The document Scientific Notation, Precision & Accuracy Class 11 Notes | EduRev is a part of the Class 11 Course Chemistry for JEE.

All you need of Class 11 at this link: Class 11

**UNCERTAINTY IN MEASUREMENT**

Many a times in the study of chemistry, one has to deal with experimental data as well as theoretical calculations. There are meaningful ways to handle the numbers conveniently and present the data realistically with certainty to the extent possible.**1.** Scientific Notation**2.** Significant Figures**3.** Dimension Analysis

**1. Scientific Notation**

Scientific Notation is a way of expressing numbers that are too big or too small to be conveniently written in __decimal form__.

In which any number can be represented in the form** N × 10**^{n}

(Where __n is an exponent having positive or negative values__ and __N can vary between 1 to 10__).

Scientific notation

**Example**

- We can write 232.508 as 2.32508 × 10
^{2}in scientific notation. Similarly, 0.00016 can be written as 1.6 × 10^{–4}. - Thus, we can write 232.508 as 2.32508 × 10
^{2}in scientific notation. Note that while writing it, the decimal had to be moved to the left by two places and same is the exponent (2) of 10 in the scientific notation. - Similarly, 0.00016 can be written as 1.6 × 10
^{–4}. Here the decimal has to be moved four places to the right and (– 4) is the exponent in the scientific notation.

**MULTIPLICATION AND DIVISION FOR EXPONENTIAL NUMBERS**

These two operations follow the same rules which are there for exponential numbers, i.e.**ADDITION AND SUBTRACTION FOR EXPONENTIAL NUMBERS**

For these two operations, first the numbers are written in such a way that they have the same exponent. After that, the coefficients (digit terms) are added or subtracted as the case may be.

Thus, for adding 6.65 × 10^{4} and 8.95 × 10^{3}, exponent is made same for both the numbers.

Thus, we get (6.65 × 10^{4}) + (0.895 × 10^{4})**PRECISION AND ACCURACY**

Every experimental measurement has some amount of uncertainty associated with it. However, one would always like the results to be precise and accurate. Precision and accuracy are often referred to while we talk about the measurement.

Precision and accuracy are often referred to while we talk about the measurement.

**Accuracy refers to the closeness of a measured value to a standard or known value****Example:** if in lab you obtain a weight measurement of 3.2 kg for a given substance, but the actual or known weight is 10 kg, then your measurement is not accurate. In this case, your measurement is not close to the known value.

**Precision refers to the closeness of two or more measurements to each other.**

Using the example above, if you weigh a given substance five times, and get 3.2 kg each time, then your measurement is very precise. Precision is independent of accuracy. You can be very precise but inaccurate, as described above. You can also be accurate but imprecise.**Example: **If on average, your measurements for a given substance are close to the known value, but the measurements are far from each other, then you have accuracy without precision.

**Example**

If the true value for a result is 2.00 g.**(a)** Student ‘A’ takes two measurements and reports the results as 1.95 g and 1.93 g.

- These values are precise as they are close to each other but are not accurate.

**(b)** Another student repeats the experiment and obtains 1.94 g and 2.05 g as the results for two measurements.

- These observations are neither precise nor accurate.

**(c) **When a third student repeats these measurements and reports 2.01g and 1.99 g as the result.

- These values are both precise and accurate.

**Examples:****Q.1. Which of the following options is not correct? ****(a) 8008 = 8.008 x 10 ^{3}**

2.0034 = 4

(a) non –digit term

(b) digit term

(c) numeral

(d) base term

In exponential notation N × 10

0.00016 can be written as 1.6 × 10

6.65 × 10

= (6.65 + 0.895) × 10

2.5 × 10

= 2.5 × 10

(a) A → Significant figures, B → accuracy

(b) A → accuracy, B → precision

(c) A → Precision, B → accuracy

(d) A → significant figures, → precision

(a) Every experimental measurement has zero amount of uncertainty associated with it

(b) One would always like the result to be precise and accurate

(c) Precision and accuracy are often referred to while we talk about the measurement

(d) Both (b) and (c)

Ans:

Every experimental measurement has some amount of uncertainty associated with it.

Question 1:Which of the following statement is correct ?

Question 2:Two students X and Y report the weight of the same substance as 5.0g and 5.00g respectively. Which of the following statements is correct ?

Offer running on EduRev: __Apply code STAYHOME200__ to get INR 200 off on our premium plan EduRev Infinity!

223 videos|452 docs|334 tests