my_val <- (c(0.1, 0.00000000123, 13/150660001, 761231, -3.243) )
my_val[1] 1.00000e-01 1.23000e-09 8.62870e-08 7.61231e+05
[5] -3.24300e+00
Notation and tables
MADS6
Wednesday, 4 March 2026
Exact numbers
Measured numbers
Note
In data science, we are frequently facing values with limited detail on their measurements. That’s not an invitation to ignore the fact.
Note
In text, we would write “three bikes and seven people”.
1km = 1000m
299 792 458 m/s (a definition)
Multiple measurements will return differing results
Measurements by different people will return different results.
Precision is naturally limited
Why we care
In data science we typically do not measure data ourselves.
The value we print to a report however conveys a meaning of certainty.
Leading zeros
| ||||||
0.000000230453400
| ||
Captive zero Trailing zeros
| Value | Digits | Explanation |
|---|---|---|
| 1642 m | 4 | All non-zero |
| 10.303 ml | 5 | Captive zeros |
| 67.0 g | 3 | Trailing measured zero |
| 0.00053503 | 5 | All leading zeros irrelevant |
| Value | Digits | Explanation |
|---|---|---|
| 1200001 m | 7 | Mostly captive zeros |
| 12.000 g | 5 | If measured |
| 0.0000000001 | 1 | All leading zeros irrelevant |
| 0.0010000001 | 8 |
Many numbers in data science are not in our “nice” range from 0 - 1000.
Math vs computer science
Should be \(1.9 \times 10^{-4}\) but we usually get to see 1.9e-4.
$1.9 \times 10^{-4}$
Exponents are a multiple of three.
# A tibble: 5 × 3
dec sci eng
<dec> <sci> <eng>
1 0.1 1 e-1 100 e-3
2 0.00000000123 1.23e-9 1.23e-9
3 0.0000000863 8.63e-8 86.3 e-9
4 761231 7.61e+5 761. e+3
5 -3.24 -3.24e+0 -3.24e+0
Using the pillar::num()
sprintf()%i - Integer values%f - Decimal numerical format (fixed)%e - Scientific notation %E with capital E%g - Best of both worlds: decimal if exponent is < -4.Many other options for padding, currency symbols
[1] "0.100000" "0.000000" "0.000000"
[4] "761231.000000" "-3.243000"
[1] "1.000000e-01" "1.230000e-09" "8.628700e-08"
[4] "7.612310e+05" "-3.243000e+00"
[1] "0.1" "1.23E-09" "8.6287E-08" "761231"
[5] "-3.243"
Error in `sprintf()`:
! invalid format '%i'; use format %f, %e, %g or %a for numeric objects
Python
Modern Python is using sprintf-style syntax in its str.format() function. Using the sprintf functions is deprecated.
Check the documentation.
Compare different numbers - Eight, 12.0, 1.76-e7, four, 3.0
Adding numbers need to be rounded to the least precise digit
[1] 11.961
[1] 12
Least precise value (4.5) carries a single digit.
Base R is doing this nicely but the result is not publication quality.
