what percentage of the numbers from 101 to 1000 have 9 in the unit's digit

a)10%

b12%

c15%

d20%

We are tasked with finding what percentage of the numbers from 101 to 1000 have 9 in the unit's digit.

### Step 1: Total numbers from 101 to 1000
The numbers from 101 to 1000 form a sequence. We can calculate the total number of terms:

\[
1000 - 101 + 1 = 900 \text{ numbers}
\]

### Step 2: Numbers with 9 in the unit's digit
A number will have 9 in its unit's digit if it ends in 9. Let's identify such numbers between 101 and 1000:

\[
109, 119, 129, \dots, 999
\]

This forms an arithmetic sequence where:
- The first term \( a = 109 \)
- The common difference \( d = 10 \)

To find the number of terms in this sequence, we use the formula for the nth term of an arithmetic sequence:

\[
a_n = a + (n - 1)d
\]

Substitute \( a_n = 999 \), \( a = 109 \), and \( d = 10 \):

\[
999 = 109 + (n - 1) \times 10
\]
\[
999 - 109 = (n - 1) \times 10
\]
\[
890 = (n - 1) \times 10
\]
\[
n - 1 = 89 \quad \Rightarrow \quad n = 90
\]

So, there are 90 numbers between 101 and 1000 that end with 9.

### Step 3: Percentage calculation
The percentage of numbers that have 9 in the unit's digit is:

\[
\text{Percentage} = \left( \frac{90}{900} \right) \times 100 = 10\%
\]

Thus, the correct answer is:
\[
\boxed{10\%}
\]

---

Would you like more details or have any questions? 

Here are 5 related questions for further exploration:
1. What percentage of numbers from 101 to 1000 have 7 in the unit's digit?
2. How many numbers from 1000 to 2000 have 9 in the tens digit?
3. What percentage of numbers from 1 to 1000 have 5 in the unit's digit?
4. How many numbers from 101 to 1000 are divisible by 9?
5. What percentage of numbers from 1 to 500 have 0 in the unit's digit?

**Tip:** When solving arithmetic sequence problems, always double-check the first term and the common difference to ensure accuracy.

What percentage of the numbers from 101 to 1000 have 9 in the unit's digit?

a) 10%
b) 12%
c) 15%
d) 20%

Find out what percentage of numbers from 101 to 1000 have 9 in the unit's digit. Using arithmetic sequences and percentage formulas, we determine that the answer is 10%. This math problem is suitable for students in Grades 6-8.

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