# 3rd Class Mathematics Playing with Numbers Operations on Numbers

Operations on Numbers

Category : 3rd Class

### A Rounding Numbers to the Nearest Ten

Rounding natural numbers to nearest ten means the given natural number is to be converted into its nearest 10. Rounding 14 to its nearest ten is 10. The nearest of 18 is 20 /therefore, on rounding 18 to its nearest ten the number 20 is obtained.

The salary of a worker in a company is Rs 4538. How much salary does the worker get in round figure to nearest 10?

(a) Rs 4530

(b) Rs 4500

(c) Rs 4540

(d) Rs 4340

(e) None of these

Explanation: Rs 4538 = Rs 4500 + Rs 38. and the nearest 10 of 38 is 40.

Successor

Successor of a number is obtained by adding 1 to the number. The successor of 1 is

1 + 1 = 2. Therefore, the successor of the number N is N + 1.

What should be added to the following to get the successor of its resulting number: 5 + 6 + 7?

(a) 1

(b) 2

(c) 3

(d) All of these

(e) None of these

Explanation 5 + 6 + 7 = 18 Hence, the successor of 18 = 18 + 1 = 19 which is obtained by adding 1 to the resulting number.

Predecessor

Predecessor of a number is obtained by subtracting 1 from the number. The predecessor of 4 = 4 - 1 = 3. Therefore, the predecessor of the number N is N - 1.

The predecessor of the resulting number of x + y + z is:

(a) (x + y + z)

(b) (x + y + z) - 1

(c) (x - 1) + y + z

(d) Both B and C

(e) None of these

Explanations

Predecessor of

Ascending Order

Ascending order of numbers in a group of numbers is the arrangement of numbers from smallest to biggest. In the ascending order of the numbers the smallest number comes first. The ascending order of the numbers: 45, 23, 34, 76, 87, 90 is 23 < 34 < 45 < 76 < 87 < 90.

There are five boxes and each box contains mangoes. The capacity of the given boxes with mangoes are 19 kg, 22 kg, 13 kg, 14 kg and 50 kg. Which one of the following options is the ascending order of the boxes?

(a) 22 kg < 50 kg < 14 kg < 19 kg < 13kg

(b) 13 kg < 14 kg < 19 kg < 22 kg < 50 kg

(c) 50 kg < 22 kg < 19 kg < 14 kg < 13 kg

(d) All of these

(e) None of these

Descending Order

Descending order is also called the decreasing order of the numbers. In descending order of more than one number, biggest number comes first and last number of the order is smallest number among them. Descending order of the numbers: 56, 34, 46, 23, 55 is 56 > 55 > 46 > 34 > 23.

There are 5 workers in a company and the salary of the workers in rupees is Rs 2234, Rs 3452, Rs 2235, Rs 5600 and Rs 7000. Which one of the following options is correct arrangement of the salary of the workers in descending order?

(a) 7000 > 5600 > 3452 > 2235 > 2234

(b) 5600 > 7000 > 3452 > 2235 > 2234

(c) 2234 > 7000 > 5600 > 2235 > 3452

(d) All of these

(e) None of these

Explanation

The descending order of the salary of the workers is 7000 > 5600 > 3452 > 2235 > 2234

Face Value and Place Value

The face value of a number is the number itself. Therefore, the face value of a number does not change on changing its place. In the number 4567, the face value of 6 is 6 if the number 6 changes its place form tens to hundred (4657) then the face value of the number 6 remains same as 6. In the place of a number changes according to the placement of the digit among the numbers. The place value of 6 in the number 4567 is 60. On changing the place of 6 in the number 4567 the number becomes 4657 and the place value of 6 in the number 4657 changes from 60 to 600.

Difference between the face and place value of 6 in the number 567423 is__.

(a) 59994

(b) 53994

(c) 59996

(d) All of these

(e) None of these

Explanations

The face value of 6 is 6 and its place value in the number 567423 is 60,000.

Hence, difference of 60,000 - 6 = 59994

Hindu Arabic or Indian Number System

The number system introduced by Indian is called Indian or Hindu Arabic number system. The base of the Indian number system is 10 and more than one digit number changes its places by ten times of the preceding places of the numbers. In the number 4563, the place of 6 is tens and the place of 5 is ten times (100) of place of 6. The place of next digit 4 is 10 times of the place of 5 (1000).

Look at the following table of place value of Indian number system:

 Ten lakhs Lakhs Ten thousand Thousand Hundred Tens Unit 9 8 7 3 5

In the above table the place values of digits of the number 98735 have been shown.

Place value of every number is counted from right of the number. The first digit from right of the number is unit second digit is tens and third, fourth, fifth digits are hundreds, thousands, ten thousands respectively.

International number system

Look at the following table of place value of International number system:

 Billions Millions Thousands Ten Billions Billions Hundred Millions Ten Millions Millions Hundred Thousand Ten Thousand Thousand Hundred Tens Ones 5 6 8 4 3 2 5 4 3 1

In the above table the place values of International number system have been shown. The first digit from the right of the number is read as ones, and second, third, fourth, fifth, sixth, seventh, eighth and ninth are tens, hundreds, thousands, ten thousands, hundred thousands, millions, ten millions, hundred millions, billions and ten billions respectively.

