Class 6 Chapter 7 - Decimals (Ex 7.1) RD Sharma Solutions Free PDF
FAQs on RD Sharma Class 6 Solutions Chapter 7 - Decimals (Ex 7.1) Exercise 7.1
1. What types of problems are covered in the RD Sharma Class 6 Solutions for Chapter 7, Exercise 7.1?
Exercise 7.1 introduces the foundational concepts of decimals. The solutions provide step-by-step methods for the following types of questions:
- Writing given decimals in a place value table to understand the position of each digit.
- Expressing decimal numbers in their word form, for example, writing 1.2 as 'One and two tenths'.
- Converting basic fractions with denominators of 10, 100, or 1000 into their decimal equivalents.
- Translating numbers written in words back into their decimal notation.
2. What is the correct method to convert a mixed fraction like 5 4/10 into a decimal as per the solutions for Ex 7.1?
To convert a mixed fraction like 5 4/10 into a decimal, you should follow these two main steps:
1. The whole number part, which is 5, is placed to the left of the decimal point.
2. The fractional part, 4/10 (four-tenths), is placed to the right of the decimal point. The first position after the decimal is the tenths place.
Combining these gives you the final answer: 5.4.
3. How do you correctly represent a fraction like 9/100 as a decimal using the place value method?
To represent 9/100 as a decimal, you must consider the place values carefully. The fraction means 'nine-hundredths'. In the decimal system, the second digit after the decimal point is the hundredths place. Since there are no tenths, you must use a zero as a placeholder in the tenths place. Therefore, the correct decimal representation is 0.09.
4. Why is a placeholder zero crucial when writing a decimal like 'seven hundredths' (0.07)?
A placeholder zero is crucial because it ensures each digit is in its correct place, giving the number its proper value. In 'seven hundredths' (0.07), the zero in the tenths place signifies that there are zero tenths. Without this zero, writing '.7' or '0.7' would mean 'seven tenths', which is a completely different and much larger value. The placeholder correctly pushes the '7' into the hundredths position, ensuring accuracy.
5. What is the fundamental difference between the place values of digits before and after the decimal point?
The fundamental difference is that digits to the left of the decimal point represent whole numbers (like Ones, Tens, Hundreds), and their value increases by a power of 10 as you move further left. In contrast, digits to the right of the decimal point represent fractional parts of a whole (like Tenths, Hundredths, Thousandths), and their value decreases by a power of 10 as you move further right.
6. How does understanding place value from Exercise 7.1 help in comparing decimals like 0.4 and 0.04?
Mastering place value in Exercise 7.1 is key to comparing decimals. By understanding this concept, you know that 0.4 means 'four tenths' (4/10) and 0.04 means 'four hundredths' (4/100). Since a tenth is a larger part of a whole than a hundredth, you can easily conclude that 0.4 is greater than 0.04. This foundational knowledge prevents the common mistake of thinking 0.04 is larger just because it has more digits.
7. In Exercise 7.1, why do the initial conversion problems focus on fractions with denominators of 10, 100, or 1000?
These problems start with denominators of 10, 100, or 1000 because our entire decimal system is a base-10 system. The place values to the right of the decimal point are named Tenths (1/10), Hundredths (1/100), and Thousandths (1/1000). Using these specific fractions makes the conversion direct and intuitive, helping students build a solid understanding of the direct relationship between fractions and decimal notation before tackling more complex conversions.
