Unit 1, Topic 1.4 Scientific Notation and Standard Form - Questions and Answers – Short & Long Questions

Chapter 1 Physical Quantities and Measurement Physics Notes | Complete Guide with Formulas & Derivations 

1.4 Scientific Notation and Standard Form Expected Board Short & Long Questions

Short Questions

1. What is scientific notation?

Answer:
Scientific notation is a method of expressing a number in a convenient form using powers of ten. It is especially useful for representing very large and very small numbers.

The general form is:

$N=a\times {10}^n$

where a is a number greater than or equal to 1 and less than 10, and n is an integer.

2. Write the general form of scientific notation.

Answer:
The general form of scientific notation is:

$N=a\times {10}^n$

where:

• N = the original number
• a = coefficient or mantissa
• 10 = base
• n = integer exponent

The coefficient normally satisfies:

$1\le a<10$

3. Why is scientific notation useful in Physics?

Answer:
Scientific notation is useful in Physics because physical quantities can be extremely large or extremely small. It provides a compact and convenient way of writing such quantities.

It helps to:

• Express very large numbers conveniently.
• Express very small numbers conveniently.
• Reduce the possibility of writing errors.
• Make multiplication and division easier.
• Compare the magnitudes of physical quantities quickly.
• Work efficiently with SI prefixes.
• Present measurements clearly in scientific calculations.

4. How are very large numbers represented in scientific notation?

Answer:
Very large numbers are represented using a positive exponent of 10 in scientific notation.

For example:

$150000000000=1.5\times {10}^{11}$

The decimal point is moved to the left, and the number of places moved becomes the positive exponent.

5. How are very small numbers represented in scientific notation?

Answer:
Very small numbers are represented using a negative exponent of 10 in scientific notation.

For example:

$0.0000000001=1\times {10}^{-10}$

The decimal point is moved to the right, and the number of places moved becomes the negative exponent.

6. What is the significance of the exponent in scientific notation?

Answer:
The exponent indicates how many places the decimal point has been moved from its original position.

• A positive exponent represents a large number.
• A negative exponent represents a small number.

For example:

$3.5\times {10}^6$

represents a large number, whereas:

$3.5\times {10}^{-6}$

represents a small number.

7. How do you multiply numbers written in scientific notation?

Answer:
To multiply numbers in scientific notation:

1. Multiply their coefficients.
2. Add their exponents.

For example:

$(2\times {10}^3)\times (4\times {10}^5)$

Multiply the coefficients:

$2\times 4=8$

Add the exponents:

$3+5=8$

Therefore:

$(2\times {10}^3)\times (4\times {10}^5)=8\times {10}^8$

8. How do you divide numbers written in scientific notation?

Answer:
To divide numbers in scientific notation:

1. Divide their coefficients.
2. Subtract the exponent of the denominator from the exponent of the numerator.

For example:

$\frac{8\times {10}^7}{2\times {10}^3}$

Divide the coefficients:

$\frac{8}{2}=4$

Subtract the exponents:

$7-3=4$

Therefore:

$\frac{8\times {10}^7}{2\times {10}^3}=4\times {10}^4$

9. What is meant by order of magnitude?

Answer:
The order of magnitude of a physical quantity is the power of 10 that gives an approximate indication of its size.

For example, a quantity written as:

$3.2\times {10}^6$

has an order of magnitude of approximately:

${10}^6$

Order of magnitude is useful for quickly comparing the sizes of physical quantities.

10. Why is scientific notation useful for expressing physical constants?

Answer:
Scientific notation is useful for expressing physical constants because many physical constants have extremely large or extremely small numerical values. Scientific notation represents them in a compact and convenient form, reducing errors and making calculations easier.

For example, the mass of an electron can be written as:

$m=9.11\times {10}^{-31}\text{ kg}$

This is much more convenient than writing the complete decimal form.

Long Questions

1. Explain scientific notation and describe how very large and very small numbers are represented.

Answer:
Scientific notation is a convenient method of representing very large and very small numbers using powers of ten.

The general form is:

$N=a\times {10}^n$

where:

• N is the original number.
• a is the coefficient.
• n is an integer exponent.

The coefficient normally satisfies:

$1\le a<10$

Very large numbers:

Very large numbers are represented using positive powers of 10.

For example:

$150000000000=1.5\times {10}^{11}$

Very small numbers:

Very small numbers are represented using negative powers of 10.

For example:

$0.0000000001=1\times {10}^{-10}$

Thus, scientific notation makes the representation and calculation of extremely large and small physical quantities much easier.

2. Explain the rules for multiplication and division using scientific notation with examples.

Answer:

Multiplication:

When multiplying numbers written in scientific notation, multiply the coefficients and add the exponents.

In general:

$(a\times {10}^m)\times (b\times {10}^n)=(a\times b)\times {10}^{m+n}$

For example:

$(2\times {10}^3)\times (4\times {10}^5)=8\times {10}^8$

Division:

When dividing numbers written in scientific notation, divide the coefficients and subtract the exponent of the denominator from the exponent of the numerator.

In general:

$\frac{a\times {10}^m}{b\times {10}^n}=\frac{a}{b}\times {10}^{m-n}$

For example:

$\frac{8\times {10}^7}{2\times {10}^3}=4\times {10}^4$

3. Describe how scientific notation is used in Physics to represent physical quantities.

Answer:
Scientific notation is widely used in Physics because physical quantities can have very different magnitudes. Some quantities are extremely large, while others are extremely small.

The general form is:

$N=a\times {10}^n$

Examples include:

• Distance from Earth to the Sun:

$1.5\times {10}^{11}\text{ m}$

• Mass of an electron:

$9.11\times {10}^{-31}\text{ kg}$

Scientific notation makes such values easier to read, compare, calculate, and communicate.

4. Explain the importance of order of magnitude in physical measurements.

Answer:
The order of magnitude provides an approximate indication of the size of a physical quantity by identifying the relevant power of ten.

For example, if a quantity is expressed as:

$3.2\times {10}^6$

its approximate order of magnitude is:

${10}^6$

Order of magnitude is important because it helps us:

• Estimate the approximate size of a physical quantity.
• Compare quantities with very different magnitudes.
• Check whether a calculated result is reasonable.
• Understand the scale of physical phenomena.
• Perform quick estimates in scientific calculations.

Therefore, order of magnitude is a useful tool for understanding and comparing physical measurements.

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