Decimals

 Mind Maps

Class V - maths: Decimals
Q) What is a fraction whose denominator is 10 or any power of 10?

Q) Write fraction 1/10 in the decimal form?

Q) Write the 1/100 in decimal form?

Q) Write the 1/1000 in decimal form?

Q) Write the 27/100 in decimal form?

Q) Subtract 56.89 from 78.12?

Q) Convert value of 67.23 into Fraction?

Q) Division of a Decimal number is 678.33/100?

Q) 1 hundred = how many thousands?

Q) 6/10 = ?

Q) 27/100 = ?

Q) 150 is a multiple of?

Q) H.C.F of 6 and 18 is?

Q) Product of two numbers = HCF * ?

Q) Which of the following is a unlike decimal? 3.45, 3.56, 3.4, 5.78?

Q) The smallest odd prime number is?

Q) If we write the fraction of 5/100, in decimal form we get 0.05, where 5 stands for?

Q) 673.45 can be written as?

Q) Write the 145.43 decimal in words?

Q) Convert the 502/1000 fraction into decimal value?

Q) Convert the 20.018 decimal value into fraction value?

Q) Convert the 10.001 decimal value into fraction value?

Q) Convert the 32/100 fraction into decimal value?

Q) What is Addition of Decimals?

Q) What is Subtraction of Decimals?

Q) What is Multiplication of Decimal?

Q) What is Division of Decimals?

Q) What is Decimals?

Q) If the product of two numbers is 88 and HCF is 4, then their LCM?

Q) Find the decimal value of 8/100?

Q) Multiply 9.7 with 4.3?

Q) Which of the following is not a like decimal? 45.89, 56.89, 12.34?

Q) Expand 3.85 in Place value form and Decimal form?

Q) Change the 0.5 and 0.42 decimals into like decimals?

Q) Rahul and Raj walked back to their homes by walking 4.5 km and 3.48 km, respectively. Who walked more distance?

Q) Write the following decimals in order from the least to the greatest: 0.25, 0.4, 0.004?

Q) Arrange the 11.1, 11.21, 11.001 decimals in ascending order?

Q) What is Reading,Writing And Converting Decimals?Give an examples?

Q) What is Comparing Decimals?Give an example?

Q) What is Converting Fractions Into Decimals and give an example?

Q) What is Place Value and Decimals and give an example?

Q) What is Addition of Decimals and give an example?

Q) I am an odd number between 35 and 40 but not a prime number. I am a multiple of 3 also. Who am I?

Q) Rahul and Naresh walked back to their homes by walking 2.5 km and 2.48 km, respectively. Who walked less distance?

Q) The distance of office from Naresh home is 1.3 km and the distance of his sports ground is 0.5 km. Which distance is more for him to travel?

DECIMALS

Definition:

"A decimal is a fraction whose denominator is 10 or any power of 10."

Introduction:

Tenths

If we divide one complete whole into 10 equal parts,each part is called one-tenth and is written as 1/10.

The fraction 1/10 can also be written in the decimal form as 0.1.

The point (.) in 0.1 is known as the decimal point and it is read as zero point one.

Similarly, 2/10=0.2, 3/10=0.3 and 4/10=0.4 and so on.

Let us see the combination of whole numbers with decimal numbers

We can see 2 complete wholes and 7/10 or 0.7.
It is read as 2.7 or two point seven

Hundredths

If we divide one-tenth into 10 equal parts,each part thus obtained is called one-hundredth and is written as "1/100".
1/100 in decimal form is written as 0.01.

Hence, we can say that 1 tenth=10 hundredths

In the figure below, out of 100 squares, 27 have been shaded.

We write this in fraction as 27/100 or 27 hundredths which can be written in decimal form as 0.27.

0.27

Let us have a look at some of the shaded parts.

Here, 6/10=0.6 and 6/100=0.06.

Thousandths

If we divide one-hundredth into 10 equal parts, each part thus obtained is called one - thousandths and is written as “1/1000”.

In the decimal form it is written as 0.001.

Hence, we can say that:

1 hundredth=10 thousandths.

We know that, the decimal consists of two parts.

• Whole number part
• Decimal part.

To read a decimal or to write the number name for the decimal, we follow the following rule given below.

Rule:

The whole number part is read as usual.
The decimal part is read as if it were a whole number, but the name of the place of the last digit on the right is attached to the number.
The word "and" is used for the decimal point

Examples:

• 672.31 is read as six hundred and seventy two and thirty one hundredths.
• 321.6 is read as three hundred and twenty one and 6 tenths.
• 0.45 is read as forty five hundredths.

The number names of decimals can also be written as another simple rule given below.

