Students can go through AP Board 6th Class Maths Notes Chapter 1 Numbers All Around us to understand and remember the concepts easily.

## AP State Board Syllabus 6th Class Maths Notes Chapter 1 Numbers All Around us

HISTORICAL NOTES:

INDIA

→ Zero: Ancient Indians invented zero. The ancient Indian Bhakshali manuscript depicts zero, which is the recorded evidence of zero which we use today. We can also find the circular symbol ‘o’ to represent zero, the earliest epigraphical evidence at Chaturbhuj temple, Gwalior, Madhya Pradesh.

→ Number system:

0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 are called digits. Every number is written using these digits. We can write infinitely many numbers using these digits.

→ Reading numbers:

There are two commonly used methods of numeration.

i) Indian system of numeration also called Hindu-Arabic system of numeration.

ii) International system of numeration. ‘

We read numbers using place value of digits. The place values enable us to read numbers easily and clearly.

→ Indian system:

The digits in a number are separated by commas as per the above table i.e., starting from right we place a comma after three digits and thereafter we place a comma after every two digits.

In other words, to read numbers in the Hindu-Arabic system of numeration digits are divided into periods namely units/thousands/lakhs/crores and so on .from right to left.

The value of each digit in a number depends upon its place in the given number.

As we move from right to left the place value increases by 10 times to its previous place.

Example: 75698425

Placing commas at correct positions we have

7, 56, 98, 425: 7 crores 56 lakhs 98 thousand 4 hundred and twenty five : Seven crores fifty six lakhs ninety eight thousand four hundred and twenty five

Example: 600540283

Placing commas at correct positions we have

60, 05, 40, 283: 60 crores 05 lakhs 40 thousand 2 hundred and eighty three : Sixty crores five lakhs forty thousand two hundred and eighty three

→ International system of numeration:

The digits in a number are separated by commas as per the table below i.e., starting from right we place a comma after three digits.

In other words, to read numbers in the International system of numeration digits are divided into periods namely units/thousands/millions/billions and so on from right to left.

Example: 52463801221

Placing commas at correct positions we have

52, 463, 801, 221: 52 billions 463 millions 801 thousands 2 hundred and twenty one: Fifty two billions four hundred sixty three millions eight hundred one thousands two hundred and twenty one

Example: 956785020412

Placing commas at correct positions we have

956, 785, 020, 412: 956 billions 785 millions 020 thousands 4 hundred and twelve : Nine hundred fifty six billions seven hundred eighty five millions twenty thousands four hundred and twelve

→ Comparison between Hindu-Arabic & International systems of numeration:

Indian | international |

1 lakh | 100 thousands |

10 lakhs | 1 million |

1 crore. | 10 millions |

10 crores | 100 millions |

100 crores | 1 billion |

Also we have higher place values mentioned in Vedic numbering system.

Eka/dasa/sata/sahasra/ayuta/laksa/niyuta/koti/sanku/mahasanku/vrnda/mahavrnda/padma/mahapadma/kharva/mahakharva/samudra/ogha/mahaugha…etc

→ Large numbers used in daily life situations:

- Areas of large countries when expressed in sq.km
- To measure water flow at dams
- To measure the weights of products like food grains
- To measure the population

Face value: The face value of a digit in a number is the digit itself.

Place value of digits:The place value of a digit in a number is the product of its face, value and the place value in which it is written in the number.

Example: Face value and the place value of 5 in the number 485796 is Face value = 5

Place value = 5 x 1000 = 5000

→ Comparison of numbers:

To compare two numbers

i) Align the digits by place value

ii) Compare the digits in each place, starting from the greatest place Ascending order : Ascending order means arrangement of numbers from the smallest to the greatest.

Descending order : Descending order means the arrangement of numbers from the greatest to the smallest.

Example : 52, 235; 75, 222 ; 86, 412 ; 1, 25, 896 ; 18, 259 ; 35, 986

Ascending order: 18, 259 ; 35,986 ; 52,235 ; 75, 222 ; 86,412 & 1,25,896 Descending order: 1, 25, 896 ; 86,412 ; 75,222 ; 52,235 ; 35,986 & 18,259

→ Rounding off and Estimation of numbers:

Rules to round off a number to a given place:

Example:

Round off 6879124 to its nearest tens, hundreds, thousands, ten thousands and lakhs.

68,79,124 when rounded off to tens: 68, 79, 120

68,79,124 when rounded off to hundreds: 68, 79, 100

68,79,124 when rounded off to thousands: 68, 79, 000

68,79,124 when rounded off to ten thousands: 68, 80, 000

68,79,124 when rounded off to lakhs: 69, 00, 000

68,79,124 when rounded off to ten lakhs: 70, 00, 000