Question

Jodi writes all the numbers between 300 and 400 with fewer than 2 ones. How many numbers does Jodi write?

Answer 1

To determine how many numbers between 300 and 400 have fewer than 2 ones, we combine cases where only one digit or none is '1'. We find that Jodi writes 99 numbers between 300 and 400 that fit this criterion.

Step-by-step explanation:

The question asks us to find how many numbers between 300 and 400 have fewer than 2 ones. To have fewer than 2 ones, a number can either have one '1' or no '1s' at all. We know that all the numbers in this range will start with a '3' since they represent the hundreds place.

For the tens place, we can have any digit from 0 to 9, which gives us 10 possibilities. However, when it comes to the ones place, if we have '1' in the tens place, we can only have digits 0, and 2-9 in the ones place to avoid having more than one '1'. If we have any other digit in the tens place, we can have any digit in the ones place including '1'. So, we have one scenario with 9 possibilities (0, 2-9) and nine scenarios with 10 possibilities each.

Therefore, we calculate the total as follows: 1 scenario * 9 possibilities + 9 scenarios * 10 possibilities = 1*9 + 9*10 = 9 + 90 = 99 numbers.

Answer 2

There are 98 numbers in between 300 and 400 with fewer than 2 ones.

Step-by-step explanation:

As we know that there are 99 numbers between 300 and 400 and we know that there we have to find the number which have fewer than 2 ones.

Since all the number except 311 have less than 2 ones which could also be said as fewer than 2 ones.

( 311 have two ones in it)

Hence, the number between 300 and 400 with fewer than 2 ones are:

98 (Since, 99-1= 98 )