RBSE Solutions Class 6 Maths Chapter 6 Decimal Numbers Important Questions

Multiple Choice Questions

Question 1. Place value of 1 in number 412 is :
(a) 1
(b) 10
(c) 100
(d) 1000
Answer: (b) 10
In simple words: In the number 412, the digit 1 is in the tens place, so its value is 10. Each place in a number represents a power of ten.

🎯 Exam Tip: Always remember that place value depends on the position of the digit in a number. The digit 1 in 412 stands for 1 group of ten.

Question 2. Place value of 9 in number 137.29 is :
(a) 9
(b) 90
(c) 0.9
(d) 0.09
Answer: (d) 0.09
In simple words: For the number 137.29, the digit 9 is in the hundredths place, which means its value is 9 divided by 100, or 0.09. Digits after the decimal point represent fractions of one.

🎯 Exam Tip: Decimal places are read as tenths, hundredths, thousandths, and so on, moving to the right of the decimal point.

Question 3. Value of 3 tenth will be :
(a) 0.3
(b) 3
(c) 0.03
(d) 30
Answer: (a) 0.3
In simple words: When we say "3 tenth", it means three out of ten equal parts, which is written as \( \frac{3}{10} \) in fraction form, and 0.3 in decimal form. The first place after the decimal point is the tenths place.

🎯 Exam Tip: The word "tenth" indicates the first decimal place, "hundredth" for the second, and "thousandth" for the third.

Question 4. Value of 47 hundredth will be :
Answer: 0.47
In simple words: "47 hundredth" means 47 parts out of 100 total parts. This can be written as the fraction \( \frac{47}{100} \) or as the decimal 0.47, where the last digit is in the hundredths place.

🎯 Exam Tip: Remember that "hundredth" tells you the second place after the decimal point. So, 47 hundredths means 47 goes into the tenths and hundredths places.

Question 5. Value of 9 thousandth will be :
(a) 0.9
(b) 0.09
(c) 0.009
(d) 0.0009
Answer: (c) 0.009
In simple words: "9 thousandth" means nine parts out of one thousand equal parts. As a fraction, it is \( \frac{9}{1000} \), and as a decimal, it is 0.009. We fill the tenths and hundredths places with zeros.

🎯 Exam Tip: For thousandths, there should be three digits after the decimal point. If there are fewer digits in the numerator, add zeros between the decimal point and the number.

Question 6. Value of 3 tens 7 hundredth will be :
(a) 3.7
(b) 30.7<
(c) 3.70
(d) 30.07
Answer: (d) 30.07
In simple words: "3 tens" means \( 3 \times 10 = 30 \). "7 hundredth" means \( \frac{7}{100} = 0.07 \). When you add them, you get \( 30 + 0.07 = 30.07 \). This combines whole numbers with decimal parts.

🎯 Exam Tip: When combining whole numbers and decimals, keep track of the place values carefully. Ensure the decimal points are aligned, and fill in any empty places with zeros if needed.

Question 7. Value of 4 mm in cm will be :
(a) 0.4
(b) 4
(c) 40
(d) 0.04
Answer: (a) 0.4
In simple words: There are 10 millimeters (mm) in 1 centimeter (cm). So, to convert millimeters to centimeters, you divide the number of millimeters by 10. \( 4 \text{ mm} \div 10 = 0.4 \text{ cm} \).

🎯 Exam Tip: Remember the basic conversion: 1 cm = 10 mm. When converting a smaller unit to a larger unit, you divide; when converting a larger unit to a smaller unit, you multiply.

Question 8. Simple form of fraction 0.52 will be :
(a) \( \frac {12}{25} \)
(b) \( \frac {13}{25} \)
(c) \( \frac {14}{25} \)
(d) \( \frac {15}{21} \)
Answer: (b) \( \frac {13}{25} \)
In simple words: To convert a decimal to a fraction, write the decimal as a fraction with a denominator of 100 (since 0.52 is 52 hundredths). Then, simplify the fraction by dividing both the top and bottom numbers by their greatest common factor. Here, \( \frac{52}{100} \) simplifies to \( \frac{13}{25} \) by dividing by 4.

