GSEB Class 6 Maths Solutions Chapter 8 Decimals Exercise 8.2

Question 1. Complete the table with the help of these boxes and use decimals to write the number:
Answer: In the first figure, 26 small parts out of 100 are shaded. This represents the decimal 0.26.
In the second figure, 100 parts plus 38 parts are shaded. This is equivalent to \( 1 + \frac{38}{100} \), which gives \( 1.38 \). This number \( 1.38 \) is shown by the shaded section.
In the third figure, 100 parts plus 28 parts are shaded. This calculates to \( 1 + \frac{28}{100} \), resulting in \( 1.28 \). This decimal \( 1.28 \) is depicted by the shaded area.
So, the completed table is shown below:

In simple words: Look at the shaded squares in each picture. Count how many out of 100 are shaded for parts after the decimal. If a full box is shaded, that's one whole. Then fill in the table with the correct number of ones, tenths, and hundredths for each example.

Exam Tip: Always clearly count the shaded parts. Remember that 100 shaded parts in a 10x10 grid represent one whole, while individual shaded parts after a whole represent tenths and hundredths.

 

Question 2. Write the numbers given in the following place value table in decimal form.

Answer:
(a) 0 hundreds + 0 tens + 3 ones + 2 tenths + 5 hundredths + 0 thousandths
\( = 0 \times 100 + 0 \times 10 + 3 \times 1 + 2 \times \frac{1}{10} + 5 \times \frac{1}{100} + 0 \times \frac{1}{1000} \)
\( = 0 + 0 + 3 + \frac{2}{10} + \frac{5}{100} + \frac{0}{1000} = 3.250 \) (or \( 3.25 \))
(b) 1 hundred + 0 tens + 2 ones + 6 tenths + 3 hundredths + 0 thousandths
\( = 1 \times 100 + 0 \times 10 + 2 \times 1 + 6 \times \frac{1}{10} + 3 \times \frac{1}{100} + 0 \times \frac{1}{1000} \)
\( = 100 + 0 + 2 + \frac{6}{10} + \frac{3}{100} + \frac{0}{1000} \)
\( = 102 + \frac{6}{10} + \frac{3}{100} + \frac{0}{1000} = 102.630 \)
(c) 0 hundreds + 3 tens + 0 ones + 0 tenths + 2 hundredths + 5 thousandths
\( = 0 \times 100 + 3 \times 10 + 0 \times 1 + 0 \times \frac{1}{10} + 2 \times \frac{1}{100} + 5 \times \frac{1}{1000} \)
\( = 0 + 30 + 0 + \frac{0}{10} + \frac{2}{100} + \frac{5}{1000} = 30.025 \)
(d) 2 hundreds + 1 ten + 1 one + 9 tenths + 0 hundredths + 2 thousandths
\( = 2 \times 100 + 1 \times 10 + 1 \times 1 + 9 \times \frac{1}{10} + 0 \times \frac{1}{100} + 2 \times \frac{1}{1000} \)
\( = 200 + 10 + 1 + \frac{9}{10} + \frac{0}{100} + \frac{2}{1000} \)
\( = 211 + \frac{9}{10} + \frac{0}{100} + \frac{2}{1000} = 211.902 \)
(e) 0 hundreds + 1 ten + 2 ones + 2 tenths + 4 hundredths + 1 thousandth
\( = 0 \times 100 + 1 \times 10 + 2 \times 1 + 2 \times \frac{1}{10} + 4 \times \frac{1}{100} + 1 \times \frac{1}{1000} \)
\( = 0 + 10 + 2 + \frac{2}{10} + \frac{4}{100} + \frac{1}{1000} = 12.241 \)
In simple words: To convert a place value table into a decimal number, multiply each digit by its corresponding place value (hundreds, tens, ones, tenths, hundredths, thousandths) and then add them up. For example, 3 ones and 2 tenths, 5 hundredths makes 3.25.

Exam Tip: Pay close attention to the place value of each digit, especially those after the decimal point. A mistake in identifying the tenths, hundredths, or thousandths place is a common error.

 

Question 3. Write the following decimals in the place value table.
(a) 0.29
(b) 2.08
(c) 19.60
(d) 148.32
(e) 200.812
Answer: First, we expand each decimal by its place value.
(a) \( 0.29 = 0 \times 1 + \frac{2}{10} + \frac{9}{100} \)
(b) \( 2.08 = 2 \times 1 + \frac{0}{10} + \frac{8}{100} \)
(c) \( 19.60 = 1 \times 10 + 9 \times 1 + \frac{6}{10} + \frac{0}{100} \)
(d) \( 148.32 = 1 \times 100 + 4 \times 10 + 8 \times 1 + \frac{3}{10} + \frac{2}{100} \)
(e) \( 200.812 = 2 \times 100 + 0 \times 10 + 0 \times 1 + \frac{8}{10} + \frac{1}{100} + \frac{2}{1000} \)
Now, we can write the given decimals in the place value table as:

In simple words: To put a decimal into a place value table, write each digit under its correct heading, like ones, tens, tenths, or hundredths. For example, in 19.60, 1 goes under tens, 9 under ones, 6 under tenths, and 0 under hundredths.

Exam Tip: Remember to include zeros for any place values that are empty, especially after the decimal point, to maintain correct alignment in the table.

