What Is Rounding to the Nearest Hundredth?
Rounding to the nearest hundredth simply means finding an approximate value of a given decimal up to two decimal places.
When we round to the nearest hundredth, the resulting decimal has only two digits after the decimal point. Thus, rounding off to two decimal places is the same as rounding to the nearest hundredth.
For example, 235.679 rounded to the nearest hundredth is 235.68.
The process of rounding to the nearest hundredth depends on the digit at the thousandths place. Decimals can be rounded off to the tenths, hundredths, thousandths, and even to the nearest whole number or integer. Rounding off the decimal numbers helps in making the calculation easier and simpler.
Before we go into the method of rounding, let’s first look at the place value chart in decimals. Let’s write the decimal number 235.679 in the decimal place value chart and find the place values.
| Hundreds 100 | Tens 10 | Ones 1 | Decimal point | Tenths $\frac{1}{10}$ | Hundredths $\frac{1}{100}$ | Thousandths $\frac{1}{1000}$ |
| 2 | 3 | 5 | 6 | 7 | 9 | |
| 200 | 30 | 5 | $\frac{6}{10} = 0.6$ | $\frac{7}{100} = 0.07$ | $\frac{9}{1000} = 0.009$ |
Thus, $235.679 = 200 + 30 + 5 + 0.6 + 0.07 + 0.009$.
The hundredths place is the second place after the decimal point.
The thousandths place is the third place after the decimal point.
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Rounding Decimals to the Nearest Hundredth: Definition
Rounding to the nearest hundredth is a process of finding an approximate value up to two decimal places. In simple words, we find an approximate value, keeping the precision of two decimal places.
So, the question is, what happens to the existing digit in the hundredths place? To round to the nearest hundredth, we always look at the digit in the thousandth place. If the digit at the thousandths place is less than 5, we round up. If the digit at the thousandths place is greater than or equal to 5, we round down.
Let’s understand the steps for rounding decimals to the nearest hundredth.
How to Round to the Nearest Hundredth
Step 1: Mark the digit at the hundredths place.
Step 2: Next, observe the digit at the ‘thousandths’ place (the digit on the right next to the hundredths place).
Here, there are two possibilities:
i) Rounding up
If the digit at the thousandth place is less than 5, keep the hundredths place digit as it is and remove all the digits to its right. This is called rounding up since the resulting number is greater than the original number.
ii) Rounding down
If the digit at the thousandth place is 5 or more than 5, then add 1 to the digit at the hundredth place and remove all the digits from its right. This is called rounding down since the resulting number is less than the original number.
Example 1: Round 78.491 to the nearest hundredth.
| Tens | Ones | Decimal point | Tenths | Hundredths | Thousandths |
|---|---|---|---|---|---|
| 7 | 8 | . | 4 | 9 | 1 |
| 9 stays. | $1 \lt 5$ |
Thousandths place digit $= 1 \lt 5$
Thus, the digit at the hundredths place will stay the same. We will remove the thousandths digit.
Rounding to the nearest hundredth, we get 78.49.
Thus, 78.491 rounded to the nearest hundredth is 78.49.
Example 2: Round to the nearest hundredth: 2.798
| Ones | Decimal point | Tenths | Hundredths | Thousandths |
|---|---|---|---|---|
| 2 | . | 7 | 9 | 8 |
| $7 + 1 = 8$Carry 1 over | $9 + 1 = 10$Keep 0 | $8\gt5$ |
Thousandths place digit $= 8 \gt 5$
Increase the digit at the tenths place (9) by 1.
$9 + 1 = 10$
Keep 0 and carry 1 over to the tenths place.
$7 + 1 = 8$
Rounding to the nearest hundredth, we get 2.80.
Thus, 2.798 rounded to the two decimal places is 2.80 or 2.8.
