CBSE Class 6 Maths: Decimals - Exercise 8.1

Understanding Decimals: The Tenths Place

Decimals are like an extension to our number system. Until now, you've mainly worked with whole numbers like 1, 5, 10, 100. But what if you have a part of a whole? For example, if you divide a chocolate bar into 10 equal pieces and eat 3 of them, you've eaten 3 out of 10 pieces. As a fraction, this is 3/10. Decimals give us another way to write this: 0.3.

The word "decimal" comes from "decem," meaning ten. This is a big clue! The first place after the decimal point represents tenths.

Let's break it down:

• Decimal Point (.): This tiny dot separates the whole number part from the fractional (decimal) part.
• Whole Number Part: Everything to the left of the decimal point (e.g., in 5.3, 5 is the whole number part).
• Decimal Part: Everything to the right of the decimal point (e.g., in 5.3, 3 is the decimal part).

Place Value Chart for Tenths:

| Hundreds | Tens | Ones | . | Tenths |
| :------- | :--- | :--- | :- | :----- |
| | | 5 | . | 3 |

Here, the digit 3 is in the tenths place, meaning its value is 3/10. So, 5.3 means "5 whole units and 3 tenths" or 5 + 3/10.

Representing and Writing Decimals (Tenths)

1. From Fractions to Decimals — If you have a fraction with a denominator of 10, converting it to a decimal is straightforward: 1. Look at the numerator: This number will go into the tenths place. 2. Place the decimal point: Write '0' followed by a decimal point, then the numerator. Example: Write 7/10 as a decimal. Step 1: The numerator is 7. Step 2: Write 0.7. This means "seven tenths".
2. From Word Form to Decimals — When you hear numbers described with "and" and "tenths," you can write them as decimals: 1. Identify the whole number part: The number before "and" is the whole number. 2. Identify the decimal part: The number before "tenths" is the digit in the tenths place. 3. Combine them: Write the whole number, then a decimal point, then the tenths digit. Example: Write "Two and five tenths" as a decimal. Step 1: The whole number part is Two (which is 2). Step 2: The tenths part is five tenths (which is 5 in the tenths place). * Step 3: Combine them as 2.5.
3. From Pictures (Shaded Portions) to Decimals — Sometimes, you'll see a picture divided into 10 equal parts, with some shaded: 1. Count the total equal parts: This should be 10 for tenths. 2. Count the shaded parts: This will be your numerator. 3. Form the fraction: Shaded parts / Total parts. 4. Convert to decimal: Follow the steps for converting fractions to decimals. Example: A square is divided into 10 equal parts, and 4 parts are shaded. Write this as a decimal. Step 1: Total parts = 10. Step 2: Shaded parts = 4. Step 3: Fraction = 4/10. Step 4: Decimal = 0.4.

Smart Tips for Mastering Decimals Ex 8.1

When working with decimals up to the tenths place, keep these pointers in mind:

1. Decimal Point is Key: Always remember to place the decimal point correctly. 3 is very different from 0.3! 3 means three whole units, while 0.3 means three-tenths of a unit.
2. Place Value Chart: If you're ever unsure, quickly draw a small place value chart (like the one above: Ones . Tenths) to help you position the digits correctly.
3. "Tenths" means one digit after the point: For tenths, there will always be exactly one digit to the right of the decimal point. If a question asks for "five tenths," it's 0.5, not 0.05 (which would be five hundredths).
4. Zero before the decimal: If there's no whole number part, always write a 0 before the decimal point (e.g., 0.7 instead of just .7). This makes your number clear and prevents confusion.

Practice Questions with Solutions

• Q: Write the following as decimals: (a) 8 tenths (b) 2 tens and 9 tenths A: Step 1: For (a) "8 tenths" means 8 parts out of 10, which is the fraction 8/10. As a decimal, this is 0.8. Step 2: For (b) "2 tens" means 20. "9 tenths" means 0.9. Combine the whole and decimal parts. Final answer: (a) 0.8 (b) 20.9
• Q: Write the following decimals as fractions: (a) 0.4 (b) 3.7 A: Step 1: For (a) 0.4 means "four tenths". This can be written as the fraction 4/10. Step 2: For (b) 3.7 means "three and seven tenths". The whole number part is 3, and the decimal part is 7/10. Combine them as a mixed fraction 3 7/10 or an improper fraction 37/10. Final answer: (a) 4/10 (b) 37/10
• Q: What is the place value of the digit '6' in the number 14.6? A: Step 1: Identify the decimal point in 14.6. The number to its left (14) is the whole number part, and the number to its right (6) is the decimal part. Step 2: The first digit to the right of the decimal point is the tenths place. Step 3: The digit '6' is in the tenths place. Final answer: The place value of '6' is 6 tenths or 6/10.
• Q: Represent the number 1.3 on a number line. A: Step 1: Understand 1.3 means "1 whole unit and 3 tenths". Step 2: Draw a number line. Mark whole numbers like 0, 1, 2. Step 3: To represent 1.3, we need to go past 1. Divide the space between 1 and 2 into 10 equal smaller parts. Step 4: Count 3 of these smaller parts from 1. The third mark after 1 will represent 1.3. Final answer: (A number line sketch with 1.3 marked between 1 and 2, at the 3rd division after 1)

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