Rounding decimals to the nearest hundredth is a fundamental skill in mathematics that helps simplify numbers and make them easier to work with. This skill is especially useful when estimating or working with measurements in real-world applications. In this tutorial, we will walk through the step-by-step process of rounding decimals to the nearest hundredth.
Understanding Decimal Place Values
Before we begin rounding decimals, it’s crucial to understand decimal place values. A decimal number consists of a whole number followed by a decimal point and decimal digits. Each decimal digit has a specific place value:
- Tens place: One place to the left of the decimal point (10^1)
- Ones place: Immediately to the left of the decimal point (10^0)
- Tenths place: One place to the right of the decimal point (10^-1)
- Hundredths place: Two places to the right of the decimal point (10^-2)
- Thousandths place: Three places to the right of the decimal point (10^-3)
For example, in the number 123.456, the digit 1 is in the tens place, 2 is in the ones place, 4 is in the tenths place, 5 is in the hundredths place, and 6 is in the thousandths place.
Step-by-Step Guide to Rounding Decimals to the Nearest Hundredth
Follow these simple steps to round decimals to the nearest hundredth:
Step 1: Identify the hundredths place
Find the digit in the hundredths place, which is two places to the right of the decimal point.
Example: In the number 37.289, the digit 8 is in the hundredths place.
Step 2: Look at the digit to the right of the hundredths place
Examine the digit immediately to the right of the hundredths place, in the thousandths place.
Example: In the number 37.289, the digit 9 is in the thousandths place.
Step 3: Determine whether to round up or down
If the digit in the thousandths place is 5 or greater, round the digit in the hundredths place up by one. If the digit is 4 or less, keep the digit in the hundredths place as it is.
Example: In the number 37.289, the digit in the thousandths place is 9, which is greater than 4. Therefore, we round the digit in the hundredths place (8) up by one.
Step 4: Round the decimal number
Replace the digit in the hundredths place with the new value from step 3, and remove all digits to the right of the hundredths place.
Example: In the number 37.289, we rounded the digit in the hundredths place (8) up to 9. The rounded decimal number is 37.29.
Practice Rounding Decimals to the Nearest Hundredth
Now, let’s practice rounding a few decimal numbers to the nearest hundredth:
- 12.345 as decimal rounded to the nearest hundredth
- Hundredths place: 3
- Thousandths place: 4 (less than 5)
- Rounded number: 12.34
- 0.9876 as decimal rounded to the nearest hundredth
- Hundredths place: 8
- Thousandths place: 7 (greater than 4)
- Rounded number: 0.99
- 145.216 as decimal rounded to the nearest hundredth
- Hundredths place: 1
- Thousandths place: 6 (greater than 4)
- Rounded number: 145.22
- 37.5004 as decimal rounded to the nearest hundredth
- Hundredths place: 5
- Thousandths place: 0 (less than 5)
- Rounded number: 37.50
- 6.8349 as decimal rounded to the nearest hundredth
- Hundredths place: 3
- Thousandths place: 4 (less than 5)
- Rounded number: 6.83
Key Takeaways for Rounding Decimals to the Nearest Hundredth
Rounding decimals to the nearest hundredth is a valuable skill for making numbers easier to work with and simplifying calculations. Remember these key points when rounding decimals to the nearest hundredth:
- Identify the digit in the hundredths place (two places to the right of the decimal point).
- Look at the digit to the right of the hundredths place (in the thousandths place).
- If the digit in the thousandths place is 5 or greater, round the hundredths digit up by one. If it’s 4 or less, keep the hundredths digit as it is.
- Replace the hundredths digit with the new value, and remove all digits to the right of the hundredths place.
By following these simple steps, you’ll be able to round decimals to the nearest hundredth with ease, making your mathematical work more efficient and accurate. Practice this skill regularly to become proficient and confident in rounding decimal numbers.