Decimals Rounded to the Nearest Hundredth: Examples
| Decimal | Decimal rounded to the nearest hundredth |
|---|---|
| 1.125 | 1.13 |
| 0.111 | 0.11 |
| 0.989 | 0.99 |
| 0.004 | $0.00 = 0$ |
| 0.005 | 0.01 |
| 24.5667 | 24.57 |
| 5.55555 | 5.56 |
Facts about Rounding to the Nearest Hundredth
When we divide a whole into 100 equal parts, we call each part one hundredth. In other words, one hundredth is one part of a 100 equal parts.
One hundredth $= \frac{1}{100}$
Rounding has important applications in estimation. In daily life, we use rounding all the time when we have to approximate a big number to a simple and short value.
Solved Examples on Rounding to the Nearest Hundredth
1. The depth of the pond is 25.198 feet. Round to the nearest hundredth.
Solution:
| Tens | Ones | Decimal point | Tenths | Hundredths | Thousandths |
|---|---|---|---|---|---|
| 2 | 2 | . | 1 | 9 | 8 |
| $1 + 1 = 2$ | $9 + 1 = 10$ Keep 0.Carry 1 over. | $8 \gt 5$ |
The thousandths place has the digit 8, which is greater than 5.
Thus, we increase the digit at the hundredths place by 1.
Hundredths place digit $= 9$
Hundredths place digit $+ 1 = 9 + 1 = 10$
Write 0 in the hundredths place and carry 1 to the tenths place.
$1 + 1 = 2$
Thus, 22.198 rounded to the nearest hundredth is 25.2.
The depth of the pond is 25.2 feet.
2. Find the approximate value of the decimal number 70.070707 correct up to two decimal places.
Solution:
Hundredths digit $= 7$
Thousandths digit $= 0$ which is less than 5.
Thus, keep the digit at hundredth place the same and remove all the digits from right.
So, 70.070707 rounded to the nearest hundredth is 70.07.
3. Round to the nearest hundredth.
i) 11.334
ii) 99.108
iii) 24.501
Solution:
| Decimal | Decimal rounded to the nearest hundredth |
|---|---|
| 11.334 | 11.33 |
| 99.108 | 99.11 |
| 24.501 | 24.50 |
Practice Problems on Rounding to the Nearest Hundredth
Round to the Nearest Hundredth – Definition, Method, Examples
____ rounded off to the nearest hundredth is 1.76.
$1.754 \approx 1.75$
$1.769 \approx 1.77$
$1.749 \approx 1.75$
However, 1.758 when rounded off to the nearest hundredth is 1.76.
What will be the approximate value of 21.344 correct to two decimal places?
The digit at hundredths place $= 4$. The digit at thousands place $= 4 \lt 5$. So, $21.344 \approx 21.34$
Round to the nearest hundredth: 26.172
$26.172 \approx 26.17$
If the grocery bill is $24.495, what’s the approximate amount you will pay?
(Round to the nearest hundredth.)
Hundredths place $= 9$
Thousandths place $= 5$
Thus, add 1 to the digit at the hundredths place.
$9 + 1 = 10$…write 0 and carry 1 over
$4 + 1 = 5$
Thus, 24 .495 rounded to the nearest hundredth is 24.50.
Frequently Asked Questions on Rounding to the Nearest Hundredth
What is rounding?
Rounding numbers means adjusting or estimating the digits of a number so that it gives an approximate value. While rounding off the numbers, we replace a number with an estimated value, which is a simpler and a shorter representation of the given number.
What is the purpose of rounding?
We generally round numbers because the rounded number is easier to understand and remember and the calculations become easier to work with.
What is the difference between rounding off to the nearest hundredths and rounding off to the nearest hundred?
While rounding off to nearest hundredths, we look at the thousandths digit to decide whether to round up or round down. The resulting decimal is approximated up to 2 decimal places. Example: $34.567 \approx 34.57$
In rounding off to the nearest hundred, we look at the tens digit. The resulting number is the closest multiple of 100. Example: $371\rightarrow 400$
