26 Basic Engineering Mathematics
3. Evaluate
√
34528 correct to 2 decimal places.
4. Evaluate
√
0.69 correct to 4 significant
figures.
5. Evaluate
√
0.025 correct to 4 decimal places.
6. Evaluate
3
√
17 correct to 3 decimal places.
7. Evaluate
4
√
773 correct to 4 significant
figures.
8. Evaluate
5
√
3.12 correct to 4 decimal places.
9. Evaluate
3
√
0.028 correct to 5 significant
figures.
10. Evaluate
6
√
2451 −
4
√
46 correct to 3 decimal
places.
Express the answers to questions 11 to 15 in
engineering form.
11. Evaluate 5 × 10 −3 × 7 × 10 8
12. Evaluate
3 × 10 −4
8 × 10 −9
13. Evaluate
6 × 10 3 × 14 × 10 −4
2 × 10 6
14. Evaluate
56.43 × 10 −3 × 3 × 10 4
8.349 × 10 3
correct to
3 decimal places.
15. Evaluate
99 × 10 5 × 6.7 × 10 −3
36.2 × 10 −4
correct to 4
significant figures.
4.3.4 Fractions
Locate the
and
functions on your calculator
(the latter function is a Shift function found above
the
function) and then check the following worked
examples.
Problem 14. Evaluate
1
4
+
2
3
(i) Press the
function.
(ii) Type in 1
(iii) Press ↓ on the cursor key and type in 4
(iv)
1
4
appears on the screen.
(v) Press → on the cursor key and type in +
(vi) Press the
function.
(vii) Type in 2
(viii) Press ↓ on the cursor key and type in 3
(ix) Press → on the cursor key.
(x) Press = and the answer
11
12
appears.
(xi) Press the S ⇔ D function and the fraction
changes to a decimal 0.9166666...
Thus,
1
4
+
2
3
=
11
12
= 0.9167 as a decimal, correct to
4 decimal places.
It is also possible to deal with mixed numbers on the
calculator. Press Shift then the
function and
appears.
Problem 15. Evaluate 5
1
5
− 3
3
4
(i) Press Shift then the
function and
appears
on the screen.
(ii) Type in 5 then → on the cursor key.
(iii) Type in 1 and ↓ on the cursor key.
(iv) Type in 5 and 5
1
5
appears on the screen.
(v) Press → on the cursor key.
(vi) Type in – and then press Shift then the
function
and 5
1
5
−
appears on the screen.
(vii) Type in 3 then → on the cursor key.
(viii) Type in 3 and ↓ on the cursor key.
(ix) Type in 4 and 5
1
5
− 3
3
4
appears on the screen.
(x) Press = and the answer
29
20
appears.
(xi) Press S ⇔ D function and the fraction changes to
a decimal 1.45
Thus, 5
1
5
− 3
3
4
=
29
20
= 1
9
20
= 1.45 as a decimal.
3. Evaluate
√
34528 correct to 2 decimal places.
4. Evaluate
√
0.69 correct to 4 significant
figures.
5. Evaluate
√
0.025 correct to 4 decimal places.
6. Evaluate
3
√
17 correct to 3 decimal places.
7. Evaluate
4
√
773 correct to 4 significant
figures.
8. Evaluate
5
√
3.12 correct to 4 decimal places.
9. Evaluate
3
√
0.028 correct to 5 significant
figures.
10. Evaluate
6
√
2451 −
4
√
46 correct to 3 decimal
places.
Express the answers to questions 11 to 15 in
engineering form.
11. Evaluate 5 × 10 −3 × 7 × 10 8
12. Evaluate
3 × 10 −4
8 × 10 −9
13. Evaluate
6 × 10 3 × 14 × 10 −4
2 × 10 6
14. Evaluate
56.43 × 10 −3 × 3 × 10 4
8.349 × 10 3
correct to
3 decimal places.
15. Evaluate
99 × 10 5 × 6.7 × 10 −3
36.2 × 10 −4
correct to 4
significant figures.
4.3.4 Fractions
Locate the
and
functions on your calculator
(the latter function is a Shift function found above
the
function) and then check the following worked
examples.
Problem 14. Evaluate
1
4
+
2
3
(i) Press the
function.
(ii) Type in 1
(iii) Press ↓ on the cursor key and type in 4
(iv)
1
4
appears on the screen.
(v) Press → on the cursor key and type in +
(vi) Press the
function.
(vii) Type in 2
(viii) Press ↓ on the cursor key and type in 3
(ix) Press → on the cursor key.
(x) Press = and the answer
11
12
appears.
(xi) Press the S ⇔ D function and the fraction
changes to a decimal 0.9166666...
Thus,
1
4
+
2
3
=
11
12
= 0.9167 as a decimal, correct to
4 decimal places.
It is also possible to deal with mixed numbers on the
calculator. Press Shift then the
function and
appears.
Problem 15. Evaluate 5
1
5
− 3
3
4
(i) Press Shift then the
function and
appears
on the screen.
(ii) Type in 5 then → on the cursor key.
(iii) Type in 1 and ↓ on the cursor key.
(iv) Type in 5 and 5
1
5
appears on the screen.
(v) Press → on the cursor key.
(vi) Type in – and then press Shift then the
function
and 5
1
5
−
appears on the screen.
(vii) Type in 3 then → on the cursor key.
(viii) Type in 3 and ↓ on the cursor key.
(ix) Type in 4 and 5
1
5
− 3
3
4
appears on the screen.
(x) Press = and the answer
29
20
appears.
(xi) Press S ⇔ D function and the fraction changes to
a decimal 1.45
Thus, 5
1
5
− 3
3
4
=
29
20
= 1
9
20
= 1.45 as a decimal.