GSEB Class 6 Maths Solutions Chapter 8 Decimals InText Questions

Try These (Page 165)

 

Question 1. Does canyon now write the following as decimals?

Answer:
(i) We have, 5 hundreds + 3 tens + 8 ones + 1 tenth
\( = 5 \times 100 + 3 \times 10 + 8 \times 1 + 1 \times \frac{1}{10} \)
\( = 500 + 30 + 8 + \frac{1}{10} \)
\( = 538 + \frac{1}{10} = 538.1 \)
(ii) We have, 2 hundreds + 7 tens + 3 ones + 4 tenths
\( = 2 \times 100 + 7 \times 10 + 3 \times 1 + 4 \times \frac{1}{10} \)
\( = 200 + 70 + 3 + \frac{4}{10} \)
\( = 273 + \frac{4}{10} = 273.4 \)
(iii) We have, 3 hundreds + 5 tens + 4 ones + 6 tenths
\( = 3 \times 100 + 5 \times 10 + 4 \times 1 + 6 \times \frac{1}{10} \)
\( = 300 + 50 + 4 + \frac{6}{10} \)
\( = 354 + \frac{6}{10} = 354.6 \)
In simple words: To change these numbers into decimals, first, write down the value of each digit according to its place (hundreds, tens, ones). Then, show the tenths as a fraction and add them all together to get the final decimal number.

Exam Tip: Remember that "tenths" means dividing by 10. When converting numbers with different place values, make sure to add them carefully to avoid errors.

 

Question 2. Write the lengths of Ravi's and Raju's pencils in 'cm' using decimals. When Ravi and Raju measured the lengths of their pencils. Ravi's pencil was 7 cm and 5 mm long and Raju's pencil was 8 cm 3 mm long.
Answer: We know that:
\( 10 \text{ mm} = 1 \text{ cm} \)
Therefore, \( 1 \text{ mm} = \frac{1}{10} \text{ cm} \)
For Ravi's pencil:
\( 5 \text{ mm} = 5 \times \frac{1}{10} \text{ cm} = \frac{5}{10} \text{ cm} \)
Now, \( 7 \text{ cm } 5 \text{ mm} = 7 \text{ cm} + \frac{5}{10} \text{ cm} \)
\( = 7.5 \text{ cm} \)
Thus, the length of Ravi's pencil is \( 7.5 \text{ cm} \).
For Raju's pencil:
\( 3 \text{ mm} = 3 \times \frac{1}{10} \text{ cm} = \frac{3}{10} \text{ cm} \)
Now, \( 8 \text{ cm } 3 \text{ mm} = 8 \text{ cm} + \frac{3}{10} \text{ cm} \)
\( = 8.3 \text{ cm} \)
Thus, the length of Raju's pencil is \( 8.3 \text{ cm} \).
In simple words: Since 10 millimeters make 1 centimeter, you can change millimeters into centimeters by dividing by 10. Then, just add the centimeter parts together to get the total length in decimal form.

Exam Tip: It is crucial to remember the conversion factor between millimeters and centimeters (10 mm = 1 cm) to perform these calculations accurately.

 

Question 3. Make three more examples similar to the one given in question 1 and solve them.
Answer: Here are three examples similar to Question 1, along with their solutions:
**Example 1:**
Hundreds: 4, Tens: 2, Ones: 6, Tenths: 8
\( 4 \text{ hundreds} + 2 \text{ tens} + 6 \text{ ones} + 8 \text{ tenths} \)
\( = 4 \times 100 + 2 \times 10 + 6 \times 1 + 8 \times \frac{1}{10} \)
\( = 400 + 20 + 6 + \frac{8}{10} \)
\( = 426 + 0.8 = 426.8 \)
**Example 2:**
Hundreds: 0, Tens: 9, Ones: 1, Tenths: 5
\( 0 \text{ hundreds} + 9 \text{ tens} + 1 \text{ one} + 5 \text{ tenths} \)
\( = 0 \times 100 + 9 \times 10 + 1 \times 1 + 5 \times \frac{1}{10} \)
\( = 0 + 90 + 1 + \frac{5}{10} \)
\( = 91 + 0.5 = 91.5 \)
**Example 3:**
Hundreds: 1, Tens: 0, Ones: 7, Tenths: 2
\( 1 \text{ hundred} + 0 \text{ tens} + 7 \text{ ones} + 2 \text{ tenths} \)
\( = 1 \times 100 + 0 \times 10 + 7 \times 1 + 2 \times \frac{1}{10} \)
\( = 100 + 0 + 7 + \frac{2}{10} \)
\( = 107 + 0.2 = 107.2 \)
In simple words: You just pick different numbers for hundreds, tens, ones, and tenths. Then you add them up the same way as in the first question, making sure to convert the tenths part to a decimal correctly.