Look at the following table of comparison between place value of Indianand International number system:

 International Hundred Billions Ten Billions Billions Hundred Millions Ten Millions Million Hundred Thousand Ten Thousand Hundred Hundred Ten Ones Indians Kharab Ten Arab Arab Ten Crore Crore Ten lakh Lakh Ten Thousand Thousand Hundred Ten Units

In the above table the comparison between the Indian and International number system have been shown. Units of the Indian number is read as ones for the International number system. One lakh of the Indian number is read as hundreds, thousands for the International numbers.

What is the equivalent of 785408 in International number system?

(a) Seventy eight thousand fifth four hundred eight

(b) Seven hundred eighty five thousand four hundred eight.

(c) Seven eighty five thousands four hundred eight

(d) All of these

(e) None of these

Expanded Form of a Number

Expanded form means expansion of number as per the place value of every digit of the number. The expanded form of the number 215 = 2 x 100 + 1 x 10 + 1 x 5.

The expanded form of the number 45673 is written as 45673 = 4 x 10000 + 5 x 1000 + 6 x 100 + 7 x 10 + 3 x 1.

The expanded form of the number 21452 is:

(a)

(b)

(c)

(d) All of these

(e) None of these

Explanations

The expanded form of the number.

Roman Numerals

Roman numerals are based on certain letters of English alphabet. There are 7 letters of English alphabet which have been adopted for the notation of Roman numerals.

The value of these letters in Indian numbers are I = 1, V= 5, X = 10, L = 50, C = 100, D = 500 and M = 1,000. The first ten Roman numerals are I = 1, II = 2, III = 3, IV = 4, V = 5, VI = 6, VII = 7, VIII = 8, IX = 9, X = 10. In the Roman numeral IX the value of X is 10 /therefore, X is subtracted by 1 to form the number 9 or IX. Therefore, the value of the numeral IX = 10 - 1 = 9.

Which one of the following options is correct for the Roman notation of the year 2011?

(a) IXMM

(b) MMIX

(c) MMXI

(d) All of these

(e) None of these

Explanation There are two thousands in the number 2011, therefore, 2000 is denoted by MM and the number 11 is denoted by XI.

Every counting number is a natural number. How many natural numbers are there between the numbers 1 and 100?

(a) 98

(b) 88

(c) 100

(d) 99

(e) None of these

Explanations Natural numbers start from 1 and continue till infinity.

Therefore, all the numbers between 1 and 100 are natural numbers.

Round the number 319 to the nearest ten.

(a) 310

(b) 320

(c) 230

(d) All of these

(e) None of these

Which one of the following options differentiates the natural as well as whole numbers?

(a) Every natural number is a whole number

(b) Natural numbers start from 0 whereas whole numbers start from 0

(c) Natural numbers start from 1 whereas whole numbers start from 0

(d) All of these

(e) None of these

Which one of the following number is a prime number?

(a) 29

(b) 28

(c) 18

(d) All of these

(e) None of these

Explanations 29 is the prime number so it has only two factors 1 and 29.

Which one of the following numbers is the only even number that is prime?

(a) 8

(b) 6

(c) 7

(d) 2

(e) None of these

Explanation 2 is only even prime number.

The successor of solution of the following statement: 345 + 5 x 3 is:

(a) 361

(b) 359

(c) 345

(d) All of these

(e) None of these

Explication 345 + 5 x 3 = 360. Hence, the successor of 360 = 360+1= 361.

Which one of the following options is the expanded form of the number 96302?

(a) 9000 + 600 + 30 + 2

(b) 90000 + 6000 + 300 + 2

(c) 900000 + 60000 + 3000 +20

(d) All of these

(e) None of these

Explanation The expanded form of 96302 = 90000 + 6000 + 300 + 2

Which one of the following numbers completes the given sequence?

2, 3, 5, 8, 12____?

(a) 19

(b) 34

(c) 17

(d) All of these

(e) None of these

Explanation Given number series = 2, 2 + 1, 3 +2, 5 + 3, 8 + 4, 12 + 5

Convert the number 2356734 into International number system.

(a) Two hundred thirty five millions six thousand seven hundred thirty - four

(b) Two millions three hundred fifty six thousand seven hundred thirty - four

(c) Twenty three millions five hundred sixty seven hundred thirty - four

(d) All of these

(e) None of these

Explanations 2356734 in International number system is read as two millions three hundred fifty six thousand seven hundred thirty four.

The number 1234 is Indian numbers. Which one of the following options is correct form of the number 1234 in Roman numerals?

(a) MCCXXXIV

(b) MIIXXXIV

(c) MIVXXX

(d) All of these

(e) None of these

• Natural numbers start from 1.
• Whole numbers start from 0.
• The number which has only two factors is called Prime number.
• A composite number has more than 2 factors.
• If the difference of two prime numbers is 2, then both the prime numbers are called twin primes.
• Face value of a number is the number itself.
• Place value of a digit in the number is space occupied by the digits.

• Concept of positional number theory was first developed in India and this number theory was laterally adopted by western world.
• Sumerians were first developed the format of time division that we use today.
• Egyptians were used the word nfr for zero.
• Irrational numbers were first discovered by Hippasus.
• Tally bars were used for counting.
• Hindu Arabic numerals are the combination of 10 digits.

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