Class 6 Exam  >  Class 6 Notes  >  Maths Olympiad Class 6  >  Chapter Notes: Decimals

Decimals Chapter Notes | Maths Olympiad Class 6 PDF Download

Introduction

  • The numbers used to represent numbers smaller than unit 1 are called decimal numbers. 
  • The decimal point or the period plays a significant part in a Decimal Number.

    Decimals Chapter Notes | Maths Olympiad Class 6
  • This period separates the fractional part and whole number part in a decimal number. 
  • Place value of a digit can be defined as the value of a digit as per the place of that digit in a number.

Tenths

As we know that, 1 cm = 10 mm, so if we have to find the opposite then
1mm = 1/10 cm
 or one-tenth cm or 0.1 cm.

Hence, the first number after the decimal represents the tenth part of the whole.

Decimals Chapter Notes | Maths Olympiad Class 6 This reads as “thirty-four point seven”.

Representation of Decimals on Number Line

To represent decimals on the number line we have to divide the gap of each number into 10 equal parts as the decimal shows the tenth part of the number.

Example: Show 0.3, 0.5 and 0.8 on the number line.

Sol: All the three numbers are greater than 0 and less than 1.so we have to make a number line with 0 and 1 and divide the gap into 10 equal parts.Then mark as shown below.

Decimals Chapter Notes | Maths Olympiad Class 6

Fractions as Decimals

It is easy to write the fractions with 10 as the denominator in decimal form but if the denominator is not 10 then we have to find the equivalent fraction with denominator 10.

Example: Convert 12/5 and 3/2 in decimal form.
Sol: Decimals Chapter Notes | Maths Olympiad Class 6

Decimals as Fractions

Example: Write 2.5 in a fraction.
Sol:Decimals Chapter Notes | Maths Olympiad Class 6

Hundredths

As we know that 1 m = 100 cm, so if we have to find the opposite then
1 cm = 1/100 m, or 
one-hundredth m or 0.01 m.
Hence, the second numbers after the decimal represent the hundredth part of the whole.Decimals Chapter Notes | Maths Olympiad Class 6

It reads as “thirteen point nine five”.

Decimal in the hundredth form shows that we have divided the number into hundred equal parts.

Example: If we say that 25 out of 100 squares are shaded then how will we write it in fraction and decimal form?Decimals Chapter Notes | Maths Olympiad Class 6

Sol: 25 is a part of 100, so the fraction will be 25/100.
In the decimal form we will write it as 0.25.

Place Value Chart

This is the place value chart which tells the place value of each digit in the decimal number. It makes it easy to write numbers in decimal form.

Decimals Chapter Notes | Maths Olympiad Class 6

Example: With the given place value chart write the number in the decimal form.

Hundreds (100)Tens (10)Ones (1)Tenths (1/10)Hundredths (1/100)
46385

Sol: According to the above table-Decimals Chapter Notes | Maths Olympiad Class 6

Recurring and Terminating Decimals

  • A terminating decimal is a decimal number which has finite number of digits after the decimal.
    Example: 0.35
  • A recurring decimal is one where its decimal representation becomes periodic or same sequence of digits keeps repeating indefinitely.
    Example: 31.213333…

Comparing Decimals

  • Any two decimal numbers can be compared by comparing their whole part and decimal parts.
  • If the whole parts are equal then the tenth parts can be compared and so on.

If the Whole Number is different

  • If the whole numbers of the decimals are different then we can easily compare them.
  • The number with the greater whole number will be greater than the other.

Example: Compare 532.48 and 682.26.
Sol: As the whole numbers are different, so we can easily find that the number with a greater whole number is greater.

Hence 682.26 > 532.48.Decimals Chapter Notes | Maths Olympiad Class 6

If the Whole Number is the Same

  • If the whole numbers of the decimals are same, then we will compare the tenth and then the hundredth part if required.
  • The number with the greater tenth number is greater than the other.

Example: Compare 42.36 and 42.68.
Sol: As the whole number is the same in both the numbers so we have to compare the tenth part.

