nagyhableany5610 nagyhableany5610
  • 21-07-2022
  • Mathematics
contestada

The positive integers $1,$ $2,$ $3,$ $\dots$ are listed in order. What is the $1000^{\rm th}$ positive integer with an odd number of digits

Respuesta :

LammettHash
LammettHash LammettHash
  • 21-07-2022

There are 9 positive integers with 1 digit (1 - 9).

There are 90 integers with 2 digits (10 - 99).

There are 900 integers with 3 digits (100 - 999).

There are 9000 integers with 4 digits (1000 - 9999).

And so on. It stands to reason that there are [tex]9\times10^{n-1}[/tex] integers with [tex]n[/tex] digits.

Now,

1000 = 9 + 900 + 91

so the 1000th positive integer with an odd number of digits is the 91th number with 3 digits, which is 190.

Answer Link

Otras preguntas

The manufacturing cost of a cell phone was $124. Sellers first marked up the cost by 20 percent. Sales were poor, so sellers decreased the markup to 15 percent.
What Are The Advantage And Disadvantage Of Democratic Style?
what groups of rocks does sandstone belong in
Why Did The Civil Rights Movement Fall Apart In The Late 1960s And Early 1970s? Was The Movement A Success?
A company sells cookies in 250-gram packs. When a particular batch of 1,000 packs was weighed, the mean weight per pack was 255 grams and the standard deviation
Choose the correctly spelled word. aufull awful
Which Of The Following Is Not A Government Debt Instrument? ... Which One Is Not A Government Bebt Instrument? T-bill, Fib, Pib, Tfc, Dsg, ...
Do you think Edward Snowden was right to leak secret NSA information about how the government spies on citizens?
what does "Sie es bitte" mean?
What territory did the Mexican- American War open up to American settlers?