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Example (PageIndex1): scientific Notation

Express each number in scientific notation.

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

Moving the decimal point 10 locations to the left gives 6.7 × 1010.

**Answer b**

The decimal suggest is assumed to be in ~ the end of the number, so relocating it three places to the left offers 1.689 × 103.

**Answer c**

In this case, we require to move the decimal suggest only one ar to the left, which returns 1.26 × 101.

To change a number in **scientific notation** to **standard form**, we reverse the process, relocating the decimal suggest to the right. Add zeros come the end of the number being converted, if necessary, to produce a variety of the ideal magnitude. Lastly, us drop the number 10 and its power.

Exercise (PageIndex2)

Express every number in standard, or conventional notation.

See more: How Much Is 800 000 Pounds In Us Dollars, 800000 Gbp To Usd

**Answer a**

Moving the decimal suggest eight places to the ideal and including zeros provide 698,000,000.

**Answer b**

Moving the decimal suggest two areas to the right provides 100.5

We can additionally use clinical notation come express numbers who magnitudes are much less than 1. For example, the quantity 0.006 centimeters deserve to be expressed together follows:

Recall that:

We usage a negative number as the strength to show the variety of places we need to move the decimal point to the appropriate to make it monitor the an initial nonzero digit so the the number is in between 1 and 10. This is shown as follows:

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