Exam Tip: When creating examples, vary the digits to practice different combinations of place values. Always double-check your arithmetic, especially when combining whole numbers with decimal parts.

Try These (Page 167)

 

Question 1. Write \( \frac{3}{2} \), \( \frac{4}{5} \), \( \frac{8}{5} \) in decimal notation.
Answer:
(i) For \( \frac{3}{2} \):
We have, \( \frac{3}{2} = \frac{3 \times 5}{2 \times 5} = \frac{15}{10} = 1.5 \)
Therefore, \( \frac{3}{2} = 1.5 \)
(ii) For \( \frac{4}{5} \):
We have, \( \frac{4}{5} = \frac{4 \times 2}{5 \times 2} = \frac{8}{10} = 0.8 \)
Thus, \( \frac{4}{5} = 0.8 \)
(iii) For \( \frac{8}{5} \):
We have, \( \frac{8}{5} = \frac{8 \times 2}{5 \times 2} = \frac{16}{10} = 1.6 \)
Thus, \( \frac{8}{5} = 1.6 \)
In simple words: To change a fraction into a decimal, try to make the bottom number (denominator) a 10 or 100. You do this by multiplying both the top and bottom numbers by the same factor. Once the denominator is 10, the top number gives you the decimal directly.

Exam Tip: When converting fractions to decimals, aim to make the denominator a power of 10 (10, 100, 1000, etc.) as it simplifies the conversion process.

Try These (Page 175)

 

Question 1.
(i) Write 2 rupees 5 paise and 2 rupees 50 paise in decimals.
(ii) Write 20 rupees 7 paise and 21 rupees 75 paise in decimals.
Answer:
(i) (a) For 2 rupees 5 paise:
\( 2 \text{ rupees} + 5 \text{ paise} = 2 \text{ rupees} + \frac{5}{100} \text{ rupees} \)
We know \( 100 \text{ paise} = 1 \text{ rupee} \)
\( \therefore 1 \text{ paise} = \frac{1}{100} \text{ rupee} \)
\( = (2 + 0.05) \text{ rupees} = \text{Rs } 2.05 \)
(b) For 2 rupees 50 paise:
\( 2 \text{ rupees} + 50 \text{ paise} = 2 \text{ rupees} + \frac{50}{100} \text{ rupees} \)
\( \therefore 1 \text{ paise} = \frac{1}{100} \text{ rupee} \)
\( = (2 + 0.50) \text{ rupees} = \text{Rs } 2.50 \)
(ii) (a) For 20 rupees 7 paise:
\( 20 \text{ rupees} + 7 \text{ paise} = 20 \text{ rupees} + 7 \times \frac{1}{100} \text{ rupees} \)
\( = 20 \text{ rupees} + 0.07 \text{ rupees} \)
\( = \text{Rs } (20 + 0.07) = \text{Rs } 20.07 \)
(b) For 21 rupees 75 paise:
\( 21 \text{ rupees} + 75 \text{ paise} = 21 \text{ rupees} + 75 \times \frac{1}{100} \text{ rupees} \)
\( = 21 \text{ rupees} + \frac{75}{100} \text{ rupees} \)
\( = \text{Rs } (21 + 0.75) = \text{Rs } 21.75 \)
In simple words: Since there are 100 paise in one rupee, you can convert paise to rupees by dividing the number of paise by 100. Then, add this decimal part to the whole number of rupees to get the total amount.

