CBSE Class 7 Mathematics Decimals Assignment Set 06

Q1. Which is greater \(18.5\) or \(17.04\)?
Answer: Compare the whole number parts of both decimals.
Whole number part of \(18.5\) is \(18\).
Whole number part of \(17.04\) is \(17\).
Since \(18 > 17\), therefore \(18.5 > 17.04\).
In simple words: Look at the number before the decimal point; 18 is greater than 17.

Exam Tip: Always make the number of decimal places equal by adding trailing zeros (e.g., compare \(18.50\) and \(17.04\)) before comparing digit by digit from left to right.

Q2. Which is lesser \(15.005\) or \(15.075\)?
Answer: Both numbers have the same whole number part, which is \(15\).
Compare the tenths place: both have \(0\) in the tenths place.
Compare the hundredths place: \(15.005\) has \(0\) and \(15.075\) has \(7\).
Since \(0 < 7\), therefore \(15.005 < 15.075\).
In simple words: Compare digits from left to right after the decimal point; 0 in the hundredth place is less than 7.

Exam Tip: When whole parts are equal, compare the digits at the tenths, hundredths, and thousandths places successively.

Q3. Convert \(\frac{15}{4}\) into decimal fraction.
Answer: Divide \(15\) by \(4\)
\(15 \div 4 = 3.75\)
Alternatively, convert the denominator to a power of \(10\):
\(\frac{15 \times 25}{4 \times 25} = \frac{375}{100} = 3.75\)
In simple words: Divide the numerator by the denominator to get the decimal value.

Exam Tip: You can multiply the numerator and denominator by a suitable number to make the denominator \(10\), \(100\), or \(1000\) for quick conversion.

Q4. Convert \(8\frac{5}{16}\) into decimal fraction.
Answer: Convert the mixed fraction into an improper fraction:
\(8\frac{5}{16} = \frac{8 \times 16 + 5}{16} = \frac{128 + 5}{16} = \frac{133}{16}\)
Now, divide \(133\) by \(16\):
\(133 \div 16 = 8.3125\)
In simple words: Change the mixed fraction to an improper fraction, then divide top by bottom.

Exam Tip: Long division with decimals requires careful placement of the decimal point and annexing zeros as needed.

Q5. Express \(235\) paisa as rupees in decimals.
Answer: We know that \(100 \text{ paisa} = \text{Rs. } 1\)
\(1 \text{ paisa} = \text{Rs. } \frac{1}{100}\)
\(235 \text{ paisa} = \frac{235}{100} \text{ rupees} = \text{Rs. } 2.35\)
In simple words: Divide the amount in paisa by 100 to convert it into rupees.

Exam Tip: To convert smaller units of currency or length to larger units, divide by the conversion factor (100 for paisa to rupees).

Q6. Express \(1213 \text{ cm}\) as metres in decimals.
Answer: We know that \(100 \text{ cm} = 1 \text{ m}\)
\(1 \text{ cm} = \frac{1}{100} \text{ m}\)
\(1213 \text{ cm} = \frac{1213}{100} \text{ m} = 12.13 \text{ m}\)
In simple words: Divide centimetres by 100 to convert to metres.

Exam Tip: Moving the decimal point two places to the left is equivalent to dividing by 100.

Q7. Convert \(8600 \text{ m}\) into km.
Answer: We know that \(1000 \text{ m} = 1 \text{ km}\)
\(1 \text{ m} = \frac{1}{1000} \text{ km}\)
\(8600 \text{ m} = \frac{8600}{1000} \text{ km} = 8.6 \text{ km}\)
In simple words: Divide metres by 1000 to convert into kilometres.

Exam Tip: Cancel out common trailing zeros in the numerator and denominator to simplify before writing the decimal.

Q8. Convert \(7 \text{ dm } 9 \text{ cm}\) into m.
Answer: Recall metric units relation with metre:
\(1 \text{ decimetre (dm)} = \frac{1}{10} \text{ m} = 0.1 \text{ m}\)
\(1 \text{ centimetre (cm)} = \frac{1}{100} \text{ m} = 0.01 \text{ m}\)
Therefore,
\(7 \text{ dm} = 7 \times 0.1 \text{ m} = 0.7 \text{ m}\)
\(9 \text{ cm} = 9 \times 0.01 \text{ m} = 0.09 \text{ m}\)
Total length in metres = \(0.7 \text{ m} + 0.09 \text{ m} = 0.79 \text{ m}\)
In simple words: Convert decimetres and centimetres into metres individually, then add them together.

Exam Tip: Always align place values properly when adding decimal measurements.

Q9. Convert \(8535 \text{ mg}\) into g.
Answer: We know that \(1000 \text{ mg} = 1 \text{ g}\)
\(1 \text{ mg} = \frac{1}{1000} \text{ g}\)
\(8535 \text{ mg} = \frac{8535}{1000} \text{ g} = 8.535 \text{ g}\)
In simple words: Divide milligrams by 1000 to convert to grams.

Exam Tip: Shifting the decimal point three places to the left gives the value in grams.

Q10. Convert \(5 \text{ km } 6 \text{ hm}\) into m.
Answer: Recall metric units relation with metre:
\(1 \text{ kilometre (km)} = 1000 \text{ m}\)
\(1 \text{ hectometre (hm)} = 100 \text{ m}\)
Therefore,
\(5 \text{ km} = 5 \times 1000 \text{ m} = 5000 \text{ m}\)
\(6 \text{ hm} = 6 \times 100 \text{ m} = 600 \text{ m}\)
Total distance in metres = \(5000 \text{ m} + 600 \text{ m} = 5600 \text{ m}\)
In simple words: Convert kilometres and hectometres into metres, then add the results.

Exam Tip: Memorize the metric prefix sequence (kilo, hecto, deca, base, deci, centi, milli) to easily handle conversions.