Tenths and Hundredths — Class 5 Mathematics (CBSE)
Based on the NCERT Math Magic Grade 5 textbook. Understand decimals as tenths and hundredths, then solve the practice set without looking at the answers.
1. Why this chapter matters
Decimals are everywhere — the price of a chocolate (Rs 10.50), your height (1.35 m), the weight of vegetables (2.5 kg). This chapter introduces students to decimal numbers, starting with tenths and hundredths. Students learn to read and write decimals, convert between fractions and decimals, and use decimals in length, weight, and money. A strong understanding of decimals is essential for measurements, percentages, and real-world calculations.
2. Understanding tenths
When a whole is divided into 10 equal parts, each part is one-tenth (1/10).
In decimal form: 1/10 = 0.1 (read as 'zero point one' or 'one-tenth')
Tenths on a number line
0 --- 0.1 --- 0.2 --- 0.3 --- 0.4 --- 0.5 --- 0.6 --- 0.7 --- 0.8 --- 0.9 --- 1.0
| Fraction | Decimal | Read as |
|---|---|---|
| 1/10 | 0.1 | One-tenth |
| 2/10 | 0.2 | Two-tenths |
| 3/10 | 0.3 | Three-tenths |
| 4/10 | 0.4 | Four-tenths |
| 5/10 | 0.5 | Five-tenths |
| 6/10 | 0.6 | Six-tenths |
| 7/10 | 0.7 | Seven-tenths |
| 8/10 | 0.8 | Eight-tenths |
| 9/10 | 0.9 | Nine-tenths |
| 10/10 | 1.0 | One (or ten-tenths) |
3. Understanding hundredths
When a whole is divided into 100 equal parts, each part is one-hundredth (1/100).
In decimal form: 1/100 = 0.01 (read as 'zero point zero one' or 'one-hundredth')
The place value of decimals
| Hundreds | Tens | Ones | Tenths | Hundredths |
|---|---|---|---|---|
| 100 | 10 | 1 | 1/10 | 1/100 |
| — | — | 3 | 4 | 5 |
3.45 = 3 ones + 4 tenths + 5 hundredths = 3 + 4/10 + 5/100
Converting fractions to decimals
| Fraction | Decimal | Explanation |
|---|---|---|
| 3/10 | 0.3 | 3 tenths |
| 7/10 | 0.7 | 7 tenths |
| 23/100 | 0.23 | 23 hundredths |
| 8/100 | 0.08 | 8 hundredths (write as 0.08) |
| 1 3/10 | 1.3 | 1 whole + 3 tenths |
| 2 45/100 | 2.45 | 2 wholes + 45 hundredths |
Converting decimals to fractions
| Decimal | Fraction | Simplified |
|---|---|---|
| 0.7 | 7/10 | 7/10 |
| 0.35 | 35/100 | 7/20 |
| 0.08 | 8/100 | 2/25 |
| 1.5 | 1 5/10 | 1 1/2 |
| 2.75 | 2 75/100 | 2 3/4 |
4. Length in decimals
We use decimals to measure length when the measurement is not a whole number.
1 metre = 100 centimetres 1 centimetre = 1/100 metre = 0.01 metre
Conversions
| Length | In metres | In decimal form |
|---|---|---|
| 1 m 25 cm | 1 + 25/100 m | 1.25 m |
| 3 m 8 cm | 3 + 8/100 m | 3.08 m |
| 75 cm | 75/100 m | 0.75 m |
| 2 m 50 cm | 2 + 50/100 m | 2.50 m |
| 10 cm | 10/100 m | 0.10 m |
Word problems with length
Problem 1: A table is 1.35 m long. How long is it in metres and centimetres? Answer: 1.35 m = 1 m + 0.35 m = 1 m + 35 cm = 1 m 35 cm.
Problem 2: A ribbon is 2.08 m long. How many centimetres is that? Answer: 2.08 m = 2 m + 0.08 m = 200 cm + 8 cm = 208 cm.
