How to Read, Write, and Convert Tenths and Hundredths
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 Tenths and Hundredths in Decimals: Simple Explanations and Examples
1. What is tenths and hundredths in decimals?
Tenths and hundredths represent specific decimal place values. The tenths place is the first digit to the right of the decimal point and shows the number of parts out of ten (1/10). The hundredths place is the second digit to the right of the decimal point and shows parts out of one hundred (1/100). For example, in 0.7, the 7 is in the tenths place, meaning 7/10, and in 0.05, the 5 is in the hundredths place, meaning 5/100.
2. How do you read 45.27 using tenths and hundredths?
The number 45.27 is read by identifying the places after the decimal: 2 is in the tenths place (which means 2/10) and 7 is in the hundredths place (which means 7/100). So, it is read as "forty-five and twenty-seven hundredths" or "forty-five point two seven."
3. How to write tenths and hundredths as fractions or in words?
To write tenths as fractions, use a denominator of 10; for example, 0.3 = 3/10. To write hundredths, use a denominator of 100; for example, 0.05 = 5/100. In words, 0.4 is "four tenths" and 0.09 is "nine hundredths." Converting decimals to words helps understand their place values clearly.
4. Is 10 hundredths equal to 1 tenth?
Yes, 10 hundredths (10/100) is equal to 1 tenth (1/10). Both represent the same decimal value 0.1 because 10/100 simplifies to 1/10 after dividing numerator and denominator by 10.
5. How can tenths and hundredths be shown on a number line or grid?
Tenths and hundredths can be represented by dividing the sections between whole numbers into 10 equal parts (tenths) or 100 equal parts (hundredths) on a number line or using a decimal grid. This visual representation helps students understand the size and position of decimals relative to whole numbers.
6. Why do some students confuse tenths with hundreds or thousandths in exams?
Students often confuse tenths with hundreds or thousandths due to the similar naming and decimal placement. Lack of clarity on place value and the position of digits after the decimal point causes this confusion. Using visual aids like place value charts and number lines can reduce these errors.
7. How do tenths and hundredths impact decimal rounding errors?
When rounding decimals, tenths and hundredths play a critical role. For example, rounding to the nearest tenth means looking at the hundredths place to decide whether to round up or down. Misunderstanding these place values can lead to incorrect rounding.
8. What mistakes occur when converting tenths or hundredths to words?
Common mistakes include mixing up tenths and hundredths, mispronouncing decimals, or confusing place values. For example, saying "four hundredths" instead of "forty hundredths" or writing 0.4 as "four hundredths" instead of "four tenths." Accurate place value knowledge prevents these errors.
9. Why is visualising tenths and hundredths on charts or number lines important for understanding?
Visualising tenths and hundredths on charts and number lines helps link abstract decimal concepts to tangible representations. It improves comprehension by showing relative sizes, helping students distinguish between place values clearly, and supporting better recall during exams.
10. How are tenths and hundredths tested differently in Class 4 and Class 5 boards?
In Class 4, the focus is usually on identifying and reading tenths and basic decimal concepts. Class 5 introduces deeper understanding of hundredths, converting decimals to fractions, and using number lines and charts for problem-solving. The complexity and application level increase accordingly for effective exam preparation.
