.

So, 5137.998 rounded to hundredth is 5138.000 which is 5138.

**Answer: 5138.**

In general we round decimals just like whole numbers: find digit on required place and examine the digit immediately to the right. If it is greater or equal than 5, increase found digit by 1 and change all digits to the right of this digit to zeros. Otherwise, leave found digit as it is and change all digits to the right of it to zeros.

Now, take a pen and paper and solve following problems.

**Exercise 1**. Round 156.43 to the nearest tenth.

**Answer: 156.4.**

Next exercise.

**Exercise 2.** Round 23.987 to the nearest hundredth.

**Answer: 23.99.**

Next exercise.

**Exercise 3**. Round 13.451 to the nearest hundredth.

**Answer: 13.45.**

Next exercise.

**Exercise 4.** Round 0.9 to the nearest ones.

**Answer: 1.**

Last exercise.

**Exercise 5.** Round 199.97 to the nearest tenth.

**Answer: 200.**