# What is the measurement 111.009 mm rounded off to four significant digits?

##### 1 Answer

Jun 14, 2016

First, you may want to review significant figures (sig figs).

The (snippeted) relevant rules are:

**PROMINENT DEFINITIONS**

- All
**nonzero digits**are significant. EX:#color(blue)(21)0# - A zero is
**sandwiched**when there is at least one nonzero digit to the left AND right. All zeros in between two nonzero digits, even if multiple zeros are adjacent, are significant. EX:#5color(blue)(00)5#

**SPECIAL CONDITIONS**

- All zeroes AFTER an implicit or explicit decimal point are subject to the following conditions:
- If the number is GREATER than
#1# (if the units digit is#1# or greater), AND the decimal point*directly*precedes the zero(es), the zero(es) are significant. Otherwise, the zeroes are NOT significant. EX:#1color(blue)(.0)50# vs.#0color(red)(.0)50# - If it is sandwiched between two nonzero digits,
**even if the decimal point**, it is significant. EX:*directly*precedes the zero#5color(blue)(.0)5#

- If the number is GREATER than

Looking at

#4# nonzero digits#2# sandwiched zeroes

For

#"111.0"color(red)(ul(0))"9 mm"#

- Since it is less than
#5# , we round it*and*everything to its right,*downwards*, as per normal algebra rounding rules. - Then we get rid of every digit past the
#5# th digit from the left, including the#5# th digit.

#"111.0"cancel(color(red)(0))cancel(color(red)(9))# #"mm"#

#=># #color(blue)("111.0 mm")#

The remaining sig figs are:

#3# nonzero digits#1# trailing zero