Numbers 10.6.8

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Calculator Use

Numbers

The procedure to use the least to the greatest calculator is as follows: Step 1: Enter the numbers separated by a comma in the input field. Step 2: Now click the button “Solve” to get the output. Step 3: Finally, the ordered list of number from the least to the greatest will be displayed in the output field. It is very easy to use: Input or paste all numbers separated by comma, space or line break. Select Ascending (from small to large) or Descending (from large to small) order. Click Sort Numbers button.

Use this calculator to add, subtract, multiply and divide numbers in scientific notation, E notation or engineering notation. Answers are provided in three formats: scientific notation, E notation and engineering notation. You can also do operations on whole numbers, integers, and decimal numbers and get answers in scientific notation.

If you mark the check box the calculator automatically determines the number of significant figures in the answer. If you do not mark the check box, answers may contain more digits than are signficant.

Caution:See note regarding significant figures calculations.

Example Calculations

Use the links below to load a sample calculation into the calculator. In each example the input forms are different, but they all produce the same answers in scientific notation and E notation.

Standard Notation

10.6.8

Standard notation is the usual way to write numbers, with or without commas and decimals. This example calculation solves the addition problem 122500 + 3655. Click on the link and then refer to the calculator above. Note that the inputs are standard notation numbers. The answers are formatted in scientific notation and E notation.

Scientific Notation

In scientific notation a large number is converted to an equivalent decimal number between 1 and 10, multiplied by 10 raised to some power. Very small numbers are converted to an equivalent decimal number between 1 and 10, multiplied by 10 raised to some negative power. In this example scientific notation calculation we're solving 1.225 × 105 + 3.655 × 103:

E Notation

E notation is also known as exponential notation. E notation is the same as scientific notation where a decimal number between 1 and 10 is multiplied by 10 raised to some power. In E notation the 'times 10 raised to a power' is replaced with the letter e in either uppercase or lowercase. The number after the 'e' indicates how many powers of 10. In this example calculation we're adding 1.225e5 and 3.655e3:

Note: Doing Math With Significant Figures

There are some cases where you would not want to auto-calculate significant figures. If your calculation involves a constant or an exact value as you might find in a formula, do not check the 'auto-calculate' box.

For example, consider the formula for diameter of a circle, d = 2r, where diameter is twice the length of the radius. If you measure a radius of 2.35, multiply by 2 to find the diameter of the circle: 2 * 2.35 = 4.70

If you use this calculator for the calculation and you mark the 'auto-calculate' box, the calculator will read the 2 as one significant figure. Your resulting calculation will be rounded from 4.70 to 5, which is clearly not the correct answer to the diameter calculation d=2r.

You can think of constants or exact values as having infinitely many significant figures, or at least as many significant figures as the least precise number in your calculation. Use the appropriate number of significant figures when you input exact values in this calculator. In this example you would want to enter 2.00 for the constant value so that it has the same number of significant figures as the radius entry. The resulting answer would be 4.70 which has 3 significant figures.

Additional Resources

See our Rounding Significant Figures Calculator for more information on significant figures.

See the Scientific Notation Converter to convert a number into scientific notation or E notation.

If you need a scientific calculator see our resources on scientific calculators.

Sunday, February 3rd, 2019

Number series is important for various competitive examinations. In this category of questions, a series of various numbers is given with a blank . We are supposed to find out a pattern between every number and its predecessor and find out the answer using the same logic.

For the purpose of better understanding of the concept, we classify them into the following categories:

  1. Series with a constant difference
  2. Series with an increasing difference
  3. Series with a decreasing difference
  4. Squares/ Cubes series
  5. Combination of different operations
  6. Miscellaneous

The best approach :

The best way of approaching number series questions is to observe the difference between various terms. If we see a constant difference, then it’s a constant difference series. If the difference is decreasing or increasing by a constant number , then it is a series of type 2 or type 3. But if there is no such increase or decrease in the difference, then try dividing the 2nd term with the first, third with the second and so on. If you obtain the same number each time, then it is a product series.

Also , if none of these seem to work, then you can try writing each term as a product of two factors and try to see if there is any pattern. If you still observe no pattern and the difference is increasing or decreasing rapidly, then try to look for square/ cube series.

If the difference is increasing and decreasing in some fixed manner, then it is a type of combination series.

Let us look at each type of series in greater depth:

1. Series with a constant difference

In this kind of series, any 2 consecutive numbers have the same difference between them.

For example : 1 , 5 , 9 , 13 , ?

We can observe that we are adding 4 to the previous number to obtain the next number. So, answer here will be 13+4 = 17.

2. Series with an increasing difference

In this type of series, the difference between two consecutive terms keep on increasing as we move forward in a series. Let us try to use this theory in a question.

1,2,4,7,11,16,?

We can clearly observe that the series is increasing with the difference : +1, +2, +3 ,+4 , +5.

So, we will obtain our number by adding 6 to 16 which gives us 22.

