Maths worksheet for Class VI from Lancer's Convent, covering decimal conversions, fractions, and arithmetic operations.

Let's solve each question from the Maths Worksheet step by step and provide clear explanations.

---

Q1. Express as meters using decimals:

We know:
- 1 meter = 100 cm
- 1 meter = 1000 mm

#### a) 40 cm
Convert cm to meters:
$$
40 \text{ cm} = \frac{40}{100} = 0.40 \text{ m}
$$

✔ Answer: 0.40 m

#### b) 200 mm
Convert mm to meters:
$$
200 \text{ mm} = \frac{200}{1000} = 0.20 \text{ m}
$$

✔ Answer: 0.20 m

---

Q2. Monica’s school is at a distance of 5.350 km from her house. She travels 1.70 km on foot and the rest by bus. How much distance does she travel by bus?

Total distance = 5.350 km
Distance walked = 1.70 km

Distance by bus = Total – Walked
$$
= 5.350 - 1.70 = 3.650 \text{ km}
$$

✔ Answer: 3.650 km

---

Q3. Write 0.12 as fractions in lowest terms

$$
0.12 = \frac{12}{100}
$$

Simplify:
$$
\frac{12}{100} = \frac{3}{25} \quad (\text{Divide numerator and denominator by 4})
$$

✔ Answer: $ \frac{3}{25} $

---

Q4. Write 'Two tens and nine tenths' in decimal form

- Two tens = 2 × 10 = 20
- Nine tenths = $ \frac{9}{10} = 0.9 $

So, total = 20 + 0.9 = 20.9

✔ Answer: 20.9

---

Q5. Which of the following is smaller?

(a) 0.7
(b) 0.07
(c) 0.007
(d) 0.0007

Compare:
- 0.7 = 0.7000
- 0.07 = 0.0700
- 0.007 = 0.0070
- 0.0007 = 0.0007

Clearly, 0.0007 is the smallest.

✔ Answer: (d) 0.0007

---

Q6. Write 78.009 in words as _______ and ________

Break it down:
- 78 = Seventy-eight
- 0.009 = Nine thousandths

So, write as:
Seventy-eight and nine thousandths

✔ Answer: Seventy-eight and nine thousandths

---

Q7. Write $ 137 + \frac{5}{100} $ in decimal form

$$
\frac{5}{100} = 0.05
$$

So,
$$
137 + 0.05 = 137.05
$$

✔ Answer: 137.05

---

Q8. Myra went to the market; she bought:

- Biscuits: Rs. 34.50
- Sweets: Rs. 98.56
- Chocolate: Rs. 28.75

Total money spent = Sum of all amounts:

$$
34.50 + 98.56 + 28.75
$$

Add step by step:

First:
34.50 + 98.56 = 133.06
Then:
133.06 + 28.75 = 161.81

✔ Answer: Rs. 161.81

---

Q9. Subtract 2.051 km from 5.20 km

Write both with same decimal places:
5.200 km – 2.051 km

Now subtract:
```
5.200
- 2.051
-------
3.149
```

✔ Answer: 3.149 km

---

Q10. Add 55.78 + 362.098 + 59.3

Align decimals:

```
55.780
362.098
+ 59.300
---------
477.178
```

Step-by-step:
- 55.78 + 362.098 = 417.878
- 417.878 + 59.3 = 477.178

✔ Answer: 477.178

---

✔ Final Answers Summary:

| Question | Answer |
|--------|--------|
| Q1a | 0.40 m |
| Q1b | 0.20 m |
| Q2 | 3.650 km |
| Q3 | $ \frac{3}{25} $ |
| Q4 | 20.9 |
| Q5 | (d) 0.0007 |
| Q6 | Seventy-eight and nine thousandths |
| Q7 | 137.05 |
| Q8 | Rs. 161.81 |
| Q9 | 3.149 km |
| Q10 | 477.178 |

Let me know if you'd like this printed or formatted differently!