In which number is the value of the 9 ten times the value of 9 in the number 920?
Let's begin by writing out the two numbers, 9 and 920, and determining the value of the digit 9 in each number:
- In the number 9, the value of the digit 9 is simply 9.
- In the number 920, the value of the digit 9 depends on its position. The 9 is in the hundreds place, so its value is 9 x 100 = 900.
Now we need to find a number in which the value of the 9 is ten times the value of the 9 in 920. In other words, we need to find a number in which the value of the digit 9 is 10 x 900 = 9000.
Let's try some numbers:
- In the number 9, the value of the digit 9 is only 9, so this doesn't work.
- In the number 99, the value of the first 9 is 9 and the value of the second 9 is 9 x 10 = 90, so the total value is 9 + 90 = 99. This doesn't work either.
- In the number 999, the value of the first two 9s is 9 + 90 = 99, and the value of the third 9 is 9 x 100 = 900, so the total value is 99 + 900 = 999. This still doesn't work.
- In the number 9999, the value of the first three 9s is 99 + 900 = 999, and the value of the fourth 9 is 9 x 1000 = 9000, so the total value is 999 + 9000 = 9999. This is the number we're looking for!
So the answer is 9999. In this number, the value of the digit 9 is ten times the value of the 9 in 920 (9000 = 10 x 900).