Maharashtra Board Class 5 Maths Part Two Chapter 9 Decimal Fractions PDF Download

Decimal Fractions

Soumitra : Sir, today I saw MRP ` 24.50 printed on a box of medicine. What does it mean?

Teacher : MRP means maximum retail price - the seller can sell that medicine for a maximum of 24 rupees and 50 paise.

Rekha : But how does '` 24.50' mean 'twenty-four rupees fifty paise'?

Teacher : '24.50' has been written in decimal form. To understand the answer to your question, you will first have to learn about decimal fractions and the way they are written.

Decimal Fractions

A fraction whose denominator is 10, 100 or 1000 or any other ten times multiple of 10 is called a decimal fraction. For example, \(\frac{5}{10}\), \(\frac{68}{100}\), \(\frac{285}{1000}\). These fractions are written in the numerator and denominator form.

It is convenient to write these fractions in another way. To use this new method, let us look at our usual method of writing numbers. In this method, we make new places for tens, hundreds, thousands and so on. The place value of each of these is 10 times that of the previous place. For example, one ten equals 10 units, one hundred equals 10 tens and so on.

Now let us think in the opposite direction. If we divide one hundred into 10 equal parts, each part is one ten. The tens place is to the right of the hundred. One ten is divided into ten parts. Each part is one unit. The units place is to the right of the tens place.

Similarly, if one unit is divided into ten equal parts, each part becomes \(\frac{1}{10}\). For this, a place is made to the right of the units place. \(\frac{1}{10}\) means 'one-tenth'. This place is called the tenths place or the first decimal place.

Teacher's Note

When you buy anything in a shop, the price is written in decimal form. For example, a pen costs ₹ 15.50 which means 15 rupees and 50 paise.

Exam Trick

Remember: The number before the dot (.) is the whole part. The number after the dot shows the fraction part. Think of it like money - before the dot is rupees, after the dot is paise.

Points to Remember

A decimal fraction has a denominator of 10, 100, or 1000.
The dot (.) is called a decimal point.
It separates the whole number from the fraction part.
\(\frac{1}{10}\) is written as 0.1 in decimal form.
We read 0.5 as 'zero point five'.

The Decimal Point

The decimal place is created for writing a fraction. When writing numbers, a dot (.) is written after the last digit of the whole part of a number to indicate the end of that part. This symbol is called a decimal point. The decimal point is used to write \(8\frac{5}{10}\) as 8.5. This is read as 'eight point five'.

\(20\frac{3}{10}\) is written as '20.3'.

'Seven tenths' can be written as '\(\frac{7}{10}\)' or '0.7'.

'\(\frac{7}{10}\)' is the usual way of writing the number and '0.7' is the decimal way.

Teacher's Note

The decimal point is very important. It tells us where the whole number ends and the fraction begins. In a price like ₹ 24.50, the dot separates rupees from paise.

Exam Trick

Always write the decimal point carefully. If you forget it or put it in the wrong place, the number will be completely different. For example, 2.5 is very different from 25.

Points to Remember

A dot (.) is called a decimal point.
The decimal point separates whole numbers from fractions.
Numbers to the left of the dot are whole numbers.
Numbers to the right of the dot are fractions.
We read the decimal point as 'point' when saying the number aloud.

Hundredths

If \(\frac{1}{10}\) is divided into 10 equal parts, each part becomes \(\frac{1}{100}\) or one hundredth.

Therefore, note that 1 tenth = 10 hundredths, or 0.1 = 0.10. By multiplying \(\frac{1}{100}\) by 10 we get \(\frac{10}{100} = \frac{1}{10}\). Therefore, it is possible to create a hundredths place next to the tenths place.

After creating a hundredths place we can write \(\frac{14}{100}\) as 0.14.

\(\frac{14}{100} = \frac{10 + 4}{100} = \frac{10}{100} + \frac{4}{100} = \frac{1}{10} + \frac{4}{100}\) meaning that when writing \(\frac{14}{100}\) in decimal form, 1 is written in the tenths place and 4 is written in the hundredths place. This fraction is written as 0.14 and is read as 'zero point one four'. Similarly, \(6\frac{57}{100}\) is written as 6.57 and \(50\frac{71}{100}\) is written as 50.71.

While writing \(\frac{3}{100}\) in decimal form, we must remember that there is no number in the tenths place and so, we put 0 in that place, which means that \(\frac{3}{100}\) is written as 0.03.

Study how the decimal fractions in the table below are written and read.

Teacher's Note

When we see a number like 7.05, the zero in the tenths place is very important. It shows that there are no tenths, only 5 hundredths. Never skip writing that zero.

Exam Trick

Remember: 0.05 is not the same as 0.5. The first one has a 0 in the tenths place, but the second one has a 5 in the tenths place. Always check where the digit is placed.

Points to Remember

Hundredths are smaller than tenths.
Ten hundredths make one tenth.
The hundredths place is to the right of the tenths place.
We can write 0.10 as 0.1 - they are the same.
In 0.05, the 5 is in the hundredths place, not the tenths place.

Place Value Of The Digits In Decimal Fractions

We can determine the place value of the digits in decimal fractions in the same way that we determine the place values of digits in whole numbers.

Example (1) In 73.82, the place value of 7 is \(7 \times 10 = 70\), and of 3, it is \(3 \times 1 = 3\).

Similarly, the place value of 8 is \(8 \times \frac{1}{10} = \frac{8}{10} = 0.8\) and the place value of 2 is \(2 \times \frac{1}{100} = \frac{2}{100} = 0.02\)

Example (2) Place values of the digits in 210.86.

Teacher's Note

Place value is the same for decimal numbers as for whole numbers. Just remember that after the decimal point, the values become smaller - tenths, then hundredths, and so on.

Exam Trick

To find the place value of any digit, multiply the digit by the value of its place. For the tenths place, multiply by 0.1. For the hundredths place, multiply by 0.01.

Points to Remember

Each digit has a place value in decimal numbers.
The place value of tenths is \(\frac{1}{10}\) or 0.1.
The place value of hundredths is \(\frac{1}{100}\) or 0.01.
Multiply the digit by its place value to find the answer.
In 73.82, the digit 8 has a place value of 0.8.

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