need help with one problem

[FrustratedMathMan]

What is the sum of the digits in the decimal(multiplied)
2^1999*5^2002

 

[pka]

2<SUP>1999</SUP>*5<SUP>2002</SUP>=10<SUP>1999</SUP>*5<SUP>3</SUP>. Now 10<SUP>1999</SUP> is a number with 1 followed by 1999 zeros.

 

[stapel]

You're gonna kick yourself....

. . .2¹⁹⁹⁹ 5²⁰⁰²

. . . . .= (2¹⁹⁹⁹ 5¹⁹⁹⁹) (5³)

. . . . .= ((2×5)¹⁹⁹⁹)(125)

. . . . .= (10¹⁹⁹⁹)(125)

. . . . .= ...

:wink:

Eliz.

 

[FrustratedMathMan]

You're gonna kick yourself....

. . .2¹⁹⁹⁹ 5²⁰⁰²

. . . . .= (2¹⁹⁹⁹ 5¹⁹⁹⁹) (5³)

. . . . .= ((2×5)¹⁹⁹⁹)(125)

. . . . .= (10¹⁹⁹⁹)(125)

. . . . .= ...

:wink:

Eliz.

so (10^1999)(125) is the farthest i can break it down???

 

[stapel]

:shock:

You really don't know what 10¹⁹⁹⁹, or, as pka put it, "1 followed by 1999 zeroes", will look like after you multiply it by 125?

Eliz.

 

[FrustratedMathMan]

:shock:

You really don't know what 10¹⁹⁹⁹, or, as pka put it, "1 followed by 1999 zeroes", will look like after you multiply it by 125?

Eliz.

Nope.

Would it be 125???

 

[Denis]

125 * 10 = 1250 : 1 followed by 1 zero
125 * 100 = 12500 : 1 followed by 2 zeroes
...
125 * 100000....1999 of them!....0000000 = 12500000...1999 of them...000