How many times does the number 1 appear between 1 and 1000?

If you prefix the numbers with $0$s so that they are all three digits, you can ask the number of $2$s in the range $000$ to $999$. You should be able to convince yourself that the digits are equally distributed in this range. There are $3000$ digits, so $300\ 2$s. Deleting $000$ and adding $1000$ does not change the result.

Number Systems is a value used for counting and measuring objects, and for performing arithmetic calculations. It is a method of writing for expressing numbers. It provides a unique representation to every number and presents the arithmetic and algebraic form of the number. It enables us to operate arithmetic operations like addition, subtraction, multiplication, and division.

An equation is a declaration that links two algebraic expressions of equal values with the ‘=’ sign. For example: In equation 8x + 4 = 7, 8x + 4 is the left-hand side expression and 7 is the right-hand side expression linked with ‘=’ sign.

What is a Number?

A word or symbol that indicates an amount is known as a number. The numbers 4, 6, 8, etc. are even numbers and 3, 5, 7, etc. are odd numbers. A number is a value formed by the combination of digits. These numbers are used to express algebraic quantities. An integer is an indication from a set of 10 characters ranging from 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Any amalgamation of integers represents a number. The size of a Number depends on the count of digits that are used for its development. For Example: 126, 128, 0.356, -12, 78, 94 etc.

Whole Numbers

Whole Numbers are the same as Natural Numbers, but they also include ‘zero’.  We can donate whole numbers by the symbol W. Whole numbers include all the natural numbers and 0 (zero).

We know that the numbers 1, 2, 3, 4, 5 are natural numbers. And the numbers 0, 1, 2, 3, 4, 5, 6 .. etc., are the whole numbers as they include 0 as well. Whole numbers are represented as W and Natural numbers are represented as N. Therefore, it is correct to say,

                                                                             W= {N} + 0

On the number line, everything which is on the right side of 0 (including 0) comes under whole numbers.

How many times does the digit 1 appear in the numbers 1 to 1,000?

Solution:

Hint: The easy method is to write the numbers in the range of 10, 100 and then count the number of 1’s in them

Steps to find out the solution:

First we will take the numbers in range of 10:

From the range of numbers 0 to 10, the digit 1 appears 2 time.

Now we add the numbers in range of 100

From the range of numbers 0 to 99, the digit 1 appears 20 times.

(They are: 1, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 31, 41, 51, 61, 71, 81, 91)

Observe that in number 11, 1 appears two times.

Now from 100 to 199 the digit 1 appears 120 times.

In this case the digit at hundreds place is 1. Therefore there are 120 1’s from 100 to 199.

Explanation- we have to find 1’s from 100, 101, 102……….. 199. At hundreds place of these 3 digit numbers 1 will come 100 times. At tens place 1 will come 10 times

That is in cases of 110, 111, 112, 113, 114…… 119. At units place 1 will come 10 times(101, 111, 121, 131……. 191) 

So add these:

100 + 10 + 10 = 120 so 1 appears 120 times.

Now from 200 to 299 we have 201, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 221, 231, 241, 251, 261, 271, 281, 291 the digit 1 appear 20 times.

Similarly,

From 300 to 399 we have 301,…311,….391. Again 20 times

From 400 to 499 we have 401,…411,…491. Again 20 times

From 500 to 599 we have 501,…511,…591. Again 20 times.

From 600 to 699 we have 601,…611,…691. Again 20 times

From 700 to 799 we have 701,…711,…791. Again 20 times

From 800 to 899 we have 801,…811,…891. Again 20 times

From 900 to 999 we have 901,…911,…991. Again 20 times

and then we have 1000 in which digit 1 appears 1 time

By adding all of the above, we get:

Total number of times = (20).(9) + 120 + 1

= 180 + 120 + 1

= 301

Therefore when we list numbers from 1 to 1000 the digit 1 is written 301 times.

Note: Don’t forget to count the digit 5 twice in numbers like 55, and also do not forget to count the digit 5 in hundredth’s place in the numbers from 500 to 599.

The Photoshop Raw format is a flexible file format for transferring images between applications and computer platforms. This format supports CMYK, RGB, and grayscale images with alpha channels, and multichannel and Lab images without alpha channels. Documents saved in the Photoshop Raw format can be of any pixel or file size, but they cannot contain layers.

The Photoshop Raw format consists of a stream of bytes describing the color information in the image. Each pixel is described in binary format, with 0 representing black and 255 white (for images with 16‑bit channels, the white value is 65535). Photoshop designates the number of channels needed to describe the image, plus any additional channels in the image. You can specify the file extension (Windows), file type (Mac OS), file creator (Mac OS), and header information.

In Mac OS, the file type is generally a four-character ID that identifies the file—for example, TEXT identifies the file as an ASCII text file. The file creator is also generally a four-character ID. Most Mac OS applications have a unique file creator ID that is registered with the Apple Computer Developer Services group.

The Header parameter specifies how many bytes of information appear in the file before actual image information begins. This value determines the number of zeroes inserted at the beginning of the file as placeholders. By default, there is no header (header size = 0). You can enter a header when you open the file in Raw format. You can also save the file without a header and then use a file-editing program, such as HEdit (Windows) or Norton Utilities (Mac OS), to replace the zeroes with header information.

You can save the image in an interleaved or non-interleaved format. If you choose interleaved, the color values (red, green, and blue, for example) are stored sequentially. Your choice depends on requirements of the application that will open the file.

How many 1s are there between 1 and 100?

∴ The digit 1 appear in number from 1 to 100 is 21.

How many times the digit 1 occurs from 100 to 1000?

∴ Required number=10×9=90.

What single digit appears most frequently between and including numbers 1 to 1000?

ANSWER: The most common digit is 1! Every number 1-9 appears precisely the same number of times in every ten numbers. But because we included the number 1,000, there's an extra occurrence of the number 1.

How many whole numbers are there between 1 and 1000?

Hence, their are 1001 whole numbers up to 1000.