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

Here is the complete solution to the maths worksheet, with step-by-step explanations for each question.

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Q1. Express as meters using decimals:

a) 40 cm

- We know that 1 meter (m) = 100 centimeters (cm).
- So, to convert cm to m, divide by 100.
- 40 cm = 40 ÷ 100 = 0.4 m

b) 200 mm

- We know that 1 meter (m) = 1000 millimeters (mm).
- So, to convert mm to m, divide by 1000.
- 200 mm = 200 ÷ 1000 = 0.2 m

✔ Answers:
a) 0.4 m
b) 0.2 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 distance – Distance walked
- Distance by bus = 5.350 – 1.70 = 3.650 km

✔ Answer: 3.650 km

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Q3. Write 0.12 as fractions in lowest terms

- 0.12 = 12/100 (since there are two decimal places)
- Simplify 12/100 by dividing numerator and denominator by their greatest common divisor, which is 4:
- 12 ÷ 4 = 3
- 100 ÷ 4 = 25
- So, 0.12 = 3/25

✔ Answer: 3/25

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Q4. Write ‘Two tens and nine tenths’ in decimal form.

- Two tens = 2 × 10 = 20
- Nine tenths = 9/10 = 0.9
- Add them together: 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 the numbers by looking at the place value:
- 0.7 = 7/10
- 0.07 = 7/100
- 0.007 = 7/1000
- 0.0007 = 7/10000
- As the denominator increases, the value decreases.
- So, the smallest is 0.0007

✔ Answer: (d) 0.0007

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Q6. Write 78.009 in words as _______ and _______

- The number 78.009 has:
- Whole part: 78 → “Seventy-eight”
- Decimal part: 009 → “Nine thousandths” (since it’s in the thousandths place)
- So, we write: Seventy-eight and nine thousandths

✔ Answer: Seventy-eight and nine thousandths

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Q7. Write 137 + 5/100 in the decimal form

- 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
+ 28.75
--------
161.81
```

✔ Answer: Rs. 161.81

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Q9. Subtract 2.051 km from 5.20 km

- Align the decimals and subtract:

```
5.200 (we can write 5.20 as 5.200 for easier subtraction)
- 2.051
--------
3.149
```

✔ Answer: 3.149 km

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Q10. Add 55.78 + 362.098 + 59.3

- Align the decimals and add:

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

✔ Answer: 477.178

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✔ Final Answers Summary:

Q1:
a) 0.4 m
b) 0.2 m

Q2: 3.650 km

Q3: 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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