Hence 42.68 > 42.36.Decimals Chapter Notes | Maths Olympiad Class 6

Addition and Subtraction of Decimals

Decimals Chapter Notes | Maths Olympiad Class 6

Addition

For example: Add: 0.19 + 2.3
Decimal numbers, 0.19 and 2.3 have two digits and one digit respectively to the right of the decimal point. So, we add a zero to the right of 2.3.Decimals Chapter Notes | Maths Olympiad Class 6

Subtraction

For example: Subtract: 39.87 - 21.98
Decimal numbers 39.87 and 21.98 have the same number of zeros after the decimal point.Decimals Chapter Notes | Maths Olympiad Class 6

Multiplication and Division of Decimals

Multiplication 

  • 2.8 × 7 (There is only one digit to the right of the decimal point in 2.8)
  • 28 × 7 (Ignoring the decimals)
  • 28 × 7 = 196
  • Now bring the decimal back after one digit from left and thus answer is 19.6

Division 

  • 3.4/2 = Quotient
  • Ignore the decimal and divide the numerator by the denominator. Here, quotient = 34/2 = 17
  • Since there is only one digit to the right of the decimal, put the decimal after one digit from left in the quotient. Therefore, quotient becomes 1.7

How to Use the Points

Point Shift Trick

Division: Point is shifted to the left by the number of zeroes in the denominator.

  • 150/100 = 1.50 ( Shifting decimal by 2 points to the left)
  • 1.5/1000 = 0.0015 ( Shifting decimal by 3 points to the left)

Decimals in Money

Example: Write 25 paise in decimals.
Sol:
100 paise = 1 Rs.
1 paise = 1/100 Rs. = 0.01 Rs.
25 paise = 25/100 Rs. = 0.25 Rs.

Decimals in Length Measurement

  • 1m = 100cm
  • 1cm = 1/100m = 0.01m ( Move decimal to left by 2 units in the numerator as there are two zeroes in the denominator )
  • 150cm = 150/100m = 1.5m

Example: If the height of Rani is 175 cm then what will be her height in meters?
Sol: 100 cm = 1 m
1 cm = 1/100 m = 0.01 m
175 cm = 175/100 mDecimals Chapter Notes | Maths Olympiad Class 6Hence, the height of Rani is 1.75 m.

Decimals in Weight Measurement

  • 1 kg = 1000 g
  • 1 g = 1/1000 kg
  • 298 g = 298/1000 kg = 0.298 kg ( Move the decimal to the left by 3 places in the numerator as there are 3 zeroes in the denominator )

Example: If the weight of a rice box is 4725 gram then what will be its weight in a kilogram?
Sol: 
1000 gm = 1 kg
1 gm = 1/1000 kg = 0.001 kgDecimals Chapter Notes | Maths Olympiad Class 6

The document Decimals Chapter Notes | Maths Olympiad Class 6 is a part of the Class 6 Course Maths Olympiad Class 6.
All you need of Class 6 at this link: Class 6
9 videos|114 docs|49 tests

Up next

FAQs on Decimals Chapter Notes - Maths Olympiad Class 6

1. How can fractions be converted into decimals?
Ans. Fractions can be converted into decimals by dividing the numerator by the denominator. For example, to convert 1/2 into a decimal, divide 1 by 2 which equals 0.5.
2. How can decimals be converted into fractions?
Ans. Decimals can be converted into fractions by writing the decimal as a fraction with the decimal number as the numerator and a power of 10 as the denominator. For example, 0.75 can be written as 75/100, which simplifies to 3/4.
3. How can decimals be compared to determine which is greater or smaller?
Ans. Decimals can be compared by looking at the place value of each digit. Begin by comparing the digits in the ones place, then move to the tenths place, hundredths place, and so on. The decimal with the greater digit in the leftmost place value is greater.
4. How can decimals be added and subtracted?
Ans. Decimals can be added and subtracted by aligning the decimal points and carrying out the addition or subtraction as usual. Place zeros as necessary to ensure the decimal points align.
5. How can decimals be multiplied and divided?
Ans. Decimals can be multiplied and divided similarly to whole numbers, but with special attention to the placement of the decimal point in the final answer. When multiplying, count the total number of decimal places in the factors and place the decimal point in the product so that the total number of decimal places matches the total in the factors. When dividing, move the decimal point to make the divisor a whole number, perform the division, and then place the decimal point in the quotient.
9 videos|114 docs|49 tests
Download as PDF

Up next

Explore Courses for Class 6 exam
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Related Searches

shortcuts and tricks

,

Viva Questions

,

MCQs

,

mock tests for examination

,

Sample Paper

,

pdf

,

Decimals Chapter Notes | Maths Olympiad Class 6

,

Semester Notes

,

Important questions

,

Objective type Questions

,

past year papers

,

ppt

,

Summary

,

study material

,

practice quizzes

,

video lectures

,

Extra Questions

,

Free

,

Previous Year Questions with Solutions

,

Decimals Chapter Notes | Maths Olympiad Class 6

,

Exam

,

Decimals Chapter Notes | Maths Olympiad Class 6

;