Rule:

The whole number part is read as usual.
The decimal point is read as point. The digit part is read digit wise

Examples:

• 235.81 is read as two hundred and thirty five point eight one.
• 984.627 is read as nine hundred and eighty four point six two seven.
• 63.02 is read as sixty three point zero two.
Converting Fractions Into Decimals

Decimals are fractions with denominators 10, 100, 1000, and higher multiples of 10.

To convert these fractions into decimals, look at the denominator.

There should be as many digits after the decimal point as there are zeros in the denominator

Examples:

• 7/10=0.7
• 34/100=0.34
• 4/100=0.04 (a zero is placed in such a way that, we get 2 decimal places)
• 673/1000=0.673
• 2/1000=0.002 (2 zeros before 2, to make 3 decimal places)
• 9 1/100=901/100=9.01 (The whole number remains the same).

Converting Decimals Into Fractions

To convert a decimal into a fraction,
write the given decimal number as the numerator with no decimal point,
and in the denominator,write 1 followed by as many zeros as there are digits after the decimal in the given number.

Examples:

1. 12.3     = 123/10     (1 decimal place; 1 followed by 1 zero)
2. 56.32     = 5632/100     (2 decimal place; 1 followed by 2 zeros)
3. 89.045     = 89045/1000     (3 decimal places; 1 followed by 3 zeros)
Place Value and Decimals

Decimals On The Place Value Chart

If we write the fraction 3/10, in decimal form, we get:

3/10=0.3, where 0.3 stands for 3 tenths.

Similarly, 3/100=0.03, where 3 stands for 3 hundredths.

3/1000=0.003, and 3 stands for 3 thousandths.

Therefore, the place value chart for decimals can be written as:

The decimal numbers shown in the chart are read as 0.356.

This decimal place value chart is an extension of the place value chart that we have learnt so far

Place Value Of Decimals

The value of each digit in a number depends upon the place it holds on the place value chart.

• Numbers get 10times bigger moving to the left.
• Moving to the right, the numbers get ten times smaller.
• To the right of the ones, the whole number 1 is divided into ten equal parts.
• The decimal point separates the whole number from the decimal part.
• Let us have a look at some examples of decimal numbers and the place value of the digits in the number.

Examples:

1. 1 5 6 . 9
2. Here 9 is at tenths place and its value is 9/10
6 is at ones place, so it is written as 6
5 at tens place and its value is 50
1 is at hundreds place or 100.

3. 0 . 2 9
4. 9 hundredths or 9/100
2 tenths or 2/10
0 ones or 0.

5. 6 7 3 . 5 1 4
6. 4 thousands or 4/1000
1 hundredths or 1/100
5 tenths or 5/10
3 ones or 3
7 tens or 70
6 hundreds or 600.

Expanded Form of Decimals

There are three ways to expand a decimal number.

1. Place value form
2. Decimal form
3. Fractional form.
4. Examples:

Expand 6.43 in all the three ways.

Solution:

5. Place value form : 6.43=6 ones + 4 tens + 3 hundredths.
6. Decimal form : 6.43=6 + 0.4 + 0.03
7. Fractional form : 6.43=6 + 4/10 + 3/100
Like and Unlike Decimals

Like Decimals:

Decimals with the same number of decimal places are called like decimals.

Examples:

• 4.5, 23.6, 0.2 are like decimals, each with one decimal place.
• 9.21, 3.67, 1.02 are like decimals, each with two decimal places.
• 7.281, 5. 697, 0.139 are like decimals, each with three decimal places.

Unlike Decimals:

Decimals having different number of decimal places are called unlike decimals.

Examples:

• 2.8, 11.54, 6.029 are unlike decimal as they have different number of decimal places.
• 1.3, 0.64, 8.921 are some more examples of unlike decimals.

We can add as many zeros to the right of the last digit after the decimal point as needed.

It does not change the value of the decimal number.

Examples:

2.6 is the same as 2.60, and 5.93 and the same as 5.930.

These decimals are known as Equivalent Decimals.

Unlike decimals can be converted into like decimals by placing zeros

Comparing Decimals

Comparing decimals is similar to comparing numbers.

Decimals are compared with the help of the digits they contain.
Certain rules are to be followed when we convert the unlike decimals into like decimals and compare their whole number part and decimal part.

Rules

1. The decimal with the greatest whole number part is the greatest and the decimal with the least whole number part is the smallest.
2. If the whole number part is same, we compare the decimals by comparing their digits at the tenths place.
3. If they are equal, digits at the hundredths place are compared and so on.