Exam Tip: Always remember the conversion factor for currency (1 Rupee = 100 Paise). Misplacing the decimal point is a common mistake, so double-check your calculations.

Try These (page 176)

 

Question 1. Can you write 4 mm in 'cm' using decimals?
Answer: Yes, we can.
Since \( 10 \text{ mm} = 1 \text{ cm} \)
Therefore, \( 1 \text{ mm} = \frac{1}{10} \text{ cm} \)
So, \( 4 \text{ mm} = 4 \times \frac{1}{10} \text{ cm} = 0.4 \text{ cm} \)
In simple words: Yes, you can. Since 10 millimeters are equal to 1 centimeter, you just divide the number of millimeters by 10 to get the value in centimeters.

Exam Tip: When converting smaller units to larger units (like mm to cm), you will typically divide. For larger to smaller, you multiply. Make sure to use the correct conversion factor.

 

Question 2. How will you write 7 cm 5 mm in 'cm' using decimals?
Answer: To write 7 cm 5 mm in 'cm' using decimals:
Since \( 10 \text{ mm} = 1 \text{ cm} \)
Now, \( 7 \text{ cm } 5 \text{ mm} = 7 \text{ cm} + 5 \text{ mm} \)
\( = 7 \text{ cm} + 5 \times \frac{1}{10} \text{ cm} \)
\( = (7 + 0.5) \text{ cm} = 7.5 \text{ cm} \)
In simple words: First, change the 5 millimeters into centimeters by dividing by 10. Then, add this decimal centimeter value to the 7 centimeters you already have.

Exam Tip: Always convert the smaller unit part into the larger unit first, then combine it with the already existing larger unit amount. This helps in clear and correct decimal representation.

 

Question 3. Can you now write 52 m as 'km' using decimals? How will you write 340m as 'km' using decimals? how will you write 2008 m in 'km'?
Answer: Yes, we can change the given 'meters' into kilometers.
We know that \( 1000 \text{ m} = 1 \text{ km} \)
\( \therefore 1 \text{ m} = \frac{1}{1000} \text{ km} \)
(a) For 52 m:
\( 52 \text{ m} = 52 \times \frac{1}{1000} \text{ km} = 0.052 \text{ km} \)
(b) For 340 m:
\( 340 \text{ m} = 340 \times \frac{1}{1000} \text{ km} \)
\( = \frac{340}{1000} \text{ km} = 0.340 \text{ km} \)
(c) For 2008 m:
\( 2008 \text{ m} = 2008 \times \frac{1}{1000} \text{ km} \)
\( = \frac{2008}{1000} \text{ km} = \frac{2000 + 8}{1000} \text{ km} = (2 + \frac{8}{1000}) \text{ km} \)
\( = (2 + 0.008) \text{ km} = 2.008 \text{ km} \)
In simple words: To change meters into kilometers, you simply divide the number of meters by 1000 because 1000 meters make up 1 kilometer. Then you write that result as a decimal.

Exam Tip: The key conversion here is 1 km = 1000 m. When dividing by 1000, remember to move the decimal point three places to the left.

Try These (page 176)

 

Question 1. Can you now write 456 g as 'kg' using decimals?
Answer: Yes, we can.
Since \( 1000 \text{ g} = 1 \text{ kg} \)
\( \therefore 1 \text{ g} = \frac{1}{1000} \text{ kg} \)
Therefore, \( 456 \text{ g} = 456 \times \frac{1}{1000} \text{ kg} \)
\( = \frac{456}{1000} \text{ kg} = 0.456 \text{ kg} \)
In simple words: To convert grams to kilograms, you need to divide the number of grams by 1000, since 1000 grams equal one kilogram. The result will be in decimal form.

Exam Tip: Metric conversions are based on powers of 10. For mass, 1000 grams = 1 kilogram. Practice moving the decimal point for quick conversions.

