What Are Tenths and Hundredths Definition Place Value Chart and Solved Examples
The concept of tenths and hundredths is essential in mathematics and helps in solving real-world and exam-level problems efficiently. Understanding tenths and hundredths prepares students for working with decimals, fractions, conversions, and place value questions in exams and daily life.
Understanding Tenths and Hundredths
A tenths and hundredths place refers to the first and second digits after the decimal point in a number. The tenths place shows how many parts out of ten the number represents (for example, 0.1), while the hundredths place shows parts out of one hundred (for example, 0.01). This concept is widely used in decimal place value, fractional part representation, and reading decimals in maths.
Decimal Place Value: Tenths and Hundredths Explained
Every decimal has digits after the decimal point, and each digit has a place value.
Tenths: The first digit after the decimal (e.g., the 2 in 4.2) represents tenths or 1/10.
Hundredths: The second digit after the decimal (e.g., the 5 in 3.25) represents hundredths or 1/100.
Here’s a helpful table to understand tenths and hundredths more clearly:
Tenths and Hundredths Place Value Table
| Number | Tenths Place | Hundredths Place | In Words |
|---|---|---|---|
| 4.72 | 7 | 2 | Four and seventy-two hundredths |
| 0.35 | 3 | 5 | Thirty-five hundredths |
| 8.1 | 1 | 0 | Eight and one tenth |
| 6.09 | 0 | 9 | Six and nine hundredths |
This table shows how each decimal number separates tenths and hundredths, helping you read and write them as words.
Conversion: Tenths and Hundredths to Fractions, Decimals, and Words
You can easily convert between decimals, fractions, and words:
2. 0.45 as a fraction: \( 0.45 = \frac{45}{100} \) (“forty-five hundredths”)
3. Write “three and seven tenths” as a decimal: \( 3.7 \)
4. Write \( \frac{13}{100} \) as a decimal: \( 0.13 \) (“thirteen hundredths”)
Practice converting between tenths/hundredths, decimals, and words to become confident in exams.
Worked Example – Expressing Decimals as Fractions and Vice Versa
Let's see how to convert a decimal into a fraction step by step:
2. The digit after the decimal is in the tenths place.
3. So, 2.3 = 2 + \(\frac{3}{10}\)
4. Therefore, 2.3 as a fraction is \( \frac{23}{10} \).
5. Now, convert 0.47 into a fraction.
6. There are digits in the tenths (4) and hundredths (7) places.
7. 0.47 = \( \frac{47}{100} \).
8. Final answers: 2.3 = 23/10, 0.47 = 47/100.
Grids and Number Lines for Tenths and Hundredths
Visual aids like grids and number lines make it easy to understand where tenths and hundredths fall between whole numbers. For example, on a line from 0 to 1, each interval of 0.1 marks a tenth, and each jump of 0.01 marks a hundredth. You can shade grids divided into 10 (for tenths) or 100 (for hundredths) to visualize these concepts.
Practice Problems
- Write the following in decimals: (a) Seven tenths, (b) Fifteen hundredths
- Express 0.58 as a fraction in lowest terms.
- Which digit is in the tenths place in 4.91?
- Create a grid to shade 0.3 and 0.07 separately.
- Convert \( \frac{9}{10} \) and \( \frac{47}{100} \) into decimals.
Common Mistakes to Avoid
- Mixing up tenths (0.1) with hundreds or thousandths (0.01, 0.001).
- Writing 0.10 as “ten” (it is “ten hundredths” or “one tenth”).
- Forgetting to line up decimal points when adding/subtracting decimals.
- Confusing the place value in words (e.g., “nine tenths” ≠ “nine hundreds”).
Real-World Applications
The concept of tenths and hundredths appears in areas such as measurements (lengths, weights), money (paisa, cents), scientific readings, and scores. Banks use hundredths for interest rates. Measurement tools often show readings to tenths or hundredths. Vedantu helps students see how maths applies beyond the classroom through such examples.
Page Summary
We explored the idea of tenths and hundredths, learned to convert between decimals, fractions, and words, and saw examples of their use on charts and number lines. Practicing these skills with Vedantu improves understanding and helps you score better in exams. For a deeper study of decimals and fractions, check these resources:
Decimal Number System | Place Value | Decimal Place Value | Comparing Fractions | Fractions on the Number Line | Conversion of Fractions to Decimals | Decimal Fraction | Rounding Decimals | Fractions and Decimals | Ones, Tens, and Hundreds
FAQs on Understanding Tenths and Hundredths in Decimal Place Value
1. What are tenths and hundredths in decimals?
Tenths and hundredths are decimal place values that represent parts of a whole divided into 10 and 100 equal parts respectively. In a decimal number:
- The tenths place is the first digit to the right of the decimal point.
- The hundredths place is the second digit to the right of the decimal point.
- For example, in 0.47, 4 represents 4 tenths (0.4) and 7 represents 7 hundredths (0.07).
2. How do you write tenths and hundredths as fractions?
Tenths are written as fractions with denominator 10, and hundredths are written with denominator 100.
- 1 tenth = 1/10
- 1 hundredth = 1/100
- 0.6 = 6/10
- 0.25 = 25/100
3. How do you convert tenths and hundredths to decimals?
To convert tenths and hundredths to decimals, place the digit in the correct decimal position.
- For tenths, write the digit in the first place after the decimal point: 3 tenths = 0.3.
- For hundredths, write the digit in the second place: 7 hundredths = 0.07.
- Example: 45 hundredths = 0.45.
4. What is the difference between tenths and hundredths?
The difference between tenths and hundredths is that tenths divide a whole into 10 parts, while hundredths divide a whole into 100 parts.
- 1 tenth = 0.1
- 1 hundredth = 0.01
- 1 tenth is equal to 10 hundredths.
5. How do you add tenths and hundredths?
To add tenths and hundredths, align the decimal points and add by place value.
- Example: 0.4 + 0.35
- Write as 0.40 + 0.35
- Add: 0.75
6. How do you round decimals to the nearest tenth or hundredth?
To round to the nearest tenth or hundredth, check the digit to the right of the place you are rounding to.
- To round 0.67 to the nearest tenth, look at the hundredths digit (7) → round up to 0.7.
- To round 0.674 to the nearest hundredth, look at the thousandths digit (4) → keep 7 → 0.67.
7. Can you give an example of tenths and hundredths in real life?
Tenths and hundredths are commonly used in money, measurements, and data.
- Money: $0.75 means 7 tenths and 5 hundredths of a dollar.
- Length: 1.25 meters means 25 hundredths of a meter.
- Time: 2.5 hours means 5 tenths of an hour.
8. How many hundredths are in one tenth?
There are 10 hundredths in one tenth. Since 1 tenth = 0.1 and 1 hundredth = 0.01, dividing 0.1 by 0.01 gives 10. This shows that 1/10 = 10/100.
9. How do you compare tenths and hundredths?
To compare tenths and hundredths, compare digits starting from the tenths place.
- Example: Compare 0.6 and 0.56.
- Write 0.6 as 0.60.
- Since 60 hundredths > 56 hundredths, 0.6 > 0.56.
10. What are common mistakes when working with tenths and hundredths?
Common mistakes with tenths and hundredths include misplacing digits and not aligning decimals.
- Confusing 0.5 and 0.05 (tenths vs hundredths).
- Not lining up decimal points when adding or subtracting.
- Forgetting that 0.1 is greater than 0.09.