 

Question 4. Write each of the following as decimals.
(a) \( 20+9+\frac{4}{10}+\frac{1}{100} \)
(b) \( 137+\frac{5}{100} \)
(c) \( \frac{7}{10}+\frac{6}{100}+\frac{4}{1000} \)
(d) \( 23+\frac{2}{10}+\frac{6}{1000} \)
(e) \( 700+20+5+\frac{9}{100} \)
Answer:
(a) \( 20+9+\frac{4}{10}+\frac{1}{100} = 29+0.4+0.01 = 29.41 \)
(b) \( 137+\frac{5}{100} = 137 + \frac{0}{10} + \frac{5}{100} = 137.05 \)
(c) \( \frac{7}{10}+\frac{6}{100}+\frac{4}{1000} = 0 + \frac{7}{10} + \frac{6}{100} + \frac{4}{1000} = 0.764 \)
(d) \( 23+\frac{2}{10}+\frac{6}{1000} = 23 + \frac{2}{10} + \frac{0}{100} + \frac{6}{1000} = 23.206 \)
(e) \( 700+20+5+\frac{9}{100} = 725 + \frac{0}{10} + \frac{9}{100} = 725.09 \)
In simple words: To convert a sum of whole numbers and fractions into a decimal, first add the whole numbers together. Then, convert each fraction into its decimal form (e.g., \( \frac{4}{10} \) is 0.4 and \( \frac{1}{100} \) is 0.01). Finally, combine all these values to get the final decimal number.

Exam Tip: Remember to fill in any missing place values with zeros when converting fractions to decimals, such as \( \frac{5}{100} \) being 0.05, not 0.5.

 

Question 5. Write each of the following decimals in words.
(a) 0.03
(b) 1.20
(c) 108.56
(d) 10.07
(e) 0.032
(f) 5.008
Answer:
(a) Zero point zero three is how it's written.
(b) One point two zero is how we say it.
(c) One hundred eight point five six can be expressed.
(d) Ten point zero seven is the verbal form.
(e) Zero point zero three two is how this number is said.
(f) Five point zero zero eight is its written word form.
In simple words: When writing decimals in words, read the whole number part first, then say "point," and then read each digit after the decimal point individually. For example, 0.03 is "zero point zero three."

Exam Tip: Always read each digit after the decimal point separately. Do not read them as a whole number (e.g., 0.56 is "zero point five six," not "zero point fifty-six").

 

Question 6. Between which two numbers in tenths place on the number line does each of the given numbers lies?
(a) 0.06
(b) 0.45
(c) 0.19
(d) 0.66
(e) 0.92
(f) 0.57
Answer:
(a) The number 0.06 is located between 0 and 0.1 on the number line.
(b) The number 0.45 is situated between 0.4 and 0.5.
(c) The number 0.19 falls between 0.1 and 0.2.
(d) The number 0.66 can be found between 0.6 and 0.7.
(e) The number 0.92 is positioned between 0.9 and 1.0.
(f) The number 0.57 exists between 0.5 and 0.6.
In simple words: To find where a decimal lies, look at its tenths digit. The number will be between that tenths digit and the next one. For example, 0.45 is between 0.4 and 0.5.

Exam Tip: To identify the range in tenths, look at the first digit after the decimal point. The number will be between that tenth and the next higher tenth (e.g., 0.19 is between 0.1 and 0.2).

 

Question 7. Write as fractions in lowest terms.
(a) 0.60
(b) 0.05
(c) 0.75
(d) 0.18
(e) 0.25
(f) 0.125
(g) 0.066
Answer:
(a) We have \( 0.60 = \frac{60}{100} \). To simplify, we divide both the numerator and denominator by 20: \( \frac{60 \div 20}{100 \div 20} = \frac{3}{5} \). So, \( 0.60 = \frac{3}{5} \).
(b) We have \( 0.05 = \frac{5}{100} \). To simplify, we divide both the numerator and denominator by 5: \( \frac{5 \div 5}{100 \div 5} = \frac{1}{20} \). So, \( 0.05 = \frac{1}{20} \).
(c) We have \( 0.75 = \frac{75}{100} \). To simplify, we divide both the numerator and denominator by 25: \( \frac{75 \div 25}{100 \div 25} = \frac{3}{4} \). So, \( 0.75 = \frac{3}{4} \).
(d) We have \( 0.18 = \frac{18}{100} \). To simplify, we divide both the numerator and denominator by 2: \( \frac{18 \div 2}{100 \div 2} = \frac{9}{50} \). So, \( 0.18 = \frac{9}{50} \).
(e) We have \( 0.25 = \frac{25}{100} \). To simplify, we divide both the numerator and denominator by 25: \( \frac{25 \div 25}{100 \div 25} = \frac{1}{4} \). So, \( 0.25 = \frac{1}{4} \).
(f) We have \( 0.125 = \frac{125}{1000} \). To simplify, we divide both the numerator and denominator by 125: \( \frac{125 \div 125}{1000 \div 125} = \frac{1}{8} \). So, \( 0.125 = \frac{1}{8} \).
(g) We have \( 0.066 = \frac{66}{1000} \). To simplify, we divide both the numerator and denominator by 2: \( \frac{66 \div 2}{1000 \div 2} = \frac{33}{500} \). So, \( 0.066 = \frac{33}{500} \).
In simple words: To change a decimal into a fraction, first write it as a fraction over 10, 100, or 1000 depending on how many digits are after the decimal point. Then, make sure to simplify this fraction by dividing the top and bottom numbers by their largest common factor until it cannot be reduced any further.

Exam Tip: Always remember to simplify the fraction to its lowest terms. This means finding the greatest common divisor (GCD) of the numerator and denominator and dividing both by it.