🎯 Exam Tip: To simplify fractions, find the largest number that can divide both the numerator and the denominator evenly, and then divide them by that number.

Very Short Answer Type Questions

Question. Fill in the blanks:
(i) First place from right side of decimal point called ____________
(ii) Number on the left side of decimal point called ____________ number.
(iii) Second place from right side of decimal point called ____________
(iv) Third place from right side of decimal point called ____________
(v) Numbers that come after the decimal point are read by their ____________.
Answer:
(i) tenth
(ii) whole
(iii) hundredth
(iv) thousandth
(v) name.
In simple words: Decimal numbers have parts before and after the decimal point. The part on the left is the whole number, and the parts on the right are fractions like tenths, hundredths, and thousandths. When you read the decimal part, you just say the digits and then the place value of the last digit.

🎯 Exam Tip: Understanding the names of decimal places (tenths, hundredths, thousandths) is key to correctly reading and writing decimal numbers. Practice with examples like 0.1, 0.01, 0.001.

Question 1. Write the place value of each digit in number 127.914.
Answer: To find the place value of each digit in the number 127.914, we look at its position:
Place value of 1 = \( 1 \times 100 = 100 \)
Place value of 2 = \( 2 \times 10 = 20 \)
Place value of 7 = \( 7 \times 1 = 7 \)
Place value of 9 = \( 9 \times \frac {1}{10} = 0.9 \)
Place value of 1 = \( 1 \times \frac {1}{100} = 0.01 \)
Place value of 4 = \( 4 \times \frac {1}{1000} = 0.004 \)
Each digit's position determines its contribution to the overall value of the number, whether it's a whole number or a fractional part.
In simple words: Each number's spot in 127.914 tells us its value. For example, the '1' before the decimal means 100, but the '1' after the decimal means one-hundredth.

🎯 Exam Tip: Clearly separate the whole number part (left of decimal) and the decimal part (right of decimal) when identifying place values. The decimal point acts as a separator.

Question 2. How we read 370.156?
Answer: The number 370.156 is read as "Three hundred seventy point one five six." When reading decimals, we say "point" for the decimal separator, and then read the digits after the decimal point individually. For example, 0.156 is read "point one five six", not "point one hundred fifty-six".
In simple words: We read the whole number part (370) normally. Then we say "point" for the dot, and read the digits after it (1, 5, 6) one by one.

🎯 Exam Tip: Always read the digits after the decimal point separately, never as a complete number. This is a common mistake students make.

Question 4. Represent numbers 0.4, 1.7 and 2.9 on number line.
Answer: To represent decimal numbers on a number line, we first identify the whole numbers between which the decimal lies. Then, we divide that segment into 10 equal parts to mark the tenths. For example, 0.4 is found by dividing the segment from 0 to 1 into 10 parts and counting 4 divisions. Similarly, 1.7 is 7 divisions after 1, and 2.9 is 9 divisions after 2.

In simple words: Draw a straight line and mark whole numbers (0, 1, 2, 3). For each gap between whole numbers, divide it into 10 smaller parts. Then, count the small parts to find your decimal numbers like 0.4, 1.7, and 2.9.

🎯 Exam Tip: When drawing a number line, ensure the spacing between whole numbers and their subdivisions is uniform for accuracy.

Short/Long Answers Type Questions

Question 1. Represent the following in decimal form :
(i) \( 4 + \frac { 7 }{ 10 } \)
(ii) \( 300 + 30 + \frac { 3 }{ 1000 } \)
(iii) \( 90 + \frac { 4 }{ 10 } + \frac { 5 }{ 100 } \)
(iv) \( 700 + 2 + \frac { 5 }{ 100 } \)
Answer: To represent each expression in decimal form, we convert the fractions to their decimal equivalents and then add them to the whole numbers:
(i) \( 4 + \frac { 7 }{ 10 } = 4 + 0.7 = 4.7 \)
(ii) \( 300 + 30 + \frac { 3 }{ 1000 } = 330 + 0.003 = 330.003 \)
(iii) \( 90 + \frac { 4 }{ 10 } + \frac { 5 }{ 100 } = 90 + 0.4 + 0.05 = 90.45 \)
(iv) \( 700 + 2 + \frac { 5 }{ 100 } = 702 + 0.05 = 702.05 \)
This process shows how to combine whole number parts and fractional decimal parts to form a complete decimal number.
In simple words: Change any fractions like \( \frac{7}{10} \) into decimals (0.7). Then, add all the whole numbers and decimal parts together. For example, 4 + 0.7 becomes 4.7.

