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Exercise 10.2 class 8 solution-uses of exponents to express numbers in standard form
Exponents are commonly used to express very large or very small numbers in standard form, also known as scientific notation. This notation is especially useful in science, engineering, and other fields where dealing with extremely large or small values is common. The standard form of a number is typically written as:
- a is a number greater than or equal to 1 and less than 10. It is often referred to as the coefficient.
- n is an integer exponent that represents the power of 10 by which you multiply the coefficient.
- Here are some common uses of exponents to express numbers in standard form:
- Large Numbers: To represent numbers that are very large, it’s more convenient to write them in standard form. For example, the speed of light in a vacuum is approximately 299,792,458 meters per second, which can be expressed as 2.99792458×10^8m/s in standard form.
- Small Numbers: For very small numbers, scientific notation is essential. For instance, the mass of an electron is approximately 9.10938356×10^-31 kilograms.
Scientific notation simplifies the representation of large and small values, making calculations and comparisons easier. It’s a useful tool for handling numbers across various scientific and technical disciplines.
Examples 10.1 – write the following numbers in standard form.
Exercise 10.2 class 8 solution-conversion from standard form number to usual decimal form
Converting a number from standard form (scientific notation) to its usual decimal form is a straightforward process. In standard form, a number is expressed as a×10n, where a is the coefficient and n is the exponent. To convert it to its decimal form, you follow these steps:
- Write Down the Coefficient (a): The coefficient a is the number part of the standard form. Write it down as it is.
- Determine the Exponent (n): The exponent n tells you how many places to move the decimal point. If n is positive, you move the decimal point to the right; if n is negative, you move it to the left.
- Move the Decimal Point: Move the decimal point in the coefficient a according to the value of n. If n is positive, move the decimal point to the right by n places, adding zeros if necessary. If n is negative, move the decimal point to the left by ∣n∣∣n∣ places, adding zeros to the right if necessary.
- Remove the Exponent (n): After moving the decimal point, remove the exponent (n).
- Optional: Round the Result: Depending on the context or the desired level of precision, you may need to round the result to a specific number of decimal places.
Convert 6.25×10^3to usual decimal form:
- The coefficient a is 6.25
- The exponent n is 3.
- Move the decimal point three places to the right: 6.25→6250
- Remove the exponent: 6250
Convert 8.75×10^-2 to usual decimal form:
- The coefficient a is 8.75
- The exponent n is −2.
- Move the decimal point two places to the left: 8.75→0.0875.
- Remove the exponent: 0.0875.
Example 10.1.2- express the number in usual form.
Example 10.1.3- comparing very large number very small numbers:
- weight of A is 2.34*10^9kg and weight of B is 1.17*10^8kg
2. 8.0210^-5 and 0.80210^-6
Exercise 10.2 class 8 solution- exercise preview
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Exercise 10.2 class 8 solution- solution pdf
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