How do you calculate #(3.6 times 10^15) × (8 × 10^21)#?

1 Answer
Sheffy
May 13, 2016

#2.88xx10^37#

Explanation:

#3.6xx 10^15 xx 8 xx 10^21#

#= 3.6xx 8 xx 10^15 xx 10^21#

Let's combine the #10"'s"#:

#= 3.6xx 8 xx 10^(15+21)#

#= 3.6xx 8 xx 10^(36)#

Multiply the numbers:

#= 28.8 xx 10^36#

This is NOT in the scientific form.

#color(red)(2.88 xx 10^n)# is the correct way of writing the number in the scientific notation .

Note: only 1 whole number should be on the left side of the decimal point. The remaining numbers come on the right side of the decimal point and this number is then multiplied by a power of #10#, as required.

Now, to write # 28.8 xx 10^36# in scientific notation.

We can write #28.8 =2.88xx10#.

Then, #28.8 xx 10^36#

#=2.88 xx 10 xx 10^36#

Combine the #10"'s"#

#=2.88 xx 10^(1+36)#

#color(red)(=2.88 xx 10^37)#

#color(blue)("Some examples to understand scientific numbers: ")#

  • #color(blue)( 80000 " in scientific notation will be " 8 xx 10^4)#
  • #color(blue)( 1234 " in scientific notation will be " 1.234xx 10^3)#
  • #color(blue)( 452.42 " in scientific notation will be " 4.5242 xx 10^2)#
  • #color(blue)( 0.004 " in scientific notation will be " 4 xx 10^-3)#
  • #color(blue)( 0.0126 " in scientific notation will be " 1.26 xx 10^-2)#
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