Question

When numbers are very small or very large, it is convenient to either express the value in scientific notation and/or by using a prefix with the unit.
A pain-relieving pill has a mass of 0.005 g. Express the pill’s mass in grams using scientific notation or in milligrams.

Answer 1

$\boxed{ \ 5.0 \times 10^{-3} \ grams \rightarrow 5.0 \ milligrams \ }$

Further explanation

Scientific notation represents the precise way scientists handle exceptionally abundant digits or extremely inadequate numbers in the product of a decimal form of number and powers of ten.  

Put differently, such numbers can be rewritten as a simple number multiplied by 10 raised to a certain exponent or power. It is a system for expressing extremely broad or exceedingly narrow digits compactly.

Scientific notation should be in the form of  

$\boxed{ \ a \times 10^n \ }$

where  

$\boxed{ \ 1 \leq a \ < 10 \ }$

The number "a" is called "mantissa" and the exponent "n" the order of magnitude.

The exponent tells about the size of the number.

• A positive exponent indicates a number greater than or equal to 1.
• A negative exponent indicates a number between 0 and 1.

From the key questions asked, we face the standard form of 0.005 grams which will be converted into scientific notation.  

$0.005 = \frac{5}{1,000}$

• The coefficient (or mantissa) is 5, which has fulfilled the interval 1 ≤ a < 10.  
• The denominator consists precisely of three zero digits.

Hence, 0.005 grams is written in scientific notation as  $\boxed{ \ 5.0 \times 10^{-3} \ grams \ }$

Because 1 milligrams is equal to 10^{- 3} grams, then

$5.0 \times 10^{-3} \ grams \times \frac{1 \ milligrams}{10^{-3} \ grams}$

Hence, 0,005 grams is 5.0 milligrams.

In science, we frequently must deal with extremely small or incredibly large quantities. For a typical example, one of the recognized limitations of the microwave frequency is 300,000,000 Hz with a photon energy of 0.00000124 eV. They with many zeros can be impractical to work with, so scientists properly implement scientific notation.

The inverse of scientific notation is the standard form. To promptly change scientific notation into standard form, we reverse the process, move the decimal point to the right or left. This expanded form is called the standard form.

$\boxed{ \ 3.0 \times 10^{8} \ Hz \ \rightarrow 300,000,000 \ Hz \ or \ 300 \ MHz \ }$

$\boxed{ \ 0.00000124 \ eV \ \rightarrow 1.24 \times 10^{-6} \ eV \ or \ 1.24 \ \mu eV \ }$  

Learn more

1. How is 0.00069 written in scientific notation? brainly.com/question/7263463
2. How to explain 3,482,000,000 in scientific notation brainly.com/question/231855
3. Convert the number expressed in standard form to scientific notation brainly.com/question/10436883

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