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Class 7 Decimals

Decimal Fractions

Reading Decimal Numbers

Convert Decimal Number into Fraction

Convert Fraction into Decimal Number

Types of Decimals

Comparison of Decimals

Addition of Decimals

Subtraction of Decimals

Multiplication of Decimals

Division of Decimals

Decimals Test

Decimals Worksheet

Answer Sheet

Decimal Fractions

Decimal number system consists a fraction whose denominator can be either ten, hundred, thousand or a power of ten can also be represented as decimal numbers. A decimal number system has two parts which are separated by a point/dot(.) known as decimal point. The number to the left of decimal point is known as Whole part or Integral part. The number to the right of decimal point is known as Decimal part.The number of digits contained in the decimal part are known as the number of Decimal places.

Decimal-Numbers-1

Reading Decimal Numbers

Values ... Thousands Hundreds Tens Ones Tenths(110) Hundredths(1100) Thousandths(11000) ...
25.4 2 5 4
256.35 2 5 6 3 5
5782.056 5 7 8 2 0 5 6
25.004 2 5 0 0 4

Example 1. 4235.678 = 4000 + 200 + 30 + 5 + 610 + 7100 + 81000

= 4000 + 200 + 30 + 5 + 0.6 + 0.07 + 0.008

It will be read as : four thousand two hundred thirty five point six seven eight.

Example 2. 0.06 = zero point zero six / point zero six

Convert Decimal Number into Fraction

Example 1. Convert 4.64 into fraction.

Solution. 4.64 = 464100 = 23250 = 43250

Example 2. Convert 0.354 into fraction.

Solution. 0.354 = 3541000 = 3541000 = 177500

Convert Fraction into Decimal Number

Method 1

Example 1. Convert 36510 to decimal form.

Solution. 36510 = 36.5
As there is one zero in denominator so the decimal point is in between 36 and 5.

Example 2. Convert 1481000 to decimal form.

Solution. 1481000 = 0.148
As there is three zeros in denominator so the decimal point is placed before 148.

Example 3. Convert 469100000 to decimal form.

Solution. 469100000 = 0.00469

Method 2

Let's see some exmaples.

Example 1. Divide 25 by 4.

Solution. 25 ÷ 4

Decimal-Numbers-2
254 = 6.25

Types of Decimals

Decimals can be classified into different kinds.

  1. Like Decimals
  2. Unlike Decimals
  3. Terminating Decimals
  4. Non-terminating/Non-repeating Decimals
  5. Recurring Decimals

Like Decimals: The Decimals consisting the same number of decimal places are called like decimals.

Example. 8.34, 20.78, 6.22 are like decimals as each of having two decimal places.

Unlike Decimals: The decimals consisting different number of decimal places are called Unlike Decimals.

Example. 7.353, 55.32, 65.4 are unlike decimals as each of having diff. decimal places.

Terminating Decimals: When a fraction is completely divisible and there is a finite number of digits after the decimal points in quotient are called as Terminating Decimals.

Example. 31.764 = 7.94 is a terminating decimal.

Non-terminating/Non-repeating Decimals: When a fraction is not completely divisible and there is not having an end term after the decimal points are called as Non-terminating Decimals.

Example. 10013 = 7.69230...

Recurring Decimals: When a fraction is not completely divisible and the decimal after digits are periodic or repeat again and again are known as Recurring or Repeating decimals.

Example. 3522 = 1.59090909...

Comparison of Decimals

First convert the decimals into like decimals. Then compare the digits of whole part. If the whole part is same then compare digits of decimal part in correspondence to their tenth, hundred, thousand etc. value.

Example 1. Compare 7.84 and 7.9.

Solution. Let's convert both the decimals into like decimals.

Now both the like decimals are 7.84 and 7.90.

Here, whole part of both the decimals are same i.e. 7. So, we have to compare the decimal part.

90 > 84

Hence, 7.9 > 7.84

Example 2. Compare 7.84, 98.4, 6.403.

Solution. Convert all the three decimals into like decimals.

        7.840, 98.400, 6.403

Now compare the whole part of the three decimals.

        98 > 7 > 6

Hence, 98.4 > 7.84 > 6.403.

Addition of Decimals

Example 1. Add 4.80, 12.043, 246.94

Solution. 4.80 + 12.043 + 246.94

Convert all the three decimals into like decimals.

        = 4.800 + 12.043 + 246.940

Decimal-Numbers-3
4.80 + 12.043 + 246.94 = 263.783.

Subtraction of Decimals

Example 1. Subtract 0.474 from 5.

Solution. 5 − 0.474

Convert both the decimals into like decimals.

        = 5.000 − 0.474

Decimal-Numbers-4
5 − 0.474 = 4.526

Multiplication of Decimals

Multiplication by 10,100,1000 or any power of 10

We have to shift the decimal point to the right by as many digits as there are zeroes in 1. Let's see some examples.

Example 1. Multiply 521.12 by 10.

Solution. 521.12 x 10 = 5211.2

Example 2. Multiply 521.12 by 100.

Solution. 521.12 x 100 = 52112.0 = 52112

Multiplication of decimals into another decimals

Example 1. Multiply 12.3 and 3.4.

Solution. 12.3 x 3.4

Multiply both the decimal by ignoring their decimal point.

        123 x 34 = 4182

Coun the number of digits present after the decimal point of both the decimal number.

= 1 + 1 = 2

Starting from the right of the product 4182 and count up to 2 places, then place the decimal point.

Hence the answer is 41.82.

Division of Decimals

Division by 10,100 or any power of 10

Shift the decimal point to the left by as many digits as there are number of zeroes in divisor.

Example 1. Divide 756.78 by 10.

Solution. 756.78 ÷ 10

By shifting decimal point one digit to the left we will have the answer

756.78 ÷ 10 = 75.678

Example 2. Divide 756.78 by 100.

Solution. 756.78 ÷ 100

By shifting decimal point two digits to the left we will have the answer

756.78 ÷ 100 = 7.5678

Decimal division by a whole number

Divide the decimal number by a whole number by simply ignoring decimal points. Mark the decimal point in quotient by completing the division in the dividend. Let's see some examples.

Example 1. Divide 0.936 by 3.

Solution. 0.936 ÷ 3

Decimal-Numbers-5

Division of Decimal by another Decimal

Convert the divisor decimal number into a natural number by shifting the decimal point by the same number of places in the right direction in the divisor and dividend both. Divide this new dividend by the new divisor in the usual way of division.

Example 1. Divide 562.5 by 12.5.

Solution. 562.5 ÷ 12.5

Decimal-Numbers-6

Class-7 Decimals Test

Decimals Test - 1

Decimals Test - 2

Class-7 Decimals Worksheet

Decimals Worksheet - 1

Decimals Worksheet - 2

Decimals Worksheet - 3

Decimals Worksheet - 4

Answer Sheet

Decimals-AnswerDownload the pdf











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