ICSE Class 6 Maths Chapter 06 Decimal Fractions

Chapter 6: Decimal Fractions

Basic Concept

A fraction whose denominator is 10 or a higher power of 10, i.e., 100, 1000, etc., is called a decimal fraction. Thus, each of \(\frac{7}{10}\), \(\frac{13}{10^2}\), \(\frac{357}{1000}\), \(\frac{29}{10^4}\) is a decimal fraction.

For such a fraction, the denominator is removed and its absence is shown by a small dot (called the decimal point) inserted in its proper place.

For example:

\(\frac{2}{10} = 0.2\), \(\frac{24}{100} = 0.24\), \(\frac{3159}{1000} = 3.159\), \(\frac{31}{10} = 3.1\), etc.

Since \(\frac{2}{10}\) and \(\frac{31}{10}\) have 10 as denominator; therefore, when 10 is removed, a dot representing a decimal point is placed just one digit from the right.

i.e. \(\frac{2}{10} = 2 = 0.2\) and \(\frac{31}{10} = 3.1\).

In the same way, when denominator is 100 and it is removed, the decimal point is placed just after two digits from the right, at the same time; so \(\frac{24}{100} = .24 = 0.24\), \(\frac{479}{100} = 4.79\), etc.

In the same way; \(\frac{5278}{1000} = 5.278\), \(\frac{5278}{10000} = 0.5278\), \(\frac{5278}{100000} = 0.05278\) and so on.

Also, \(\frac{3}{5} = \frac{3 \times 2}{5 \times 2} = \frac{6}{10} = 0.6\); \(\frac{17}{20} = \frac{17 \times 5}{20 \times 5} = \frac{85}{100} = 0.85\), etc.

A fraction whose denominator can be expressed as 10 or some higher power of 10 is also a decimal fraction.

3-1 means 3 + 0.1. Here 3 is the integral part and 0.1 is the decimal part.

Teacher's Note

Decimal fractions are used every day when dealing with money, measurements, and prices in shops.

Number Of Decimal Places

The number of digits in the decimal part of a number is the number of decimal places in it.

For example:

In 3.462, the decimal part is .462, which contains three digits. Therefore, the number 3.462 has 3 decimal places.

Similarly, 4.83 has 2 decimal places; 0.0478 has 4 decimal places and so on.

When a number has only the decimal part, such as .7, .83, .403, etc., it is always advised to write a zero before the decimal point. i.e. write .7 as 0.7; .83 as 0.83; .403 as 0.403 and so on.

Teacher's Note

Understanding decimal places helps when reading prices on receipts or measuring ingredients in cooking.

Like And Unlike Decimal Numbers

The given decimal numbers are said to be like decimal numbers, if they have the same number of decimal places. Otherwise, they are called unlike decimal numbers.

For example:

5.7, 0.8, 329.2 and 50.6 are like decimal numbers.

26.03, 8.87, 0.52 and 400.04 are like decimal numbers.

2.6, 40.32, 0.009, 3.0728 and 328.2 are unlike decimal numbers.

Note: Unlike decimal numbers can be converted into like decimal numbers.

For example:

Consider the unlike decimal numbers: 5.8, 239.06 and 0.5497

In these numbers, 5.8 has one decimal place, 239.06 has two decimal places and 0.5497 has four decimal places.

Since 0.5497 has the maximum number of decimal places (four decimal places), make the decimal places in each given decimal number equal to four.

Thus, 5.8 = 5.8000, 239.06 = 239.0600 and 0.5497 = 0.5497

Therefore, the given unlike decimal numbers 5.8, 239.06 and 0.5497 are converted into the like decimal numbers 5.8000, 239.0600 and 0.5497.

Similarly, the unlike decimal numbers 320.98, 0.07325 and 53.4 will be 320.98000, 0.07325 and 53.40000 as like decimal numbers.

The value of a given decimal fraction does not change, if one or more zeroes are placed on the right side of it.

Teacher's Note

Converting unlike decimals to like decimals is similar to finding a common denominator when adding fractions.

Conversion Of A Given Fraction Into A Decimal Fraction

1. When the denominator is 10, 100, 1000, etc.

Steps:

1. Count the number of zeroes in the denominator of the given fraction.

2. In the numerator, mark the decimal point after as many digits (counting from extreme right to left) as the number of zeroes in the denominator. At the same time, remove the denominator.

For example:

In the fraction \(\frac{327}{100}\), the denominator is 100, which has two zeroes in it. Therefore, in the numerator 327, mark the decimal point after two digits from right to left, giving 3.27.

Thus \(\frac{327}{100} = 3.27\). Similarly, \(\frac{7}{10} = .7 = 0.7\), \(\frac{14}{1000} = 0.014\) and so on.

In \(\frac{14}{1000}\), the denominator has three zeroes, and so the decimal point is to be marked after 3 digits from the right of the numerator 14. Since 14 has only two digits, write one zero to the left of 14 and then place the decimal point.

Teacher's Note

This method of converting fractions to decimals is the foundation for understanding place value in the decimal system.

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