How do you write #0.000 000 000 154# in scientific notation?

2 Answers
Mar 9, 2016

Answer:

#0.000000000154=1.54*10^-10#

Explanation:

#0.000000000154=1.54*10^-10#[Ans]

Mar 9, 2016

Answer:

In depth explanation of how to obtain#" "1.54xx10^(-10)#

Explanation:

We need to be able to convert this number so that it looks line 1.54 but in such a way that its actual value has not changed.

Consider the example of 32. This would will to look like 3.2

If we divide it by 10 we then have#" "32/10 =3.2#

But this has changed its value so we need a slightly different approach.

#color(blue)("Point 1")#

#color(brown)("If we multiply a number by 1 we do not change its value")#

#color(blue)("Point 2")#

#color(brown)("The value of 1 can be presented in many ways")#
For this type of calculation we need it to be of format #n/n# where #n# is any number other than zero

#color(blue)("Method")#

The way to use this method for our example is to do this:

#32xx10/10#

#32/10 xx10#

Divide the denominator of 10 into 32 giving

#3.2xx10#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Using this method to solve your question")#

Given:#" "0.000000000154#

To achieve 1.54 we need to keep the decimal point where it is and slide the number towards the left for 10 digits.

To mathematically achieve this we have #0.000000000154xx10^10#

But #10^10# is not the value 1

So we need to multiply by #10^10/10^10# giving

#0.000000000154xx10^10xx1/10^10#

Apply the process of #0.000000000154xx10^10# leaving

#1.54xx 1/10^10#

But another way of writing #1/10^10" is "10^(-10)# which means #-: 10^10#

This gives: #1.54xx10^(-10)#