Examples:

1. The distance of school from Hamed’s home is 3.3 km and the distance of his sports ground is 3.25 km. Which distance is more for him to travel?
2. Solution:

Distance of school from Hamed’s home=3.3 km

Distance of his sports ground from home=3.25 km.

3.3 has 1 decimal place whereas 3.25 has two decimal places.

To make the decimals into like decimals, we put a zero beside 3.3 to make it 3.30.

So, now it becomes easy for us to compare,

3.30 km is greater than 3.25 km,

i.e., 3.30 ˃ 3.25.

So, the distance of school from Hamed’s home is more than the distance of his sports ground.

3. Write the following decimals in order from the least to the greatest:
4. 0.6, 0.65, 0. 006.

Solution:

Change all the decimals to 3 decimal places.

0.600, 0.650, 0.006

The decimals in order from the least to the greatest are:

0.006, 0.600, 0.650.

There are certain rules to be followed in order to add the decimals.

Rules

• Convert the unlike decimals into like decimals.
• Write the addends one below the other so that the decimal points of all the addends are one below the other.
• Place the decimal point in the sum directly below the decimal points in the addends.

Examples:

Solution:

Convert the following decimals into like decimals.

• Change in the order of addends does not affect the sum of decimals
• Examples:

7.21 + 5.97=13.18 and 5.97 + 7.21=13.18.

• The sum of a decimal number and zero is the same decimal number.

Examples:

13.9 + 0=13.9 and 0 + 2.6=2.6.

Subtraction of Decimals

There are certain rules to be followed in order to subtract the decimals

Rules

• Convert the unlike decimals into like decimals
• Write the smaller number below the greater number so that the decimal points are one below the other.
• Subtract the same as we subtract the whole numbers.
• Put the decimal point in the difference directly below the decimal points in the minuend and the subtrahend.

Examples:

Subtract 78.6 from 79.006

Solution:

Converting the decimals into like decimals, we get:

Properties Of Decimal Subtraction

• Any decimal number subtracted from itself gives the difference as zero.
• Examples:

6. 25 _ 6. 25=0 ; 7.06 _ 7. 06=0.

• If zero is subtracted from a decimal number, the difference is the same decimal number.

Examples:

1.3 _ 0=1.3 and 9.27 _ 0=9.27

Multiplication of Decimals

Multiplication Of A Decimal By A Whole Number

There are certain rules to be followed to multiply decimal by a whole number.

Rules

• Multiply the numbers as whole numbers ignoring the decimal point.
• Count the number of decimal places in the multiplicand and multiplier, and add the number of decimal places.
• Put the decimal point in the product form the right, after as many digits as the total number of decimal places.

Examples:

Find the product of 243.7 and 9.

Solution:

Multiplication Of A Decimal By 10, 100 And 1000.

When we multiply a decimal number by 10, 100 and 1000, the value of the digits changes.

Examples:

• 5.81 × 10=58.1 Value of each digit has increased by one place
• 2.975 × 100=297.5 Value of each digit has increased by 2 places
• 6.792 × 1000=6792 Decimal point may not be given as it has become a whole number
• 13.5 × 100=1350 A zero is placed to make 2 places of decimals.

Multiplication Of A Decimal By A Decimal

Examples:

Multiply 5.13 by 1.7.

Solution:

We multiply the same way as we do for whole numbers ignoring the decimal point.

Properties Of Decimal Multiplication

• The order of decimal numbers can be changed in multiplication. The product remains the same.
• Examples:

2.8 × 6.2=17. 36 and 6. 2 × 2. 8=17. 36.

• The product of a decimal number and 1 is the decimal number itself.
• Examples:

5.4 × 1=5.4 and 1 × 5.4=5.4.

• The product of a decimal number and zero is zero.
• Examples:

8.5 × 0=0 and 0 × 8.5=0.

Division of Decimals

Division Of A Decimal By A Whole Number

Rules to follow for division of a decimal by a whole number.

Rules

• Divide the decimals as the division of whole numbers is done.
• Place the decimal point in the quotient directly above the decimal point in the dividend.

Examples:

Divide 8.6 by 2

Solution:

Division Of A Decimal By 10, 100, 1000

Examples:

Divide 38. 94 by 10

Solution:

So, our required answer is 3.894.

When decimals are divided by 10, 100, or 1000,
the value of each division will become smaller by the number of zeros in the divisor.

31. 74 ÷10=3. 174         (The decimal point has shifted 1 place to the left)

284. 55 ÷100=2. 8455         (The decimal point has shifted 2 places to the left)

891. 35 ÷1000=0. 89135         (The decimal point has shifted 3 places to the left)

98.89 ÷1000=0. 09889.         (An extra zero is placed to complete the decimal places).

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