Hundredths: The Tiny Titans of the Decimal World
What Exactly is a Hundredth?
Imagine a whole pizza. Now, imagine cutting it into one hundred perfectly equal slices. Each of those tiny slices represents one hundredth of the pizza. Mathematically, we write this as $ \frac{1}{100} $. The number 1 on top (the numerator) tells us we have one piece, and the number 100 on the bottom (the denominator) tells us that the whole was split into 100 pieces.
In our decimal number system, which is based on the number ten, the hundredths place is the second digit to the right of the decimal point. Let's look at a place value chart to see where it fits.
| Hundreds | Tens | Ones | Decimal Point | Tenths | Hundredths | Thousandths |
|---|---|---|---|---|---|---|
| 100 | 10 | 1 | . | $ \frac{1}{10} $ | $ \frac{1}{100} $ | $ \frac{1}{1000} $ |
| - | - | 5 | . | 2 | 7 | 4 |
In the number 5.274 from the table above, the digit 7 is in the hundredths place. This means we have 7 hundredths, or $ 7 \times \frac{1}{100} = \frac{7}{100} $.
Connecting Fractions, Decimals, and Visuals
Understanding hundredths is about seeing the connection between different representations. A fraction like $ \frac{35}{100} $ is exactly the same as the decimal 0.35. The denominator 100 in the fraction tells us we are dealing with hundredths, and this directly corresponds to the two decimal places.
Visual models are incredibly helpful. A 10 \times 10 grid, which has 100 small squares, is a perfect tool. The entire grid represents one whole. Each small square is one hundredth ($ \frac{1}{100} $). If you shade 35 squares, you have shaded $ \frac{35}{100} $ of the whole, which is 0.35.
Hundredths in Action: Real-World Applications
The concept of hundredths is not just a math class idea; it is everywhere in our daily lives. Recognizing it helps us make sense of the world.
Money and Finance
This is the most common application. In many currencies, like the US Dollar and the Euro, the main unit is divided into 100 cents.
- 1 dollar = 100 cents.
- Therefore, 1 cent = $ \frac{1}{100} $ of a dollar = 0.01 dollars.
- If you have $4.78, this means you have 4 whole dollars and 78 hundredths of a dollar (or 78 cents).
Measurement
In the metric system, which is based on powers of ten, hundredths are frequently used.
- Meters: 1 centimeter = $ \frac{1}{100} $ of a meter = 0.01 meters. A meter stick is divided into 100 centimeters.
- Liters: 1 centiliter = $ \frac{1}{100} $ of a liter = 0.01 liters.
- Kilograms: 1 gram = $ \frac{1}{1000} $ of a kilogram, but a centigram is $ \frac{1}{100} $ of a gram, showing how the prefix "centi-" always means "one hundredth."
Percentages
The word "percent" literally means "per hundred." So, 1\% is defined as one hundredth.
- 1\% = \frac{1}{100} = 0.01
- 45\% = \frac{45}{100} = 0.45
- 100\% = \frac{100}{100} = 1 (the whole)
If you score 87\% on a test, it means you got 87 out of 100 points possible. You are dealing with hundredths!
Operations with Hundredths
Adding, subtracting, multiplying, and dividing numbers involving hundredths follows the same rules as other decimals. The key is to correctly align the decimal points.
| Operation | Example | Explanation |
|---|---|---|
| Addition | $ 0.25 + 0.07 = 0.32 $ | 25 hundredths + 7 hundredths = 32 hundredths. Line up the decimal points to ensure you are adding digits in the same place value. |
| Subtraction | $ 0.50 - 0.15 = 0.35 $ | 50 hundredths - 15 hundredths = 35 hundredths. Again, aligning decimals is crucial. |
| Multiplication | $ 0.03 \times 4 = 0.12 $ | 3 hundredths multiplied by 4 equals 12 hundredths. You can think of it as $ 3 \times 4 = 12 $, and since you multiplied two numbers with a total of two decimal places, the answer must also have two decimal places. |
| Division | $ 0.45 \div 5 = 0.09 $ | 45 hundredths divided into 5 equal groups gives 9 hundredths in each group. |
Common Mistakes and Important Questions
Q: Is 0.10 the same as 0.1? Why or why not?
A: This is a common point of confusion. While they represent the same value (one tenth), they are written differently. 0.10 means "ten hundredths" ($ \frac{10}{100} $). If you simplify $ \frac{10}{100} $, it reduces to $ \frac{1}{10} $, which is 0.1. So, 0.10 and 0.1 are equal in value, but 0.10 shows a greater degree of precision, indicating that you measured to the nearest hundredth.
Q: When reading a decimal like 0.07, why do we say "seven hundredths" and not "zero point zero seven"?
A: Saying "seven hundredths" is more mathematically meaningful because it directly states the place value of the digit 7. It reinforces the concept that this number is composed of 7 parts out of 100. While "zero point zero seven" is not incorrect, the place value method is preferred for building a deeper understanding of decimals.
Q: What is the most common mistake when adding or subtracting hundredths?
A: The most frequent error is misaligning the decimal points. For example, writing 0.5 + 0.05 as:
0.5
+0.05
-----
0.10 (Correct)
...is correct. But if the decimals are not lined up, you might incorrectly add the 5 (tenths) to the 5 (hundredths), getting a wrong answer like 0.55. Always line up the decimal points!
Footnote
1 CPI (Consumer Price Index): A measure that examines the weighted average of prices of a basket of consumer goods and services, such as transportation, food, and medical care. It is calculated by taking price changes for each item in the predetermined basket of goods and averaging them. Changes in the CPI are used to assess price changes associated with the cost of living.
2 Decimal System: A number system based on the number 10, in which numbers are represented using the digits 0 through 9 and a decimal point to separate the whole number part from the fractional part.
3 Place Value: The numerical value that a digit has by virtue of its position in a number. For example, in the number 0.05, the 5 is in the hundredths place, giving it a value of five hundredths.