Decimals Class 6 Maths Notes

Key Points about Decimals

• Decimals are numbers used to represent parts of a whole, extending the place value system to include values less than one.
• A decimal point separates the whole number part (left of the point) from the fractional part (right of the point).
• The place values to the right of the decimal point are tenths (1/10), hundredths (1/100), thousandths (1/1000), and so on.
• To add or subtract decimals, always align the decimal points vertically, ensuring corresponding place values are stacked.
• Comparing decimals involves comparing the whole number parts first, then moving right from the decimal point, comparing digits at the tenths, hundredths, and subsequent places.
• Adding trailing zeros to the right of the last digit in a decimal does not change its value (e.g., 0.5 = 0.50 = 0.500). These are called equivalent decimals.
• To convert a fraction to a decimal, divide the numerator by the denominator.
• To convert a decimal to a fraction, write the decimal as a fraction with a power of 10 in the denominator (e.g., 0.7 = 7/10, 0.25 = 25/100) and then simplify.

Important Terms

Decimal

A number that uses a decimal point to represent a part of a whole number, typically written with a whole number part and a fractional part.

Decimal Point

A dot or period that separates the whole number part from the fractional part in a decimal number.

Tenths

The first place value to the right of the decimal point, representing fractions with a denominator of 10 (e.g., 0.1 means 1/10).

Hundredths

The second place value to the right of the decimal point, representing fractions with a denominator of 100 (e.g., 0.01 means 1/100).

Like Decimals

Decimals that have the same number of decimal places (e.g., 2.35 and 4.81 are like decimals).

Unlike Decimals

Decimals that have a different number of decimal places (e.g., 5.2 and 1.75 are unlike decimals).

Equivalent Decimals

Decimals that look different but have the same value (e.g., 0.4 and 0.40).

Understanding Decimals: Place Value

Just like whole numbers have a place value system (ones, tens, hundreds, thousands, etc.), decimals extend this system to represent values smaller than one. The decimal point acts as a separator, clearly distinguishing the whole number part on its left from the fractional part on its right. Each digit in a decimal number holds a specific place value, which determines its contribution to the overall value of the number.

To the left of the decimal point, the place values are familiar: ones, tens, hundreds, and so on. For example, in the number 123.456, '3' is in the ones place, '2' in the tens place, and '1' in the hundreds place.

To the right of the decimal point, the place values represent fractions with denominators that are powers of 10:

• The first digit immediately to the right of the decimal point is in the tenths place. It represents a value divided by 10 (e.g., in 123.456, '4' is 4/10).
• The second digit to the right is in the hundredths place. It represents a value divided by 100 (e.g., in 123.456, '5' is 5/100).
• The third digit to the right is in the thousandths place. It represents a value divided by 1000 (e.g., in 123.456, '6' is 6/1000).

So, the number 123.456 can be read as "one hundred twenty-three and four hundred fifty-six thousandths" or expressed as 100 + 20 + 3 + 4/10 + 5/100 + 6/1000. Understanding this place value system is crucial for accurately reading, writing, comparing, and performing operations with decimal numbers.

Converting Fractions to Decimals and Vice-versa

Decimal Operations: Examples

• 1. Addition: Add 15.36 and 7.8. `` 15.36 + 07.80 (add a zero to align decimal places) ------- 23.16 ``
• 2. Subtraction: Subtract 4.5 from 12.15. `` 12.15 - 04.50 (add a zero to align decimal places) ------- 07.65 ``
• 3. Comparison: Which is greater: 0.7 or 0.68? Compare the whole number parts: both are 0. Compare the tenths place: 7 (in 0.7) vs 6 (in 0.68). Since 7 > 6, 0.7 is greater than 0.68. (Think of it as 0.70 vs 0.68).

Exam Tips for Decimals

1. Align Decimal Points Carefully: This is the most common error in addition and subtraction. Always ensure the decimal points are directly below each other. Add trailing zeros to smaller decimals to make them 'like decimals' for easier calculation (e.g., 5.2 + 3.14 becomes 5.20 + 3.14).
2. Place Value is Key: When comparing decimals, start from the leftmost digit (whole number part), then move to the tenths, hundredths, and so on. If you're comparing 0.3 and 0.25, think of them as 0.30 and 0.25; 30 hundredths is more than 25 hundredths.
3. Simplify Fractions: When converting decimals to fractions, always remember to simplify the resulting fraction to its lowest terms. For example, 0.50 = 50/100, which simplifies to 1/2.
4. Practice Reading Decimals: Understand that 0.45 is read as "forty-five hundredths" and not "zero point forty-five". This reinforces the place value concept.

Practice Questions with Solutions

• Q: Write the decimal number for "Two hundred five and forty-seven thousandths". A: 205.047
• Q: Convert the fraction 3/5 to a decimal. A: 3 ÷ 5 = 0.6
• Q: Arrange the following decimals in ascending order: 1.2, 1.02, 1.201, 1.002. A: 1.002, 1.02, 1.2, 1.201
• Q: Calculate: 18.75 - 6.2. A: 18.75 - 6.20 = 12.55

Frequently Asked Questions