species island bill_len bill_dep
1 Adelie Dream 32.1 15.5
2 Adelie Dream 33.1 16.1
3 Adelie Torgersen 33.5 19.0
4 Adelie Dream 34.0 17.1
5 Adelie Torgersen 34.1 18.1
6 Adelie Torgersen 34.4 18.4
7 Adelie Biscoe 34.5 18.1
8 Adelie Torgersen 34.6 21.1
9 Adelie Torgersen 34.6 17.2
10 Adelie Biscoe 35.0 17.9
11 Adelie Biscoe 35.0 17.9
12 Adelie Torgersen 35.1 19.4
13 Adelie Torgersen 35.2 15.9
14 Adelie Biscoe 35.3 18.9
15 Adelie Biscoe 35.5 16.2
16 Adelie Torgersen 35.5 17.5
17 Adelie Dream 35.6 17.5
18 Adelie Biscoe 35.7 16.9
19 Adelie Dream 35.7 18.0
20 Adelie Torgersen 35.7 17.0
21 Adelie Biscoe 35.9 19.2
22 Adelie Torgersen 35.9 16.6
23 Adelie Dream 36.0 18.5
24 Adelie Dream 36.0 17.9
25 Adelie Dream 36.0 17.8
26 Adelie Dream 36.0 17.1
27 Adelie Torgersen 36.2 16.1
28 Adelie Dream 36.2 17.3
29 Adelie Torgersen 36.2 17.2
30 Adelie Dream 36.3 19.5
31 Adelie Dream 36.4 17.0
32 Adelie Biscoe 36.4 17.1
33 Adelie Dream 36.5 18.0
34 Adelie Biscoe 36.5 16.6
35 Adelie Torgersen 36.6 17.8
36 Adelie Dream 36.6 18.4
37 Adelie Torgersen 36.7 19.3
38 Adelie Torgersen 36.7 18.8
39 Adelie Dream 36.8 18.5
40 Adelie Dream 36.9 18.6
41 Adelie Dream 37.0 16.9
42 Adelie Dream 37.0 16.5
43 Adelie Dream 37.2 18.1
44 Adelie Torgersen 37.2 19.4
45 Adelie Dream 37.3 17.8
46 Adelie Torgersen 37.3 20.5
47 Adelie Dream 37.3 16.8
48 Adelie Dream 37.5 18.9
49 Adelie Dream 37.5 18.5
50 Adelie Dream 37.6 19.3
51 Adelie Biscoe 37.6 19.1
52 Adelie Biscoe 37.6 17.0
53 Adelie Biscoe 37.7 18.7
54 Adelie Biscoe 37.7 16.0
55 Adelie Torgersen 37.7 19.8
56 Adelie Torgersen 37.8 17.1
57 Adelie Torgersen 37.8 17.3
58 Adelie Biscoe 37.8 18.3
59 Adelie Biscoe 37.8 20.0
60 Adelie Dream 37.8 18.1
61 Adelie Biscoe 37.9 18.6
62 Adelie Biscoe 37.9 18.6
63 Adelie Dream 38.1 18.6
64 Adelie Biscoe 38.1 17.0
65 Adelie Biscoe 38.1 16.5
66 Adelie Dream 38.1 17.6
67 Adelie Biscoe 38.2 18.1
68 Adelie Biscoe 38.2 20.0
69 Adelie Dream 38.3 19.2
70 Adelie Torgersen 38.5 17.9
71 Adelie Torgersen 38.6 21.2
72 Adelie Biscoe 38.6 17.2
73 Adelie Torgersen 38.6 17.0
74 Adelie Torgersen 38.7 19.0
75 Adelie Biscoe 38.8 17.2
76 Adelie Dream 38.8 20.0
77 Adelie Torgersen 38.8 17.6
78 Adelie Torgersen 38.9 17.8
79 Adelie Dream 38.9 18.8
80 Adelie Biscoe 39.0 17.5
81 Adelie Torgersen 39.0 17.1
82 Adelie Dream 39.0 18.7
83 Adelie Torgersen 39.1 18.7
84 Adelie Torgersen 39.2 19.6
85 Adelie Dream 39.2 21.1
86 Adelie Dream 39.2 18.6
87 Adelie Torgersen 39.3 20.6
88 Adelie Torgersen 39.5 17.4
89 Adelie Dream 39.5 16.7
90 Adelie Dream 39.5 17.8
91 Adelie Dream 39.6 18.8
92 Adelie Biscoe 39.6 17.7
93 Adelie Torgersen 39.6 17.2
94 Adelie Dream 39.6 18.1
95 Adelie Biscoe 39.6 20.7
96 Adelie Torgersen 39.7 18.4
