Question

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

Answer : The mass represented in scientific notation as $5.0\times 10^{-3}g$  and the mass in milligram is, 5 mg

Explanation :

Scientific notation : It is the representation of expressing the numbers that are too big or too small and are represented in the decimal form with one digit before the decimal point times 10 raise to the power.

For example :

5000 is written as $5.0\times 10^3$

889.9 is written as $8.899\times 10^{-2}$

In this examples, 5000 and 889.9 are written in the standard notation and $5.0\times 10^3$  and $8.899\times 10^{-2}$  are written in the scientific notation.

If the decimal is shifting to right side, the power of 10 is negative and if the decimal is shifting to left side, the power of 10 is positive.

As we are given the 0.005 g in standard notation.

Now converting this into scientific notation, we get:

$\Rightarrow 0.005g=5.0\times 10^{-3}g$

As, the decimal point is shifting to right side, thus the power of 10 is negative.

Thus, the mass represented in scientific notation as $5.0\times 10^{-3}g$

Now we have to determine the mass in milligram.

The conversion used from gram to kilogram is:

1 gram = 1000 milligram

or,

1 g = 1000 mg

As we are given the mass 0.005 grams.

As, 1 gram mass = 1000 mg

So, 0.005 gram mass = $\frac{1000g}{1g}\times 0.005mg=5mg$

The mass in milligram is, 5 mg

Answer 2

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

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 negatifive 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/1898080
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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