Chem 2.3 - Using Scientific Measurements

A | B |
---|---|

How many significant figures are in the number 20? | 1 |

How many significant figures are in the number 20. ? | 2 (the decimal place makes the zero significant) |

How many significant figures are in the number 20.0 ? | 3 |

How many significant figures are in the number 0.04604 ? | 4 |

1

## How many significant figures 50 has?

Trailing zero: Counts as a significant figure if the number contains a decimal point. However, it does not count if the number does not contain a decimal point. Example: 50.00 (

**4 significant figures**), 50 (**1 significant**figure), 50. (**2 significant figures**).2

## How many significant figures are in 1000?

so 1000. is our

**four**-significant-figure answer. (from rules 5 and 6, we see that in order for the trailing zeros to "count" as significant, they must be followed by a decimal. Writing just "1000" would give us only**one significant**figure.)3

## How many sig figs are in 200?

c) Trailing zeros are zeros at the right end of the number. Trailing zeros are only significant if the number contains a decimal point. For example, the number

**200**has only one significant figure, while the number**200**. has three, and the number 200.00 has five**significant figures**.4

## What are the rules of significant figures?

There are three rules on determining how many significant figures are in a number:

**Non**-zero digits are always significant. Any zeros between two significant digits are significant. A final zero or trailing zeros in the decimal portion ONLY are significant.5

## What is the rule for multiplying significant figures?

The following

**rule**applies for**multiplication**and division: The LEAST number of**significant figures**in any number of the problem determines the number of**significant figures**in the answer.6

## Are zeros before the decimal significant?

Leading

**zeros**are not**significant**. For example, 0.00052 has two**significant**figures: 5 and 2. Trailing**zeros**in a number containing a**decimal**point are**significant**. For example, 12.2300 has six**significant**figures: 1, 2, 2, 3, 0 and 0.7

## How do you count significant figures?

**Rules for Numbers WITHOUT a Decimal Point**

- START counting for sig. figs. On the FIRST non-zero digit.
- STOP counting for sig. figs. On the LAST non-zero digit.
- Non-zero digits are ALWAYS significant.
- Zeroes in between two non-zero digits are significant. All other zeroes are insignificant.

8

## How many significant figures are in the number 500?

How does sig figs checking work?

1234 | = | 4 significant figures |
---|---|---|

500 | = | 1 significant figure |

500. | = | 3 significant figures |

1300 | = | 2 significant figures |

2.000 | = | 4 significant figures |

9

## Is the zero at the end of a decimal significant?

Zeroes placed before other digits are not

**significant**; 0.046 has two**significant**digits. Zeroes placed between other digits are always**significant**; 4009 kg has four**significant**digits. Zeroes placed**after**other digits but behind a**decimal**point are**significant**; 7.90 has three**significant**digits.10

## Is there any value of 0?

**Zero**is not "nothing",

**zero**is also not the absence of

**value**,

**zero**is a

**value**. You can say that you

**have**3 objects (apples, bananas, cars, etc), but you can never

**have**3. 3 is a concept that does not "exist" in reality. It is simply a language used to describe dimensions of real objects.

11

## Do zeros to the right count as significant figures?

The trailing

**zeros do**not**count**as**significant**. Trailing**zeros**in a number containing a decimal point are**significant**. For example, 12.2300 has six**significant figures**: 1, 2, 2, 3, 0, and 0. The number 0.000122300 still has only six**significant figures**(the**zeros**before the 1 are not**significant**).12

## How many significant figures does 100.0 have?

3. Trailing zeros in a number are significant only if the number contains a.

decimal point.

Example: 100.0 has

decimal point.

Example: 100.0 has

**4 significant figures**.13

## Are significant figures exact numbers?

Most

**exact numbers**are integers: exactly 12 inches are in a foot, there might be exactly 23 students in a class.**Exact numbers**are often found as conversion factors or as counts of objects.**Exact numbers**can be considered to have an infinite**number**of**significant figures**.14

## What kind of numbers are exact?

Exact numbers are those that have defined values or are integers that result from counting numbers of objects. For example, by definition, there are exactly

**12**eggs in a dozen, exactly**1000**g in a kilogram, and exactly**2.54**cm in an inch.15

## What is the meaning of intermediate calculations?

**Intermediate calculations**are truncated;

**intermediate**steps and final answers are rounded. An

**intermediate calculation**is any math function within a formula. An

**intermediate**step is the value that is carried forward into another

**calculation**.

16

## What are measured and exact numbers?

(When you ask for seating in a restaurant, the

**number**of people is an integer, an**exact number**.)**Measured numbers**are an estimated amount,**measured**to a certain**number**of significant figures without the benefit of any natural unit or**numbers**that come from a mathematical operation such as averaging.17

## Are fractions exact numbers?

If you do arithmetic with

**exact numbers**(and they aren't too large) the answer that you get back is exactly right. In Maple, rational**numbers**(integers and**fractions**) are**exact**. If you do arithmetic with rational**numbers**, your answer will be correct to the last digit. Here are some examples.18

## Is Pi considered an exact number?

No

**number**can claim more fame than**pi**. Defined as the ratio of the circumference of a circle to its diameter,**pi**, or in symbol form, π, seems a simple enough concept. But it turns out to be an "irrational**number**," meaning its**exact**value is inherently unknowable.19

## What is an inexact number?

Exact and

**inexact numbers**.**Numbers**are of two kinds: exact and**inexact**. An exact**number**has a value that has no uncertainty associated with it. Exact**numbers**occur in definitions, in counting, and in simple fractions. An**inexact number**has a value that has a degree of uncertainty associated with it.