97 Adelie Biscoe 39.7 18.9
98 Adelie Biscoe 39.7 17.7
99 Adelie Dream 39.7 17.9
100 Adelie Dream 39.8 19.1
101 Adelie Biscoe 40.1 18.9
102 Adelie Torgersen 40.2 17.0
103 Adelie Dream 40.2 20.1
104 Adelie Dream 40.2 17.1
105 Adelie Torgersen 40.3 18.0
106 Adelie Dream 40.3 18.5
107 Adelie Biscoe 40.5 17.9
108 Adelie Biscoe 40.5 18.9
109 Adelie Biscoe 40.6 18.6
110 Adelie Biscoe 40.6 18.8
111 Adelie Torgersen 40.6 19.0
112 Adelie Dream 40.6 17.2
113 Adelie Dream 40.7 17.0
114 Adelie Dream 40.8 18.4
115 Adelie Dream 40.8 18.9
116 Adelie Dream 40.9 18.9
117 Adelie Torgersen 40.9 16.8
118 Gentoo Biscoe 40.9 13.7
119 Chinstrap Dream 40.9 16.6
120 Adelie Biscoe 41.0 20.0
121 Adelie Torgersen 41.1 17.6
122 Adelie Dream 41.1 19.0
123 Adelie Biscoe 41.1 18.2
124 Adelie Biscoe 41.1 19.1
125 Adelie Dream 41.1 18.1
126 Adelie Torgersen 41.1 18.6
127 Adelie Dream 41.1 17.5
128 Adelie Biscoe 41.3 21.1
129 Adelie Dream 41.3 20.3
130 Adelie Biscoe 41.4 18.6
131 Adelie Torgersen 41.4 18.5
132 Adelie Torgersen 41.5 18.3
133 Adelie Dream 41.5 18.5
134 Adelie Biscoe 41.6 18.0
135 Gentoo Biscoe 41.7 14.7
136 Adelie Torgersen 41.8 19.4
137 Adelie Torgersen 42.0 20.2
138 Adelie Biscoe 42.0 19.5
139 Gentoo Biscoe 42.0 13.5
140 Adelie Torgersen 42.1 19.1
141 Adelie Dream 42.2 18.5
142 Adelie Biscoe 42.2 19.5
143 Adelie Dream 42.3 21.2
144 Chinstrap Dream 42.4 17.3
145 Adelie Torgersen 42.5 20.7
146 Chinstrap Dream 42.5 16.7
147 Chinstrap Dream 42.5 17.3
148 Gentoo Biscoe 42.6 13.7
149 Adelie Biscoe 42.7 18.3
150 Gentoo Biscoe 42.7 13.7
151 Adelie Torgersen 42.8 18.5
152 Gentoo Biscoe 42.8 14.2
153 Adelie Torgersen 42.9 17.6
154 Gentoo Biscoe 42.9 13.1
155 Adelie Torgersen 43.1 19.2
156 Adelie Dream 43.2 18.5
157 Adelie Biscoe 43.2 19.0
158 Gentoo Biscoe 43.2 14.5
159 Chinstrap Dream 43.2 16.6
160 Gentoo Biscoe 43.3 13.4
161 Gentoo Biscoe 43.3 14.0
162 Gentoo Biscoe 43.4 14.4
163 Gentoo Biscoe 43.5 14.2
164 Gentoo Biscoe 43.5 15.2
165 Chinstrap Dream 43.5 18.1
166 Gentoo Biscoe 43.6 13.9
167 Gentoo Biscoe 43.8 13.9
168 Gentoo Biscoe 44.0 13.6
169 Adelie Dream 44.1 19.7
170 Adelie Torgersen 44.1 18.0
171 Gentoo Biscoe 44.4 17.3
172 Gentoo Biscoe 44.5 14.3
173 Gentoo Biscoe 44.5 14.7
174 Gentoo Biscoe 44.5 15.7
175 Gentoo Biscoe 44.9 13.3
176 Gentoo Biscoe 44.9 13.8
177 Gentoo Biscoe 45.0 15.4
178 Gentoo Biscoe 45.1 14.5
179 Gentoo Biscoe 45.1 14.5
180 Gentoo Biscoe 45.1 14.4
181 Gentoo Biscoe 45.2 15.8
182 Gentoo Biscoe 45.2 13.8
183 Gentoo Biscoe 45.2 16.4
184 Gentoo Biscoe 45.2 14.8
185 Chinstrap Dream 45.2 17.8
186 Chinstrap Dream 45.2 16.6
187 Gentoo Biscoe 45.3 13.7
188 Gentoo Biscoe 45.3 13.8
189 Gentoo Biscoe 45.4 14.6
