CBSE Class 6 Mathematics – 7. Decimals (Notes)

Revision Notes on Decimals

Learning Goal

1. Decimal (Fractions whose denominator is exponent of 10. Ie. 10, 100, 1000 etc.)
2. Part of decimal (Whole part & decimal part)
3. Type of decimal (Like and Unlike decimal)
4. Comparing Decimal Numbers
5. Write the decimal no into words.
6. Write the decimal no in figure.
7. Write the decimal no in words.
8. Place value
9. Expended form and short form.
10. Ascending and descending order.
11. Converting a decimal into fraction.
12. Converting a fraction into decimal
13. Operations on decimals.

Decimal Numbers

Fractions whose denominators are exponent of 10 are called Decimal Fractions. OR

Fractions whose denominators are 10, 100, 1000 etc are called Decimal Fractions.

We use dots to write decimal numbers.

Dot is called decimal point that separate the whole part and decimal part.

Part of Decimal Numbers

Example

With the given place value chart write the number in the decimal form.

Hundreds  (100)	Tens  (10)	Ones  (1)	Tenths (1/10)	Hundredths (1/100)
4	6	3	8	5

Solution

According to the above table-

Like and Unlike Decimals Examples

Like Decimals

Those decimal numbers that have the equal number of digits after the decimal point are called like decimals.

Ex- 2.46, 16.09, and 103.87 etc.

Unlike Decimals

Those decimal numbers that have the unequal number of digits after the decimal point are called unlike decimals.

Ex- 82.4, 216.09, and 3.875 etc.

 

Convert Unlike Decimals into Like Decimals

Add zeros to the right of the decimal place.

1. Write the given expression
2. Then, convert unlike decimals into like decimals by putting 0s to the right of the decimal point

Q 1. Convert the following decimals to like decimals: 1.7, 2.35, 6.135.

Ans: Follow the below-given steps to convert the unlike decimals into the like decimals, i.e.

1. Write the given decimals

1.7, 2.35, 6.135

2. Further, we need to convert each of the decimal numbers to the like decimal number, which has an equal number of digits after the decimal point

1.700, 2.350, 6.135

Comparing Decimals

1. If the whole number is different.

In this case the number with the greater whole number will be greater than the other.

Example

Compare 532.48 and 682.26.

Solution:

As the whole numbers are different and 682 > 532

Hence 682.26 > 532.48

2. If the whole number is the same

In this case compare the tenth and then the hundredth part if required.

The number with the greater tenth number is greater than the other.

Example

Compare 42.36 and 42.68.

Solution

Here the whole number is the same in both the numbers so we have to compare the tenth part. And tenth part 6 > 3

Hence 42.68 > 42.36

How to Convert Decimal into Fractions?

Write the given decimal in the form of a ratio (p/q), where the denominator is equal to 1.

Put zeros with denominator 1 as many as there are decimal places.

Simply the resulting fraction.

Example

Write 2.5 in a fraction.

Solution

2.5 = 2510  = 52

How to Convert Fractions into Decimal?

Divide the numerator by denominator till a nonzero remainder is obtained.

Put a decimal point in the dividend as well as in the quotient.

Put a zero on the right of decimal in the dividend as well as on the right of the remainder.

Divide again just we do in whole numbers.

Repeat above step till the remainder is zero.

Example

Using Decimals

Generally, decimals are used in money, length and weight.

1. Money

Example: 1

Write 25 paise in decimals.

Solution:

100 paise = 1 Rs.

1 paise = 1/100 Rs. = 0.01 Rs.

25 paise = 25/100 Rs. = 0.25 Rs.

Example: 2

Write 7 rupees and 35 paise in decimals.

Solution:

7 rupees is the whole number, so

7 + 35/100 = 7 + 0.35 = 7.35 Rs.

2. Length

Example

If the height of Rani is 175 cm then what will be her height in meters?

Solution

100 cm = 1 m

1 cm = 1/100 m = 0.01 m

175 cm = 175/100 m

Hence, the height of Rani is 1.75 m.

3. Weight

Example

If the weight of a rice box is 4725 gram then what will be its weight in a kilogram?

Solution

1000 gm = 1 kg

1 gm = 1/1000 kg = 0.001 kg

Addition or Subtraction of Decimal numbers

Change into like decimals if they are unlike and add or subtract as we do for whole numbers.

Example: 1

Add 22.3 and 34.1

Solution:

Example: 2

Add 1.234 and 4.1.

Solution:

Example

Subtract 243.86 from 402.10.

Solution

  

Representation of Decimals on Number Line

To represent decimals on the number line we have to divide the gap of each number into 10 equal parts as the decimal shows the tenth part of the number.

Example

Show 0.3, 0.5 and 0.8 on the number line.

Solution

All the three numbers are greater than 0 and less than 1.so we have to make a number line with 0 and 1 and divide the gap into 10 equal parts.

Then mark as shown below.