1.3 Floating Point Form
1.3 Floating Point Form
1.3 Floating Point Form
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36 Chapter 1 Numeric Types in Matlab<br />
<strong>1.3</strong> Exercises<br />
In Exercises 1-8, place the given number<br />
in 4-digit base ten floating point<br />
form. In each case, calculate the absolute<br />
and relative error made.<br />
1. 1 885 934<br />
2. 12 345 612<br />
13. 1 789.23456, n = 5<br />
14. 0.008456174 · 10 −6 , n = 3<br />
15. 0.0000456712345 · 10 −11 , n = 6<br />
16. 18.9123456 · 10 6 , n = 4<br />
3. 0.0001234567<br />
4. 0.0085188342<br />
5. 888.456123<br />
6. 1 765.33458<br />
7. 0.0002312316<br />
8. 0.00000556781245<br />
In Exercises 9-12, a 4-digit base ten<br />
floating point approximation x ∗ of a<br />
real number x is given. Determine a<br />
range of possible values for x.<br />
9. 2.446 · 10 −12<br />
10. 4.453 · 10 8<br />
11. 5.684 · 10 5<br />
12. 1.104 · 10 −6<br />
In Exercises 13-16, Place the given<br />
number into n digit floating point format<br />
for the given value of n, calculate<br />
the relativer error, then use the result<br />
to determine the the number of significant<br />
digits in the approximation.
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