Writing Large Numbers in Standard Form

As an experienced high school mathematics teacher, I often encounter students who struggle with representing large numbers in a clear and concise manner. One of the most important skills in this area is the ability to write numbers in standard form, also known as scientific notation.

Understanding Standard Form

Standard form, or scientific notation, is a way of expressing very large or very small numbers in a compact and easily readable format. The general structure of a number in standard form is:

a × 10^b

where 'a' is a number between 1 and 10, and 'b' is an integer (whole number) that represents the number of places the decimal point needs to be moved.

For example, the number 73,005,046 can be written in standard form as:

7.3005046 × 10^7

In this case, 'a' is 7.3005046, and 'b' is 7, indicating that the decimal point needs to be moved 7 places to the right.

Writing 73 Million, 5 Thousand, 46 in Standard Form

Now, let's apply this concept to the specific number given: 73 million, 5 thousand, 46.

To write this number in standard form, we need to first convert it to a single number without any commas or spaces:

73,005,046

Next, we need to determine the value of 'a' and 'b' in the standard form equation:

a × 10^b

To find 'a', we need to move the decimal point so that the first non-zero digit is to the left of the decimal point. In this case, the first non-zero digit is 7, so 'a' becomes 7.3005046.

To find 'b', we need to count the number of places the decimal point needs to be moved. In this case, the decimal point needs to be moved 7 places to the right, so 'b' becomes 7.

Therefore, the number 73 million, 5 thousand, 46 written in standard form is:

7.3005046 × 10^7

This compact representation makes it easier to compare and manipulate large numbers, which is an essential skill in advanced mathematics and science.