Scientific Understanding

**What sections should I know before attempting to learn this section?**

—> Introduction to Significant Figures

—> Significant Figures **Part 4 (All Zeros)**

**How do you multiply and divide significant figures?**

Multiplying and dividing significant figures will require you to give an answer that also has the correct number of significant figures. By contrast, multiplying and dividing is much more common than adding and subtracting in chemistry and therefore, this section will be far most useful than the previous one. Some teachers will demand that you give every numbered answer involved with multiplying and dividing with significant figures. However, it will not be a main focus on this website. Multiplying and dividing significant figures comes down to how many significant figures each number you are given has. Make sure you have reviewed the significant figures sections before you attempt this one. Both multiplying and dividing significant figures have the same rule. That rule is, the FINAL ANSWER of a multiplication and division problem should be rounded to the number of significant figures that is the least amount of any figures used in the multiplication or division. Let us demonstrate below.

**Examples**: Give the answer to the multiplication and division problems with the correct number of significant figures.

35.6 * 42 = ?

Problem | Calculator Shows | Correct Answer |

42 * 35.6 = | 1495.2 | 1500 |

78.12 / 63.951 = ?

Problem | Calculator Shows | Correct Answer |

78.12 = | 1.221560257… | 1.222 |

63.951 |

(357.2 * 2.395) / (169 * 84.756) = ?

Problem | Calculator Shows | Correct Answer |

357.2 * 2.395 = | 0.0597255023… | 0.0597 |

169 * 84.756 |

**VIDEO Multiplying and Dividing Significant Figures Demonstrated Example 1**: What would the answer be to the correct number of significant figures for the problem below?

**324 * 56.89 = ?**

What answer do I get on calculator when I multiply them?

Answer : 18432.36

How many significant figures is 324?

Answer: 3

How many significant figures is 56.89?

Answer: 4

How many significant figures should the answer be?

Answer: 3 (least amount figures used)

How do I round 18432.36 to 3 significant figures?

COMPLETE ANSWER: 18400

**VIDEO Multiplying and Dividing Significant Figures Demonstrated Example 2**: What would the answer be to the correct number of significant figures for the problem below?

**(3.78 * 9.42) / (5.126 * 7.3) = ?**

What answer do I get on calculator when I multiply them?

Answer : 0.95157109337837…

How many significant figures is 3.79?

Answer: 3

How many significant figures is 9.42?

Answer: 3

How many significant figures is 5.126?

Answer: 4

How many significant figures is 7.3?

Answer: 2

How many significant figures should the answer be?

Answer: 2 (least amount figures used)

How do I round 0.95157109337837… to 2 significant figures?

COMPLETE ANSWER: 0.95

**PRACTICE PROBLEMS**: Determine the answer with the correct significant figures for the problems below.

800 * 90 = | 70000 |

61.48 / 85 = | 0.72 |

0.862 * 1.3659 = | 1.18 |

0.00528 / 0.0063 = | 0.84 |

(21.75 * 40) / (14 * 6.3) = | 10 |

(96.32 * 17.4) / 237.15 = | 7.07 |