1,200

So, the shape of the model for 10,000 will be long. Possible answer: each model is 10 times the size of the previous model, so the model for 100,000 will be 10 times the size of the model for 10,000. Possible answer: use 10 ten thousands longs to make a flat that shows 100,000.

The place value is the position of a digit in a number. It determines the value that the number holds. Let’s take a basic example: Comparing the numbers 700, 70, and 7; the digit “7” has a different value depending on its place within the number.

In our decimal number system, the value of a digit depends on its place, or position, in the number. Each place has a value of 10 times the place to its right.

When alone, each number (or digit) is in the ones place. That means its value is simply the digit itself. For example, 9 stands for 9 ones, and 4 stands for 4 ones.

3900

∴ The required numbers are 4, 24, 40, 44, 48, 64, 84. Clearly, there are 7 such numbers. Was this answer helpful?

The first 100 whole numbers are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25,26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74.

There are 18 whole numbers from 1 to 100 that contain the digit 2 exactly once. They are 2, 12, 20, 21, 23, 24, 25, 26, 27, 28, 29, 32, 42, 52, 62, 72, 82, and 92. Nine of these numbers have 2 in the units position, and nine have the digit 2 in the tens position.

Now we have over counted by 1 because we extended the range so there are 531440 numbers that don’t contain any 1 so there must be 999999−531440=468559 that do contain at least one 1. HINT: Consider those integers as six character strings over the alphabet {0,1,2,3,4,5,6,7,8,9}. How many strings don’t contain 1?