Question

Match the numbers on the left with their equivalent expressions written in scientific notation on the right. You may wish to watch the videos Powers of 10, Parts 1 and 2, before you begin.

Answer 1

Scientific notation expresses numbers as a coefficient multiplied by a power of 10, simplifying the representation and computation of large or small numbers. Moving the decimal to determine a coefficient and exponent transforms numbers into a more manageable form for arithmetic operations.

Step-by-step explanation:

Understanding Scientific Notation

Scientific notation is a method of expressing numbers as a coefficient multiplied by a power of 10. It's a convenient and compact way to handle very large or very small numbers. For instance, the number 56,900 is written as 5.69 × 10⁴ in scientific notation because the decimal point is moved 4 places to the left to place the first non-zero digit at the beginning. Similarly, for very small numbers like 0.000028, the number is expressed as 2.8 × 10⁻⁵ because the decimal is moved 5 places to the right, giving a negative exponent.

To convert a number to scientific notation, first identify the coefficient by arranging the number so only one non-zero digit is to the left of the decimal point. Then, count how many places you move the decimal to achieve this and that becomes your exponent on the power of 10. For multiplication and division, scientific notation greatly simplifies the process. You multiply or divide the coefficients and add or subtract the exponents, respectively.

For example, if you wanted to multiply (3 × 10⁵) by (2 × 10¹), you would multiply the coefficients (3×2) and add the exponents (5+1), resulting in 6 × 10⁶.

Answer 2

The question is incomplete. I'll give a general method on how to solve questions like this..

Step-by-step explanation:

Scientific notation is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10.

It is used because it makes it easier when dealing with very big or very small numbers.

Take for example, 43000000 could be written as 4.3 * 10^7 or 4.3E7.

To figure out the power of 10, think "how many places do I move the decimal point?"

When the number is 10 or greater, the decimal point has to move to the left, and the power of 10 is positive.

When the number is smaller than 1, the decimal point has to move to the right, so the power of 10 is negative.

Now let's solve the following.

1. 68000 = 6.8*10^4 or 6.8E4

2. 0.0000007 = 7*10^-7 or 7E-7