190 Chinstrap Dream 45.4 18.7
191 Gentoo Biscoe 45.5 13.7
192 Gentoo Biscoe 45.5 13.9
193 Gentoo Biscoe 45.5 15.0
194 Gentoo Biscoe 45.5 14.5
195 Chinstrap Dream 45.5 17.0
196 Adelie Biscoe 45.6 20.3
197 Chinstrap Dream 45.6 19.4
198 Gentoo Biscoe 45.7 13.9
199 Chinstrap Dream 45.7 17.3
200 Chinstrap Dream 45.7 17.0
201 Adelie Torgersen 45.8 18.9
202 Gentoo Biscoe 45.8 14.6
203 Gentoo Biscoe 45.8 14.2
204 Chinstrap Dream 45.9 17.1
205 Adelie Torgersen 46.0 21.5
206 Chinstrap Dream 46.0 18.9
207 Gentoo Biscoe 46.1 13.2
208 Gentoo Biscoe 46.1 15.1
209 Chinstrap Dream 46.1 18.2
210 Gentoo Biscoe 46.2 14.5
211 Gentoo Biscoe 46.2 14.9
212 Gentoo Biscoe 46.2 14.4
213 Gentoo Biscoe 46.2 14.1
214 Chinstrap Dream 46.2 17.5
215 Gentoo Biscoe 46.3 15.8
216 Gentoo Biscoe 46.4 15.6
217 Gentoo Biscoe 46.4 15.0
218 Chinstrap Dream 46.4 18.6
219 Chinstrap Dream 46.4 17.8
220 Gentoo Biscoe 46.5 13.5
221 Gentoo Biscoe 46.5 14.5
222 Gentoo Biscoe 46.5 14.4
223 Gentoo Biscoe 46.5 14.8
224 Chinstrap Dream 46.5 17.9
225 Gentoo Biscoe 46.6 14.2
226 Chinstrap Dream 46.6 17.8
227 Gentoo Biscoe 46.7 15.3
228 Chinstrap Dream 46.7 17.9
229 Gentoo Biscoe 46.8 15.4
230 Gentoo Biscoe 46.8 16.1
231 Gentoo Biscoe 46.8 14.3
232 Chinstrap Dream 46.8 16.5
233 Gentoo Biscoe 46.9 14.6
234 Chinstrap Dream 46.9 16.6
235 Chinstrap Dream 47.0 17.3
236 Gentoo Biscoe 47.2 15.5
237 Gentoo Biscoe 47.2 13.7
238 Gentoo Biscoe 47.3 15.3
239 Gentoo Biscoe 47.3 13.8
240 Gentoo Biscoe 47.4 14.6
241 Gentoo Biscoe 47.5 14.2
242 Gentoo Biscoe 47.5 14.0
243 Gentoo Biscoe 47.5 15.0
244 Chinstrap Dream 47.5 16.8
245 Gentoo Biscoe 47.6 14.5
246 Chinstrap Dream 47.6 18.3
247 Gentoo Biscoe 47.7 15.0
248 Gentoo Biscoe 47.8 15.0
249 Gentoo Biscoe 48.1 15.1
250 Chinstrap Dream 48.1 16.4
251 Gentoo Biscoe 48.2 14.3
252 Gentoo Biscoe 48.2 15.6
253 Gentoo Biscoe 48.4 14.6
254 Gentoo Biscoe 48.4 16.3
255 Gentoo Biscoe 48.4 14.4
256 Gentoo Biscoe 48.5 14.1
257 Gentoo Biscoe 48.5 15.0
258 Chinstrap Dream 48.5 17.5
259 Gentoo Biscoe 48.6 16.0
260 Gentoo Biscoe 48.7 14.1
261 Gentoo Biscoe 48.7 15.1
262 Gentoo Biscoe 48.7 15.7
263 Gentoo Biscoe 48.8 16.2
264 Gentoo Biscoe 49.0 16.1
265 Chinstrap Dream 49.0 19.5
266 Chinstrap Dream 49.0 19.6
267 Gentoo Biscoe 49.1 14.8
268 Gentoo Biscoe 49.1 14.5
269 Gentoo Biscoe 49.1 15.0
270 Gentoo Biscoe 49.2 15.2
271 Chinstrap Dream 49.2 18.2
272 Gentoo Biscoe 49.3 15.7
273 Chinstrap Dream 49.3 19.9
274 Gentoo Biscoe 49.4 15.8
275 Gentoo Biscoe 49.5 16.2
276 Gentoo Biscoe 49.5 16.1
277 Chinstrap Dream 49.5 19.0
278 Gentoo Biscoe 49.6 16.0
279 Gentoo Biscoe 49.6 15.0
280 Chinstrap Dream 49.6 18.2
281 Chinstrap Dream 49.7 18.6
282 Gentoo Biscoe 49.8 16.8
