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Here is the same answer, some nuances are shown. The function / method numerical_approx(...) has the short hand n(...)and its arguments / options are prec=None, digits=None, algorithm=None. For us, the first two are interesting.
Please also compare with:
https://doc.sagemath.org/html/en/reference/misc/sage/misc/functional.html
Consider a number, and let us see what n() does with it.
sage: a = 56789.3456
sage: a.n(digits=2)
57000.
sage: a.n(digits=8)
56789.346
sage: a.n(prec=2)
49000.
sage: a.n(prec=6)
56000.
sage: a.n(prec=8)
57000.
sage: f"{a:e}"
'5.67893456000000e+4'
So digits what we want (prec is working binary, digits thinks in a decimal world). Now an example with matrices:
import random
random.seed('75986')
A = matrix(RR, 5, 5, [random.uniform(0, 10^random.choice([-4..10])) for count in range(5^2)])
And we obtain our test matrix:
sage: A
[ 63543.3389328726 0.000736538191035056 0.000895407805608647 0.0000106867455934270 5.15508298915226e6]
[ 7.86559376536411e7 0.00655431229353655 6.12649210201700e9 5.74262540915562e7 5.01590930940852e7]
[ 0.272774522172060 0.567796814218967 503.414415232817 0.504025659604463 99609.9284950566]
[ 0.727489291982834 7.42982613086165e6 8.14891687426721e8 3.29252151209820e6 1.85713734568604e6]
[ 2.32144069623205e6 2.71752136036553e7 9.12158172757762e9 0.0000526060634628119 2915.02383079855]
Now we can try:
sage: n(A, digits=5)
[ 63543. 0.00073654 0.00089541 0.000010687 5.1551e6]
[ 7.8656e7 0.0065543 6.1265e9 5.7426e7 5.0159e7]
[ 0.27277 0.56780 503.41 0.50403 99610.]
[ 0.72749 7.4298e6 8.1489e8 3.2925e6 1.8571e6]
[ 2.3214e6 2.7175e7 9.1216e9 0.000052606 2915.0]
and (depending on what we want) this is almost in all cases good enough. The five "main digits" are shown in each case. But we also have the entry 0.00089541 which is not rounded, instead, five relevant decimals are shown. If we really want a rounding (or truncation), we can define a new matrix (and call it B) with the rounded entries:
sage: matrix(5, 5, [round(entry, 3) for entry in A.list()])
[ 63543.339 0.001 0.001 0.0 5155082.989]
[ 78655937.654 0.007 6126492102.017 57426254.092 50159093.094]
[ 0.273 0.568 503.414 0.504 99609.928]
[ 0.727 7429826.131 814891687.427 3292521.512 1857137.346]
[ 2321440.696 27175213.604 9121581727.578 0.0 2915.024]
sage: A.apply_map(lambda entry: round(entry, 3))
[ 63543.339 0.001 0.001 0.0 5155082.989]
[ 78655937.654 0.007 6126492102.017 57426254.092 50159093.094]
[ 0.273 0.568 503.414 0.504 99609.928]
[ 0.727 7429826.131 814891687.427 3292521.512 1857137.346]
[ 2321440.696 27175213.604 9121581727.578 0.0 2915.024]
Sometimes this is what we want...
