You are watching: When is expressing numbers using scientific notation useful

Example (PageIndex1): scientific Notation

Express each number in clinical notation.

67,000,000,000 1,689 12.6**Answer a**

Moving the decimal allude 10 areas to the left provides 6.7 × 1010.

**Answer b**

The decimal point is assumed to be at the finish of the number, so relocating it three areas to the left gives 1.689 × 103.

**Answer c**

In this case, we need to move the decimal point only one place to the left, which yields 1.26 × 101.

To adjust a number in **scientific notation** to **standard form**, us reverse the process, relocating the decimal allude to the right. Include zeros to the end of the number being converted, if necessary, to create a variety of the ideal magnitude. Lastly, we drop the number 10 and also its power.

Exercise (PageIndex2)

Express every number in standard, or typical notation.

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**Answer a**

Moving the decimal allude eight places to the best and adding zeros offer 698,000,000.

**Answer b**

Moving the decimal point two areas to the right offers 100.5

We can likewise use clinical notation come express numbers whose magnitudes are less than 1. Because that example, the amount 0.006 centimeters deserve to be expressed as follows:

Recall that:

We use a an adverse number together the strength to suggest the variety of places we have to move the decimal allude to the ideal to do it follow the an initial nonzero number so that the number is in between 1 and also 10. This is illustrated as follows:

Numbers that are less than one have a an adverse power in scientific notation. If the decimal point is relocated to the ideal n places, the strength (n) of 10 is negative. -->