283 Gentoo Biscoe 49.8 15.9
284 Chinstrap Dream 49.8 17.3
285 Gentoo Biscoe 49.9 16.1
286 Gentoo Biscoe 50.0 16.3
287 Gentoo Biscoe 50.0 15.2
288 Gentoo Biscoe 50.0 15.3
289 Gentoo Biscoe 50.0 15.9
290 Chinstrap Dream 50.0 19.5
291 Gentoo Biscoe 50.1 15.0
292 Chinstrap Dream 50.1 17.9
293 Gentoo Biscoe 50.2 14.3
294 Chinstrap Dream 50.2 18.8
295 Chinstrap Dream 50.2 18.7
296 Chinstrap Dream 50.3 20.0
297 Gentoo Biscoe 50.4 15.3
298 Gentoo Biscoe 50.4 15.7
299 Gentoo Biscoe 50.5 15.9
300 Gentoo Biscoe 50.5 15.9
301 Gentoo Biscoe 50.5 15.2
302 Chinstrap Dream 50.5 19.6
303 Chinstrap Dream 50.5 18.4
304 Chinstrap Dream 50.6 19.4
305 Gentoo Biscoe 50.7 15.0
306 Chinstrap Dream 50.7 19.7
307 Gentoo Biscoe 50.8 17.3
308 Gentoo Biscoe 50.8 15.7
309 Chinstrap Dream 50.8 18.5
310 Chinstrap Dream 50.8 19.0
311 Chinstrap Dream 50.9 19.1
312 Chinstrap Dream 50.9 17.9
313 Chinstrap Dream 51.0 18.8
314 Gentoo Biscoe 51.1 16.3
315 Gentoo Biscoe 51.1 16.5
316 Gentoo Biscoe 51.3 14.2
317 Chinstrap Dream 51.3 19.2
318 Chinstrap Dream 51.3 18.2
319 Chinstrap Dream 51.3 19.9
320 Chinstrap Dream 51.4 19.0
321 Gentoo Biscoe 51.5 16.3
322 Chinstrap Dream 51.5 18.7
323 Chinstrap Dream 51.7 20.3
324 Chinstrap Dream 51.9 19.5
325 Chinstrap Dream 52.0 18.1
326 Chinstrap Dream 52.0 19.0
327 Chinstrap Dream 52.0 20.7
328 Gentoo Biscoe 52.1 17.0
329 Gentoo Biscoe 52.2 17.1
330 Chinstrap Dream 52.2 18.8
331 Gentoo Biscoe 52.5 15.6
332 Chinstrap Dream 52.7 19.8
333 Chinstrap Dream 52.8 20.0
334 Gentoo Biscoe 53.4 15.8
335 Chinstrap Dream 53.5 19.9
336 Chinstrap Dream 54.2 20.8
337 Gentoo Biscoe 54.3 15.7
338 Gentoo Biscoe 55.1 16.0
339 Chinstrap Dream 55.8 19.8
340 Gentoo Biscoe 55.9 17.0
341 Chinstrap Dream 58.0 17.8
342 Gentoo Biscoe 59.6 17.0
343 Adelie Torgersen NA NA
344 Gentoo Biscoe NA NA
gt| species | island | bill_len | bill_dep |
|---|---|---|---|
| Gentoo | Biscoe | 44.5 | 14.3 |
| Adelie | Torgersen | 38.6 | 21.2 |
| Gentoo | Biscoe | 45.3 | 13.7 |
| Chinstrap | Dream | 52.8 | 20.0 |
| Adelie | Torgersen | 37.3 | 20.5 |
| Chinstrap | Dream | 43.2 | 16.6 |
| Gentoo | Biscoe | 47.5 | 14.2 |
| Gentoo | Biscoe | 52.2 | 17.1 |
| Chinstrap | Dream | 50.8 | 19.0 |
| Gentoo | Biscoe | 46.1 | 13.2 |
gt| Species | Island | Bill length (mm) | Bill depth (mm) |
|---|---|---|---|
| Adelie | Dream | 35.6 | 17.5 |
| Gentoo | Biscoe | 55.9 | 17.0 |
| Gentoo | Biscoe | 43.2 | 14.5 |
| Adelie | Torgersen | 37.2 | 19.4 |
| Adelie | Torgersen | 34.6 | 17.2 |
| Adelie | Dream | 36.0 | 18.5 |
| Chinstrap | Dream | 52.2 | 18.8 |
| Adelie | Dream | 32.1 | 15.5 |
| Adelie | Dream | 37.2 | 18.1 |
| Adelie | Biscoe | 38.1 | 17.0 |
gt() centers factors by default.