 

Question 2. How will you write 2 kg 9 g in 'kg' using decimals?
Answer: To write 2 kg 9 g in 'kg' using decimals:
\( 2 \text{ kg } 9 \text{ g} = 2 \text{ kg} + 9 \text{ g} \)
\( = 2 \text{ kg} + (9 \times \frac{1}{1000}) \text{ kg} \)
We know \( 1000 \text{ g} = 1 \text{ kg} \)
\( \therefore 1 \text{ g} = \frac{1}{1000} \text{ kg} \)
\( = (2 + 0.009) \text{ kg} = 2.009 \text{ kg} \)
In simple words: First, change the 9 grams into kilograms by dividing it by 1000. Then, add this decimal kilogram amount to the 2 kilograms you already have.

Exam Tip: When combining units, always convert the smaller unit into the larger unit first to express the total value uniformly as a decimal.

Try These (page 178)

 

Question 1. Find
(i) 0.29 + 0.36
(ii) 0.7 + 0.08
(iii) 1.54 + 1.80
(iv) 2.66 + 1.85
Answer:
(i) For 0.29 + 0.36:

\( \therefore \) (9 + 6) hundredths = 15 hundredths = 1 tenths + 5 hundredths
Thus, \( 0.29 + 0.36 = 0.65 \)
(ii) For 0.7 + 0.08:
Thus, \( 0.7 + 0.08 = 0.78 \)
(iii) For 1.54 + 1.80:
Thus, \( 1.54 + 1.80 = 3.34 \)
Note: 5 tenths + 8 tenths = 13 tenths and 13 tenths = 10 tenths + 3 tenths = 1 one + 3 tenths
(iv) For 2.66 + 1.85:
Thus, \( 2.66 + 1.85 = 4.51 \)
In simple words: When adding decimals, make sure to line up the decimal points and digits in the same place value columns (ones under ones, tenths under tenths, etc.). Then, add them just like regular numbers, carrying over if needed.

Exam Tip: Always align the decimal points vertically when adding or subtracting decimals to ensure that digits of the same place value are combined correctly.

Try These (page 180)

 

Question 1. Subtract 1.85 from 5.46
Answer: 1.85 and 5.46 are 'like decimals'.
To subtract, we arrange them vertically:
    5.46
-   1.85
    3.61
Here, 1 is borrowed from 'ones' and given to tenths such that:
4 tenths + 10 tenths = 14 tenths
5 ones - 1 one = 4 ones
In simple words: To subtract decimals, write the bigger number on top, lining up the decimal points. Subtract each column starting from the right, borrowing from the next column if the top digit is smaller than the bottom digit.

Exam Tip: Borrowing in decimal subtraction works exactly like whole number subtraction, but always remember to borrow from the next higher place value column after the decimal point.

 

Question 2. Subtract 5.25 from 8.28.
Answer: 5.25 and 8.28 are 'like decimals'.
To subtract, we arrange them vertically:
    8.28
-   5.25
    3.03
In simple words: Line up the decimal points of both numbers. Then, subtract the bottom number from the top number column by column, moving from right to left.

Exam Tip: When the digits in each column allow for direct subtraction without borrowing, the process becomes simpler. Always check your work with addition.

 

Question 3. Subtract 0.95 from 2.29.
Answer: 0.95 and 2.29 are 'like decimals'.
To subtract, we arrange them vertically:
    2.29
-   0.95
    1.34
In simple words: Place the larger number (2.29) above the smaller number (0.95), ensuring their decimal points are lined up. Perform the subtraction from right to left, borrowing from the next column if necessary, just like with whole numbers.

Exam Tip: Pay close attention to borrowing across the decimal point. When borrowing from the 'ones' place to the 'tenths' place, you are essentially borrowing a '1' which becomes '10 tenths'.

 

Question 4. Subtract 2.25 from 5.68
Answer: 2.25 and 5.68 are 'like decimals'.
To subtract, we arrange them vertically:
    5.68
-   2.25
    3.43
In simple words: Write the numbers one under the other, aligning the decimal points. Then, subtract the digits in each column, starting from the rightmost digit, without needing to borrow in this particular problem.

Exam Tip: Always double-check that you are subtracting the correct numbers from each other. In "Subtract A from B", B is the number you start with, and A is the amount being taken away.