## Science 122## Laboratory |

It is also useful in resolving ambiguous zeros in determining the number of significant figures. Since our number system is based on '10' it is called a decimal system ("deci" = "ten" in Latin). Numbers are in columns with each column representing a power of ten.

In this system zeros are placeholders; they represent an empty column.

## Multiplying by ten adds a zero (2 x 10 = 20) or moves the decimal point to the right (2.72 x 10 = 27.2)

## Dividing by ten subtracts a zero (20/10 = 2) or moves the decimal point to the left (27.2/10 = 2.72)

## HOW TO DO IT: Zeros |
## Count how many zeros in the number.## Make that number a power of ten.## Multiply the first digit by that power of ten. |
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## 2 zeros --> 10 x 10 --> 10 |
## 100 = 1 x 10 |
## 200 = 2 x 10 |
## 300 = 3 x 10 |
## 400 = 4 x 10 |

## 3 zeros --> 10 x 10 x 10 --> 10 |
## 1000 = 1 x 10 |
## 2000 = 2 x 10 |
## 3000 = 3 x 10 |
## 4000 = 4 x 10 |

## 4 zeros --> 10 x 10 x 10 x 10 --> 10 |
## 10000 = 1 x 10 |
## 20,000 = 2 x 10 |
## 30,000 = 3 x 10 |
## 40,000 = 4 x 10 |

## HOW TO DO IT: Decimals |
## Place the decimal point after the first significant digit.## Count how many digits, including zeros to the right or left of the decimal point.## Make that number a power of ten.## Multiply the resulting number by that power of ten. |
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## 2 decimals --> 10 x 10 --> 10 |
## 176 = 1.76 x 10 |
## 241 = 2.41 x 10 |
## 327 = 3.27 x 10 |
## 496 = 4.96 x 10 |

## 3 decimals --> 10 x 10 x 10 --> 10 |
## 1762 = 1.762 x 10 |
## 2417 = 2.417 x 10 |
## 3274 = 3.274x 10 |
## 4963 = 4.963 x 10 |

## 4 decimals --> 10 x 10 x 10 x 10 --> 10 |
## 17,625 = 1.7625 x 10 |
## 24,178 = 2.41 x 10 |
## 32,741 = 3.2741 x 10 |
## 49,632 = 4.9632 x 10 |

Example:249.8is rounded to 3 significant figures to become2.50 x 10^{2}

Example: the average distance from the Sun to the Earth is 93,000,000 mi.## Using powers-of-ten notation, this can be written as

## 93,000,000 miles = 9.3 x 10^7 mi or 9.3 x10

^{7 }mi