🎯 Exam Tip: Pay close attention to the denominator of each fraction (10, 100, 1000) as it tells you how many decimal places to use for that part.

Question 2. Convert the following decimals into fractions and simplify them:
(i) 2.75
(ii) 0.045
(iii) 0.02
(iv) 0.6
Answer: To convert decimals into fractions, we first write the decimal as a fraction with a power of 10 in the denominator (based on the number of decimal places). Then, we simplify the fraction to its lowest terms:
(i) For 2.75: We can write 2.75 as \( \frac{275}{100} \). Now, simplify the fraction.
\( \frac{275}{100} = \frac{275 \div 25}{100 \div 25} = \frac{11}{4} \)
(ii) For 0.045: We can write 0.045 as \( \frac{45}{1000} \). Now, simplify the fraction.
\( \frac{45}{1000} = \frac{45 \div 5}{1000 \div 5} = \frac{9}{200} \)
(iii) For 0.02: We can write 0.02 as \( \frac{2}{100} \). Now, simplify the fraction.
\( \frac{2}{100} = \frac{2 \div 2}{100 \div 2} = \frac{1}{50} \)
(iv) For 0.6: We can write 0.6 as \( \frac{6}{10} \). Now, simplify the fraction.
\( \frac{6}{10} = \frac{6 \div 2}{10 \div 2} = \frac{3}{5} \)
This process helps in understanding the relationship between decimal numbers and common fractions.
In simple words: To change a decimal to a simple fraction, first write it as a fraction with a bottom number like 10, 100, or 1000. Then, divide both the top and bottom numbers by the largest number that goes into both, until you can't divide them any more.

🎯 Exam Tip: The number of digits after the decimal point tells you the denominator: one digit means /10, two means /100, three means /1000, and so on.

Question 3. Sohan bought 7.423 kg rice and 6.129 kg pulse. How much total kg things Sohan bought?
Answer: To find the total weight of things Sohan bought, we need to add the weight of the rice and the pulse. This is a simple addition problem involving decimals.
Weight of rice = 7.423 kg
Weight of pulse = 6.129 kg
Total things bought = Weight of rice + Weight of pulse
Total things bought = \( 7.423 \text{ kg} + 6.129 \text{ kg} \)
Total things bought = \( 13.552 \text{ kg} \)
Therefore, Sohan bought a total of 13.552 kg of items.
In simple words: Sohan bought rice and pulse. To find out how much he bought in total, we just add the weights of the rice and the pulse together.

🎯 Exam Tip: When adding decimals, always align the decimal points vertically to ensure you are adding digits of the same place value correctly.

Question 4. Sunita has 93.12 l oil. She sold 67.19 l oil from it. How much oil left with her?
Answer: To find out how much oil is left with Sunita, we need to subtract the amount of oil sold from the total amount of oil she had. This is a decimal subtraction problem.
Total oil Sunita has = 93.12 l
Oil sold = 67.19 l
Remaining oil = Total oil - Oil sold
Remaining oil = \( 93.12 \text{ l} - 67.19 \text{ l} \)
Remaining oil = \( 25.93 \text{ l} \)
So, Sunita has 25.93 l of oil left with her.
In simple words: Sunita had some oil, and she sold a part of it. To know how much oil is still left, we take away the amount she sold from the amount she started with.

🎯 Exam Tip: For subtraction of decimals, similar to addition, line up the decimal points to avoid errors in place value calculations.