Number System

Reading and writing numbers in the Indian Number System The place value chart in the Indian Number System can be represented as follows:

Periods Lakhs Thousands ones

Place

Ten lakhs

Lakhs Ten

thousands Thousands Hundreds Tens Ones

T L L T Th Th H T O

In the Indian Number System, lakhs and crores come after thousands. For example: 1732256 can be placed in the place value chart as follows:

T L L T Th Th H T O

1 7 3 2 2 5 6

All the digits in the same period are read together and the name of the period (except ones) is read together. The periods in numerals are separated by commas.

1732256 can be read and written in the Indian Number System as follows: Seventeen lakh thirty-two thousand two hundred fifty-six and 17,32,256 respectively The expanded form of the number is obtained by multiplying the digits in the number with the place value and separating them with ‘+’ sign. Expanded form of 17,32,256 = 10,00,000 + 7,00,000 + 30,000 + 2,000 + 200 + 50 + 6

Reading and writing numbers in the International System. The place value chart in the International System can be written as follows:

Periods

Millions Thousands ones

Place

Hun

dred

mil

lion

s

Ten

mil

lion

s

Mil

lion

s

Hun

dred

thou

sand

s

Ten

Tho

usan

ds

Tho

usan

ds

Hun

dred

s

Ten

s

One

s

H M T M M H Th T Th Th H T O

In the International System, millions comes after thousands. For example: 1732256 can be placed in the place value chart as follows:

H M T M M H Th T Th Th H T O

1 7 3 2 2 5 6

All the digits in the same period are read together and the name of the period (except the ones) is read together. The periods in the numerals are separated by commas.

1732256 can be read in the International System as one million, seven hundred thirty-two thousands, two hundred fifty six. 1732256 can be written in the International System as 1,732,256. Expanded form of 1,732,256 = 1,000,000 + 7,00,000 + 30,000 + 2,000 + 200 + 50 + 6

Representing numbers on abacus Abacus is a calculating tool. It consists of beads that can slide on vertical spikes. Numbers can be represented on an abacus by inserting suitable number of beads in the spikes.

Number of beads in the spike in the ones column = 5 Number of beads in the spike in the tens column = 6 Number of beads in the spike in the hundreds column = 3 Number of beads in the spike in the thousands column = 7 Number of beads in the spike in the ten thousands column = 3 Number of beads in the spike in the lakhs column = 4

The number represented on the abacus is 4,37,365.

Representing numbers on number line To draw a number line, we take a line and mark a point on it, labelling it as 0. Then, we mark the points to the right of zero at equal intervals and label them as 1, 2, 3 …, as follows:

On the number line, we can say that out of any two whole numbers, the number to the right of the other number is greater.

Comparing and ordering numbers Rule 1: If numbers with different number of digits are given, then the number that has more digits is greater. Example: 2,56,325 > 97,325 Rule 2: If numbers having the same number of digits are given, the the number with the greater digit at the leftmost place is greater. If the leftmost digits are the same, then we compare the next digit to the right and continue until the digits are different. Example: 6258 < 6289 Arranging numbers in the ascending order means arranging the numbers from smaller to greater. 325 < 437 < 567 < 892 << 1023

325, 437, 567, 892, 1023 are in the ascending order Arranging numbers in the descending order means arranging the numbers from greater to smaller. 1023 > 892 > 576 > 437 > 325

1023, 892, 567, 437, 325 are in the descending order

Formation of numbers from given digits The greatest and smallest numbers, without repetition, can be formed using any number of digits by arranging them in the descending and ascending order respectively. For example, if we form a 4-digit number from the digits, 9, 2, 7 and 3, then Greatest number = 9732 Smallest number = 2379 When repetition of digits is allowed, then the greatest number can be formed by writing the greatest digit as many times as the number is required. Similarly, the smallest number can be formed by writing the smallest digit as many times as required. Greatest number (with repetition) = 9999 Smallest number (with repetition) = 2222

Roman numerals Roman numeral is another system for writing numerals. In this system, symbols are used for representing numbers. The symbols are I, V, X, L, C, D and M.

Number 1 5 10 50 100 500 1000

Roman I V X L C D M

numeral

Rule 1: Any symbol cannot be repeated more than 3 times. Rule 2: If a smaller symbol is written to the left of a bigger symbol, then subtract it from the bigger symbol. Rule 3: If a smaller symbol is written to the right of a bigger symbol, then add it to the bigger symbol. Rule 4: V, L and D cannot be written to the left of a bigger symbol. Rule 5: V, L and D cannot be repeated, whereas I, X, C and M can be repeated

1 I

2 II

3 III

4 IV

5 V

6 VI

7 VII

8 VIII

9 IX

10 X

20 XX

25 XXV

30 XXX

39 XXXIX

45 XLV

49 XLIX

50 L

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