gt| Species | Island |
Bill dimensions (mm)
|
|
|---|---|---|---|
| Length | Depth | ||
| Chinstrap | Dream | 52.0 | 18.1 |
| Adelie | Torgersen | 35.9 | 16.6 |
| Adelie | Torgersen | 39.7 | 18.4 |
| Adelie | Torgersen | 42.8 | 18.5 |
| Adelie | Biscoe | 37.6 | 17.0 |
| Adelie | Dream | 40.2 | 17.1 |
| Gentoo | Biscoe | 45.5 | 15.0 |
| Gentoo | Biscoe | 46.1 | 13.2 |
| Chinstrap | Dream | 58.0 | 17.8 |
| Chinstrap | Dream | 46.5 | 17.9 |
gtpenguins |>
select(species, island, contains("bill")) |>
sample_n(10) |>
gt() |>
cols_align(
align = "left",
columns = c(species, island)) |>
cols_label(
species = "Species",
island = "Island",
bill_len = "Length" ,
bill_dep = "Depth"
) |>
tab_spanner("Bill dimensions (mm)", contains("bill")) |>
tab_options(column_labels.background.color = "#00A4E1") | Species | Island |
Bill dimensions (mm)
|
|
|---|---|---|---|
| Length | Depth | ||
| Chinstrap | Dream | 49.6 | 18.2 |
| Adelie | Dream | 37.6 | 19.3 |
| Gentoo | Biscoe | 45.4 | 14.6 |
| Gentoo | Biscoe | 51.3 | 14.2 |
| Gentoo | Biscoe | 43.8 | 13.9 |
| Chinstrap | Dream | 52.8 | 20.0 |
| Adelie | Dream | 40.9 | 18.9 |
| Adelie | Torgersen | NA | NA |
| Adelie | Torgersen | 41.1 | 17.6 |
| Adelie | Torgersen | 35.9 | 16.6 |
gtpenguins |>
select(species, island, contains("bill")) |>
sample_n(10) |>
gt() |>
cols_align(align = "left", columns = c(species, island)) |>
cols_label(
species = "Species",
island = "Island",
bill_len = "Length" ,
bill_dep = "Depth"
) |>
tab_spanner("Bill dimensions (mm)", contains("bill")) |>
tab_options(column_labels.background.color = "#00A4E1") |>
tab_style(
style = cell_text(size = pct(120)),
locations = cells_body()) |>
tab_style(
style = cell_text(weight = "bold"),
locations = list(cells_column_labels(),
cells_column_spanners()))| Species | Island |
Bill dimensions (mm)
|
|
|---|---|---|---|
| Length | Depth | ||
| Chinstrap | Dream | 51.3 | 19.9 |
| Gentoo | Biscoe | 45.4 | 14.6 |
| Adelie | Torgersen | 36.2 | 17.2 |
| Adelie | Biscoe | 43.2 | 19.0 |
| Gentoo | Biscoe | 46.5 | 13.5 |
| Adelie | Biscoe | 41.1 | 18.2 |
| Gentoo | Biscoe | 45.5 | 13.9 |
| Adelie | Biscoe | 35.5 | 16.2 |
| Adelie | Dream | 36.0 | 17.1 |
| Chinstrap | Dream | 50.2 | 18.8 |