5. Decimals in money
Rupees and paise use decimals.
1 rupee = 100 paise 1 paisa = 1/100 rupee = Re 0.01
| Amount | In rupees (decimal) |
|---|---|
| 75 paise | Rs 0.75 |
| 5 rupees 50 paise | Rs 5.50 |
| 12 rupees 5 paise | Rs 12.05 |
| 200 paise | Rs 2.00 |
| 1 rupee 1 paisa | Rs 1.01 |
6. Decimals in weight
1 kilogram = 1000 grams 1 gram = 1/1000 kg = 0.001 kg
For Class 5, we focus on tenths and hundredths of a kilogram.
| Weight | In kilograms (decimal) |
|---|---|
| 500 g | 0.50 kg |
| 250 g | 0.25 kg |
| 1 kg 200 g | 1.20 kg |
| 3 kg 50 g | 3.05 kg |
7. Comparing decimals
To compare decimals:
- Write the numbers one below the other, lining up the decimal points.
- Fill any empty places with zeros.
- Compare digits from left to right.
Example: Which is larger: 0.35 or 0.4?
0.35 0.40 (write 0.4 as 0.40)
Compare: 3 tenths vs 4 tenths. 0.4 is larger.
Example: Arrange in ascending order: 2.5, 2.05, 2.55, 2.45.
2.05 < 2.45 < 2.5 < 2.55
8. Activity corner
Activity 1: Measure the height of 5 family members in centimetres. Convert each to metres using decimals. Arrange from shortest to tallest.
Activity 2: Collect 10 bills or receipts from home. Write each amount in words (e.g., Rs 45.75 = forty-five rupees and seventy-five paise).
Activity 3: Draw a number line from 0 to 1. Mark 0.1, 0.25, 0.33, 0.5, 0.67, 0.75, 0.9. Label each with both the fraction and the decimal.
9. Common mistakes
- Mistake: Writing 0.5 as 0.50 but thinking they are different Fix: 0.5 and 0.50 are equal. Adding trailing zeros does not change the value.
- Mistake: Writing 0.05 when they mean 0.5 Fix: 0.5 = 5/10 (five-tenths). 0.05 = 5/100 (five-hundredths). They are very different.
- Mistake: Forgetting to write the zero before the decimal point (writing .75 instead of 0.75) Fix: Always write the zero before the decimal point for numbers less than 1.
10. Key facts
- 1/10 = 0.1 (one-tenth)
- 1/100 = 0.01 (one-hundredth)
- 1 m = 100 cm, so 1 cm = 0.01 m
- Re 1 = 100 paise, so 1 paisa = Re 0.01
- To compare decimals, line up the decimal point and compare digits left to right.
- Adding a zero at the end of a decimal does not change its value.
- Always write the zero before the decimal for numbers less than 1.
11. Self-test
- Write 7/10 as a decimal.
- Write 0.35 as a fraction.
- Which is larger: 0.6 or 0.58?
- Convert 3 m 45 cm to metres using decimals.
- Write Rs 75.80 in words.
12. Answer key
-
Write 7/10 as a decimal. Answer: 0.7 (seven-tenths).
-
Write 0.35 as a fraction. Answer: 35/100 = 7/20 (simplified).
-
Which is larger: 0.6 or 0.58? Answer: 0.6 is larger. Write as 0.60 and 0.58. Compare tenths: 6 tenths > 5 tenths.
-
Convert 3 m 45 cm to metres using decimals. Answer: 3 m 45 cm = 3 + 45/100 = 3.45 m.
-
Write Rs 75.80 in words. Answer: Seventy-five rupees and eighty paise.
13. Quick revision
- Tenths = 1/10 = 0.1. Hundredths = 1/100 = 0.01.
- To convert cm to m, divide by 100.
- To convert paise to rupees, divide by 100.
- Compare decimals by aligning decimal points.
- Practise with money, length, and weight examples.
- Always simplify fractions when converting from decimals.
