Express the following numbers in usual form

I. 3.02 x 10^ - 6

II. 4.5 x 10^4

III. 3 x 10^ - 8

IV. 1.0001 x 10^9

V. 5.8 x 10^12

VI. 3.61492 x 10^6

To express numbers in usual form, we convert them from scientific notation to standard decimal notation. Scientific notation is a convenient way to represent very large or very small numbers, using powers of ten. Let’s break down each of the numbers you provided step by step.

Understanding Scientific Notation

In scientific notation, a number is typically written as a x 10^n, where:

• a is a number greater than or equal to 1 and less than 10.
• n is an integer that indicates how many places to move the decimal point.

If n is positive, we move the decimal point to the right; if n is negative, we move it to the left.

Converting Each Number

I. 3.02 x 10^-6

Here, we have a negative exponent, which means we move the decimal point 6 places to the left:

3.02 becomes 0.00000302.

II. 4.5 x 10^4

With a positive exponent of 4, we move the decimal point 4 places to the right:

4.5 becomes 45000.

III. 3 x 10^-8

Again, we have a negative exponent, so we move the decimal point 8 places to the left:

3 becomes 0.00000003.

IV. 1.0001 x 10^9

For this number, we move the decimal point 9 places to the right:

1.0001 becomes 1000100000.

V. 5.8 x 10^12

Here, we move the decimal point 12 places to the right:

5.8 becomes 5800000000000.

VI. 3.61492 x 10^6

Finally, we move the decimal point 6 places to the right:

3.61492 becomes 3614920.

Summary of Usual Forms

Now, let’s summarize the conversions:

• I. 3.02 x 10^-6 = 0.00000302
• II. 4.5 x 10^4 = 45000
• III. 3 x 10^-8 = 0.00000003
• IV. 1.0001 x 10^9 = 1000100000
• V. 5.8 x 10^12 = 5800000000000
• VI. 3.61492 x 10^6 = 3614920

Understanding how to convert between scientific notation and usual form is a valuable skill, especially in fields like science and engineering where you often deal with very large or very small quantities.