# How do you write 0.076 000 000 in scientific notation?

Mar 30, 2015

Okay start off by removing excess 0's

0.076 000 000= 0.076

Then this in fraction ;

$\frac{76}{1000}$

Then decimal in in fraction;

$\frac{7.6}{100}$

$\therefore 0.076 000 000 = 7.6$ x $\frac{1}{100} = 7.6$ x${10}^{- 2}$

Mar 30, 2015

The answer is $7.6000000 \times {10}^{- 2}$.

According to the rules for significant figures, trailing zeroes after a decimal are significant, so the six trailing zeroes should remain in the answer. http://www.chemteam.info/SigFigs/SigFigRules.html

A number written in scientific notation includes a coefficient times the base 10 raised to some power. The coefficient consists of a non-zero, single-digit integer, 1 - 9 inclusive, in front of the decimal.

When converting a number written in standard form, such as $0.076000000$, you move the decimal to the right two places, so that the coefficient becomes $7.6000000$. The exponent (power) on the base 10 is equal in number to the number of places the decimal was moved. If the decimal is moved to the right, the exponent is negative. If the decimal is moved to the left, the exponent is positive. So in this example, the decimal was moved to the right two places, so the number in scientific notation is $7.6000000 \times {10}^{- 2}$.

Other examples:
$3502 = 3.502 \times {10}^{3}$
$3502.000 = 3.502000 \times {10}^{6}$
$0.00000298 = 2.98 \times {10}^{- 6}$
$0.000002980 = 2.980 \times {10}^{- 6}$