Math worksheet for Class VI covering decimal conversions, fractions, and real-life word problems.

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

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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

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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

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Q3. Write 0.12 as fractions in lowest terms

Write 0.12 as a fraction:
$$
0.12 = \frac{12}{100}
$$

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

✔ Answer: $ \frac{3}{25} $

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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

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Q5. Which of the following is smaller?

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

Compare decimals:

- 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

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Q6. Write 78.009 in words as ________ and ________

Break it down:
- Whole number part: 78 → "Seventy-eight"
- Decimal part: 0.009 → "Nine thousandths"

So, we write:
Seventy-eight and nine thousandths

✔ Answer: Seventy-eight and nine thousandths

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

We have:
$$
\frac{5}{100} = 0.05
$$
So,
$$
137 + 0.05 = 137.05
$$

✔ Answer: 137.05

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Q8. Myra went to the market; she bought a packet of biscuits for Rs. 34.50, a packet of sweets for Rs. 98.56 and a chocolate for Rs. 28.75. Find the total money spent by her.

Add all amounts:
$$
34.50 + 98.56 + 28.75
$$

Step-by-step addition:
- 34.50 + 98.56 = 133.06
- 133.06 + 28.75 = 161.81

✔ Answer: Rs. 161.81

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Q9. Subtract 2.051 km from 5.20 km

Align decimals:
$$
5.200 - 2.051 = ?
$$

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

✔ Answer: 3.149 km

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Q10. Add 55.78 + 362.098 + 59.3

First, align decimals:

$$
\begin{array}{r}
55.780 \\
+ 362.098 \\
+ 59.300 \\
\hline
\end{array}
$$

Now add:
- 55.780 + 362.098 = 417.878
- 417.878 + 59.300 = 477.178

✔ Answer: 477.178

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✔ Final Answers Summary:

| Q# | 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 |

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