3. Series with a decreasing difference

In this type of series, the difference between two consecutive terms keep on decreasing as we move forward in a series. Let us try to use this with some modification in the previous question that we did.

16,11,7,4,2, ?

We can clearly observe that the series is decreasing with the difference : -5, -4, -3 ,-2 .

So, we will obtain our number by subtracting 1 from 2 which gives us 1.

4. Squares/ Cubes series

We can have series where the terms are related to the squares/ cubes of numbers. We can have a lot of variations here. Let us look at some of the possibilities.

1, 9, 25, 49 , ?

We can observe that the above series is square of odd numbers starting from one. So our answer will be 9^2 = 81.

Let us look at another example:

1 , 1 , 2 , 4 , 3 , 9 , 4 , ?

We observe here that the series is formed by writing numbers starting from 1 along with its square as the next number i.e. ( 1 , 12) , (2, 22) and so on. So we obtain our answer as 16 which is 42.

Consider the following question:

9 , 28 , ? , 126.

The answer for above question will be 65, let us discuss how.

9 , 28 , ? , 126.

( 23+1) (33+1) (53+1)

The blank should have 43+1. Hence, the answer is 65.

5. Combination of different operations

This kind of series has more than 1 type of arithmetic operations which have been performed or it can also have 2 different series which have been combined to form a single series. This kind of series is the the most asked and the most important among all the types of series that we have discussed so far.

Consider the series:

1, 3 , 6 , 2 , 6 , 9 , 3 , 9 , ?

The first term 1 is multiplied by 3 to give the second term, 3 has been added to the second term to get the third term. The next term is 2 which is 1 more than the 1st term. It is multiplied with 3 to give next term and the process is continued. With this process, we obtain our answer as 12.

Consider the series:

6, 10 , 7, 11 , 8 , 12 , ?

We can see that the above series is a combination of 2 simple series:

1st , 3rd , 5th terms make an increasing series of 6 , 7 , 8….. . The 2nd , 4th and 7th term make a series of 10 , 11 , 12… . So, our answer will be 9 which is the 7th term of the original series.

6. Miscellaneous series

Some series do not come under any of the above mentioned categories but are very important and also asked in many examinations.

The series of prime numbers or any other related operation done on it comes under this category.

Consider the example:

9, 25 , 49 , 121 , ?

The above series is the squares of prime numbers. So next term will be square of 13 which is 169.

Try out the following questions:

1. 49 , 1625 , 3649 , ?

Solution : Each term in the above series is combination of squares of 2 numbers i.e.

22 32 , 42 52 , 62 72 . So, our answer will be 6481.

Numbers 10.6.8

2. Look at this series: 40, 40, 26, 26 , 12 , ? … What number should come next?

Solution:Answer is 12. Each number is repeated or firstly 0 is added to each number and then 14 is subtracted from it.

3. 2 , 4 , 11 , 37 , ?

Solution: (2*1) + 2 =4

(4*2) + 3 = 11

(11*3) + 4 =37

(37*4) + 5 = 153

4. 6 , 3 , 3, 4.5 , 9, ?

Solution : We see that no decreasing or increasing difference logic is applicable here. So, we find out the ratios of every term with its predecessor. We get the following values: 0.5 , 1 , 1.5 , 2 . This makes it clear that 9 should be multiplied by 2.5 in order to obtain the next number.

Therefore, the answer is 9* 2.5 = 22.5 .

5. 8 , 15 , 26 , 39 , ?

Number 1068

Solution: Let us start by finding out the difference between every pair of consecutive terms:

15-8=7

26-15=11

39-26=13

We observe that the difference is the series of prime numbers. According to this logic , 17 should be added to 39 to obtain the answer. Hence, the answer is 56.

6. Consider the series: 42, 40, 36, 34, 30, 28, … What number should come next?

Solution: 24 is the answer . we are performing the operations : – 2, -4. )

7. 24 , 30 , 36 , 42 , 54 , 60 , 68 . Find out the wrong term in the series.

Solution: Each term is the sum of 2 consecutive prime numbers.

24 = 11+ 13

30 = 13+ 17

36= 17+ 19

So, according to this logic, 54 is the wrong term. We should have 52 in its place.

8. 17 , ? , 102 , 408 , 2040 . Find out the missing number.

Solution: We can see that the series is increasing rapidly. Let us find out the ratios of every 2 consecutive terms.

2040/ 408 = 5

Numbers 10.6.8 Pdf

408/ 102 =4

102/ ? =3

Therefore , our answer is 34.

9. 49, 47, 45 , 42 , 40 ,38 , 35, 33 ,31 , 28, ? , ?

Solution: 26 24 is the answer. It is an alternating subtraction series where 2 is subtracted twice and then 3 is subtracted one and this pattern is continued.

10. 1 , 8 , 9 , 64 , 25 , 216 , ?

