Rounding to the nearest hundredth is a fundamental skill in mathematics, crucial for various applications from everyday calculations to complex scientific computations. This guide provides a clear and concise method for mastering this essential skill, regardless of your current mathematical proficiency. We'll cover the process step-by-step, offering examples to solidify your understanding.
Understanding Hundredths
Before diving into the rounding process, let's clarify what a hundredth represents. In the decimal system, numbers are represented using place values. Moving right from the decimal point, we have tenths (1/10), hundredths (1/100), thousandths (1/1000), and so on. Rounding to the nearest hundredth means adjusting the number to the closest value with only two digits after the decimal point.
The Rounding Process: A Step-by-Step Guide
Rounding to the nearest hundredth involves these simple steps:
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Identify the hundredths digit: Locate the digit in the hundredths place (the second digit after the decimal point).
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Examine the thousandths digit: Look at the digit immediately to the right of the hundredths digit (the thousandths place).
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Round up or down:
- If the thousandths digit is 5 or greater (5, 6, 7, 8, or 9), round the hundredths digit up by adding 1 to it.
- If the thousandths digit is less than 5 (0, 1, 2, 3, or 4), keep the hundredths digit as it is.
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Drop any digits to the right of the hundredths place: After rounding, eliminate all digits beyond the hundredths place.
Examples to Illustrate
Let's solidify your understanding with a few practical examples:
Example 1: Round 3.14159 to the nearest hundredth.
- Hundredths digit: 4
- Thousandths digit: 1
- Since 1 < 5, we keep the hundredths digit as 4.
- Result: 3.14
Example 2: Round 2.786 to the nearest hundredth.
- Hundredths digit: 8
- Thousandths digit: 6
- Since 6 ≥ 5, we round the hundredths digit up (8 + 1 = 9).
- Result: 2.79
Example 3: Round 15.999 to the nearest hundredth.
- Hundredths digit: 9
- Thousandths digit: 9
- Since 9 ≥ 5, we round the hundredths digit up (9 + 1 = 10). This carries over to the tenths place.
- Result: 16.00
Example 4: Rounding with zeros. Round 4.504 to the nearest hundredth.
- Hundredths digit: 0
- Thousandths digit: 4
- Since 4 < 5, we keep the hundredths digit as 0
- Result: 4.50
Practical Applications of Rounding to the Nearest Hundredth
Rounding to the nearest hundredth is valuable in many real-world situations:
- Financial calculations: Dealing with money often requires rounding to the nearest cent (hundredth of a dollar).
- Scientific measurements: Many scientific measurements are expressed to a specific number of decimal places, often involving hundredths.
- Engineering and design: Precision in engineering and design frequently requires rounding to the nearest hundredth for accuracy.
Mastering rounding to the nearest hundredth is a simple yet powerful tool that significantly improves accuracy and efficiency in various numerical operations. By following the steps outlined above and practicing with examples, you can confidently tackle this essential mathematical skill.