Concise Mathematics Class 7 ICSE Solutions for Chapter 4 - Decimal Fractions

To convert a decimal into a fraction, we will have to put 1 in the denominator under the decimal point and annex it with as many zeros as is the number of digits after the decimal point.

Next is to eliminate the decimal point and decrease the fraction to its lowest terms. Therefore,

\[0.50=\frac{50}{100}=\frac{1}{2}5.007=\frac{5007}{1000}\]

Annexing zeros to the very right of a decimal fraction will not result in changing its value. For example, 0.5 = 0.50 = 0.500, etc.

How to Convert a Decimal to a Fraction?

You will be able to convert a decimal to a fraction using the following steps:

Step 1: For the numerator, write down all the digits in the decimal number without the decimal point.

Step 2: The denominator is defined as a multiple of 10. The number of zeros is the number of decimal places on the extreme right of the decimal point.

Step 3: Simplify the fraction to its lowest terms whenever possible.

Conversion of a Mixed Recurring Decimal into Vulgar Fraction:

In the numerator, consider the difference between the number created by all the digits followed by the decimal point (taking repeated digits only once) and created by the digits which are not repeated. In the denominator, consider the number created by as many 9’s as there are repeating digits just after as many zeros as is the number of non-repeating digits. Therefore,

0.16 =

16−1

16−1 ÷ 90 = 15 ÷ 90 = 1/6

Mathematical Operations on Decimal Fractions

Following are the various operations conducted on the decimal fractions:-

1. Addition and Subtraction of Decimal Fractions: The assigned numbers are placed in such a way under each other that the decimal points fall in one column. The numbers are organized in such a way that they can now be added or subtracted in a standard manner.

2. Multiplication of Decimal Fractions: Under this operation, we will require to multiply the assigned numbers contemplating them without the decimal point. Now, in the product, the decimal point is terminated to attain as many places of decimal as is the sum total of the number of decimal places in the assigned numbers. Assume that we have to find the product (.3 x .03 x .003). Now, 3 x 3 x 3 = 27. Next, Sum of decimal places = (1 + 2 + 3) = 6. .3 x .03 x .003 = .000027.

3. Multiplication of a Decimal Fraction by a Power of 10: Move the point of decimal to the extreme right by as many positions as is the power of 10. Hence, 7.1546 x 100 = 71546 Or 0.086 x 10000 = 0.0860 x 10000 = 860.

4. Division of a Decimal Fraction By a Decimal Fraction: Multiplying both the divisor and the dividend by an appropriate power of 10 in order to make the divisor a whole number. Now, follow the procedure as above. Therefore 

\[\frac{0.00099}{0.11}=\frac{0.00099\times100}{0.11\times100}=\frac{0.099}{11}=0.009v\]

5. Division of a Decimal Fraction by a Counting Number: Dividing the assigned number without taking into account the decimal point by the given counting number. In this case, we will have to put the decimal point in the quotient in order to provide as many places of decimal as there are in the dividend. Assume that we have to find the quotient (0.0204 + 17). Now, 46839= 12. Dividend comprises 4 places of decimal. So, \[\frac{0.0468}{39}\] = 0.0012.

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