Solution: The answer for this is 49. The following pattern is being followed:

Numbers 10.6.8 Book

12 , 23 , 32 , 43 , 52 , 63 , 72.

11. 1 , 4 , 9 , 1 , 6 , 2 , 5 , ? , ?

Solution: At a first glance it is very difficult to see any kind of pattern here. Any kind of pattern among increasing, decreasing, product , square , cube etc does not seem to be working here.

But we can observe that 1 , 4 , 9 are squares of 1 , 2 , 3 respectively. And after that should come 16 but instead of that we have 1 ,6 . After that instead of 25 , we have 2, 5. So , we can come to the conclusion that when the squares start taking 2 digits, instead of writing them as a 2 digit number , we simply separate them into 2 different terms. So, our next term will be 3 ,6 .

Tip: During the exam, if you feel that you are not able to figure out the pattern in 30-45 seconds, it is better to leave the question for the time being and move on to the next one. You can revisit the question later , if time permits.

Numbers 10.6.8 Version

CAT Questions related to Logical Reasoning

All questions from CAT Exam Logical Reasoning
Logical Reasoning – Set 1: A high security research lab requires the researchers to set a pass key sequence based on the scan of the five fingers of their left hands.
Logical Reasoning – Set 2: Eight friends: Ajit, Byomkesh, Gargi, Jayanta, Kikira, Manik, Prodosh and Tapesh are going to Delhi from Kolkata
Logical Reasoning – Set 3: In an 8 X 8 chessboard a queen placed anywhere can attack another piece if the piece is present in the same row
Logical Reasoning – Set 4: A tea taster was assigned to rate teas from six different locations – Munnar, Wayanad, Ooty, Darjeeling, Assam and Himachal.
Logical Reasoning – Set 5: Four cars need to travel from Akala (A) to Bakala (B). Two routes are available, one via Mamur (M) and the other via Nanur (N).
Logical Reasoning – Set 6: A new airlines company is planning to start operations in a country.
Logical Reasoning – Set 7: In a square layout of size 5m × 5m, 25 equal sized square platforms of different heights are built.
Logical Reasoning – Set 8: There are 21 employees working in a division, out of whom 10 are special-skilled employees (SE) and the remaining are regular skilled employees (RE).
Logical Reasoning – Set 9: Healthy Bites is a fast food joint serving three items: burgers, fries and ice cream.

Numbers 10.6.8

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    • 4.9/5(118votes )

    1. Nice article. Categorising number series and then explaining each is very helpful.

    2. Such an informative article… Thanks a lot.

    3. 367
      564
      Then
      478
      ?
      The answer is not 675

    4. □+□+□=30 fill box given below number 1,3,5,7,9,11,13,15 you can repeat any number

    5. □+□+□=30
      fill boxes given below numbers
      1,3,5,7,9,11,13,15
      You can also repeat any number

    6. 2.3 : 8 :: 3.4 : ?

    7. 7, 23, 55,?, 91

    8. 8,108,576,2000,5400,? Next number in this series

    9. 13 68 42 26 55 ??

    10. Complete the series given below. 2,2,2,2,5,9,2,10,__________
      a) 15. C) 28
      D) 23 b)13

    11. what comes next 18 11 13 21.5 45

    12. 48,55,11? Please tell me the series type and next number in the series ?

    13. 0,0,20,115 next no.

    14. Given the series:5+3+9+6+13+12+17+24+….Calculate the sum of the first 30 terms of the series.

    15. 6,10,8,12,24,60
      Find wrong term

    16. 11+13+6=30.

      We can use 9 as six as well.

    17. 18:5::12:? Find ratio
      Ans:a )4 b) 10 c)3 d) 6

    18. 6,4,15,49?solve this
      A.105
      B.145
      C.188
      D.201

      Tell me this tricky answer

    19. 46 21 25 39 54 32
      13 15 19
      9 13 ?

    20. 55,100,59,50,?
      Challenge

    21. I want to solve some problems

    22. Can anyone send answer to this? 2,5,3,8,5,11,6,__??

    23. 4 ,25 ,81?

    24. Pls tell me soon
      13 ,17,23,33,49,75—?
      Pls solve this series n tell me

    25. 6,32,152,450,? Solve it

    26. 18,16,10,4,? Solve it

    27. 1,1,2,5,8,?,21

    28. 49 56 26
      91 72 19
      51 68 ?
      Please solve this

    29. 64,32,16,8,_,_ please solve this..

    30. 12 5 16
      8 7 18
      6 3 ?

    31. 3 ,3,9,11,59,? Ke bad kya hoga

    32. 26. 18. 10. 1. 9. 7. 5. 4. 1. 10. 5. ?

    33. 3:35 :: 19:? Plz ans

    34. 28 7 21
      44 2 ?
      36 4 22
      Please solve this

    35. 21,?, 45,180,185
      Options
      42,33 , 41,63

    36. 13,17,26,42,67
      options 103,91,109,111

    37. 8.5.13.53.276.?

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