What are the multiples of 9 up to 1000?
Understand the Problem
The question is asking for all the multiples of 9 that fall within the range from 1 to 1000. To solve this, we will list all the numbers that can be expressed as 9 times an integer, ensuring that the result is less than or equal to 1000.
Answer
Answer for screen readers
The multiples of 9 that fall within the range from 1 to 1000 are:
$$ 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, 117, 126, 135, 144, 153, 162, 171, 180, 189, 198, 207, 216, 225, 234, 243, 252, 261, 270, 279, 288, 297, 306, 315, 324, 333, 342, 351, 360, 369, 378, 387, 396, 405, 414, 423, 432, 441, 450, 459, 468, 477, 486, 495, 504, 513, 522, 531, 540, 549, 558, 567, 576, 585, 594, 603, 612, 621, 630, 639, 648, 657, 666, 675, 684, 693, 702, 711, 720, 729, 738, 747, 756, 765, 774, 783, 792, 801, 810, 819, 828, 837, 846, 855, 864, 873, 882, 891, 900, 909, 918, 927, 936, 945, 954, 963, 972, 981, 990, 999 $$
Steps to Solve
- Identify the first multiple of 9 The first multiple of 9 is simply 9 multiplied by 1.
$9 \times 1 = 9$
- Identify the last multiple of 9 within the range Next, we need to find the largest integer ( n ) such that ( 9n \leq 1000 ). To do this, we can divide 1000 by 9.
$$ n = \left\lfloor \frac{1000}{9} \right\rfloor $$
Calculating that gives:
$$ n \approx 111.11 \implies n = 111 $$
- List all multiples of 9 Now that we have determined that the largest integer ( n ) is 111, we can find all the multiples of 9 from 1 to 111. The multiples of 9 can be represented as:
$$ 9, 18, 27, \ldots, 9n $$
Thus:
$$ 9 \times 1, 9 \times 2, \ldots, 9 \times 111 $$
- Write down the multiples Calculating the multiples of 9 yields:
The multiples are:
$$ 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, 117, 126, 135, 144, 153, 162, 171, 180, 189, 198, 207, 216, 225, 234, 243, 252, 261, 270, 279, 288, 297, 306, 315, 324, 333, 342, 351, 360, 369, 378, 387, 396, 405, 414, 423, 432, 441, 450, 459, 468, 477, 486, 495, 504, 513, 522, 531, 540, 549, 558, 567, 576, 585, 594, 603, 612, 621, 630, 639, 648, 657, 666, 675, 684, 693, 702, 711, 720, 729, 738, 747, 756, 765, 774, 783, 792, 801, 810, 819, 828, 837, 846, 855, 864, 873, 882, 891, 900, 909, 918, 927, 936, 945, 954, 963, 972, 981, 990, 999$$
The multiples of 9 that fall within the range from 1 to 1000 are:
$$ 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, 117, 126, 135, 144, 153, 162, 171, 180, 189, 198, 207, 216, 225, 234, 243, 252, 261, 270, 279, 288, 297, 306, 315, 324, 333, 342, 351, 360, 369, 378, 387, 396, 405, 414, 423, 432, 441, 450, 459, 468, 477, 486, 495, 504, 513, 522, 531, 540, 549, 558, 567, 576, 585, 594, 603, 612, 621, 630, 639, 648, 657, 666, 675, 684, 693, 702, 711, 720, 729, 738, 747, 756, 765, 774, 783, 792, 801, 810, 819, 828, 837, 846, 855, 864, 873, 882, 891, 900, 909, 918, 927, 936, 945, 954, 963, 972, 981, 990, 999 $$
More Information
Multiples of 9 are found by multiplying 9 by whole numbers (1, 2, 3, ...) until the product exceeds 1000. Because 9 is a