CBSE Class 7 Mathematics Decimals Assignment Set 07

VII - Mathematics Assignment No 1 - Fractions and Decimals

Question 1. Arrange the digits of the decimal 846.125 in the place value chart. Hence write the place value of each digit. Also write the above number in the expanded form.
Answer: Place Value Chart:
Hundreds (100) = 8
Tens (10) = 4
Ones (1) = 6
Tenths (\(\frac{1}{10}\)) = 1
Hundredths (\(\frac{1}{100}\)) = 2
Thousandths (\(\frac{1}{1000}\)) = 5
Place values of each digit:
8 = \(800\) or \(8 \times 100\)
4 = \(40\) or \(4 \times 10\)
6 = \(6\) or \(6 \times 1\)
1 = \(0.1\) or \(1 \times \frac{1}{10}\)
2 = \(0.02\) or \(2 \times \frac{1}{100}\)
5 = \(0.005\) or \(5 \times \frac{1}{1000}\)
Expanded form:
\(800 + 40 + 6 + \frac{1}{10} + \frac{2}{100} + \frac{5}{1000} = 846.125\)
In simple words: Break down the number into its whole number and decimal parts, then write each digit according to its position.

Exam Tip: Always align the decimal point when creating place value charts to avoid mixing up whole numbers and decimals.

Question 2. Add the following decimals: 7.8, 18.67, 49.5 and 109.01
Answer: Align the numbers by their decimal points and pad with zeros to make equal decimal places:
7.80
18.67
49.50
+ 109.01
_________
184.98
In simple words: Line up the decimal points and add column by column from right to left.

Exam Tip: Adding trailing zeros helps prevent alignment errors when adding decimals of different lengths.

Question 3. Simplify: \(35.3 - 17.5 + 18.9 - 21.32\)
Answer: Group the positive and negative terms together using BODMAS:
Positive terms: \(35.3 + 18.9 = 54.2\)
Negative terms: \(17.5 + 21.32 = 38.82\)
Now subtract: \(54.20 - 38.82\)
\(= 15.38\)
In simple words: Add all positive numbers first, add all negative numbers together, and then find the difference.

Exam Tip: Be careful with subtraction and borrowing when aligning decimal places.

Question 4. Write in short form: \(7000 + 300 + 5 + \frac{5}{10} + \frac{8}{100} + \frac{7}{1000}\)
Answer: Combine the whole number parts:
\(7000 + 300 + 5 = 7305\)
Combine the fractional parts into decimals:
\(\frac{5}{10} + \frac{8}{100} + \frac{7}{1000} = 0.5 + 0.08 + 0.007 = 0.587\)
Add whole and decimal parts together:
\(7305 + 0.587 = 7305.587\)
In simple words: Add the whole numbers and place the fractional parts after the decimal point based on their denominators.

Exam Tip: Check missing place values (like the tens place here) and put a zero if necessary.

Question 5. Arrange the following decimals in ascending order: 38.01, 28.32, 4.321, 7.021, 48.007
Answer: Compare the whole number parts first:
Whole parts are 4, 7, 28, 38, 48.
Since all whole number parts are distinct, arrange them directly:
\(4.321 < 7.021 < 28.32 < 38.01 < 48.007\)
In simple words: Ascending order means arranging numbers from the smallest to the largest.

Exam Tip: Always compare whole number parts first before looking at decimal digits.

Question 6. Arrange the following decimals in descending order: 77.56, 77.013, 77.19, 77.024, 77.010
Answer: All whole number parts are 77. Compare the decimal places by padding with zeros to 3 decimal places:
77.560, 77.013, 77.190, 77.024, 77.010
Comparing the decimal parts (560, 013, 190, 024, 010):
\(560 > 190 > 024 > 013 > 010\)
Descending order:
\(77.56 > 77.19 > 77.024 > 77.013 > 77.010\)
In simple words: Descending order means arranging numbers from the largest to the smallest.

Exam Tip: Equalize the number of decimal digits by adding trailing zeros to easily compare them.