How do you simplify and write #0.0007 xx 190# in scientific notation?

2 Answers
May 23, 2017

Answer:

See a solution process below:

Explanation:

First, write each term in scientific notation:

For #0.0007# we need to move the decimal point 4 places to the right therefore the exponent of the 10s term will be negative:

#0.0007 = 7.0 xx 10^-4#

For #190# we need to move the decimal point 2 places to the left therefore the exponent of the 10s term will be positive:

#190 = 1.9 xx 10^2#

We can now rewrite this expression as:

#0.0007 xx 190 => (7.0 xx 10^-4)(1.9 xx 10^2) => #

#(7.0 xx 1.9)(10^-4 xx 10^2) => 13.3(10^-4 xx 10^2)#

We can now use this rule of exponents to combine the 10s terms:

#x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))#

#13.3(10^color(red)(-4) xx 10^color(blue)(2)) => 13.3 xx 10^(color(red)(-4) + color(blue)(2)) => 13.3 xx 10^-2#

To put this in true scientific notation we need to move the decimal point one place to the left so we need to add #1# to the 10s exponent:

#13.3 xx 10^-2 => 1.33 xx 10^(-2 + 1) => 1.33 xx 10^-1#

May 23, 2017

Answer:

A lot of detail provided to help with understanding.

#"1.33xx10^(-1)#

Explanation:

Note that #10^0=1" and that "10^1=10#

#0.0007->0.0007xx1/10^0#

#0.0007->0.007xx1/10^1#

#0.0007->0.07xx1/10^2#

#0.0007->0.7xx1/10^3#

#0.0007->7.0xx1/10^4#
..............................................................................

#190->190xx10^0#

#190->19.0xx10^1#
...........................................................................

So we can write: #" "0.0007xx190# as

#7xx19xx1/10^4xx10#

Not that #7xx19# is the same as #(7xx20)-7=140-7=133# giving:

#133xx1/10^4xx10" "->133xx1/10^3#

but #133" is the same as "1.33xx10^2# giving:

#1.33xx10^2/10^3#

#1.33xx1/10^" "->" "1.33xx10^(-1)#