Question

express each number in scientific notation.

1. 0.0259 = _______
2. 902 = _______
3. 55,820 = _______
4. 0.315 = _______
5. 0.00973 = _______
6. 10,006 = _______
7. 856 = _______
8. 0.2058 = _______
9. 0.00072 = _______
10. 5,008 = _______
11. 0.001216 = _______
12. 0.00145 = _______

Explanation:

Step1: Move decimal to 1-10, count left moves

For 0.0259: Shift decimal right 2 times.
$0.0259 = 2.59 \times 10^{-2}$

Step2: Move decimal to 1-10, count right moves

For 902: Shift decimal left 2 times.
$902 = 9.02 \times 10^{2}$

Step3: Move decimal to 1-10, count right moves

For 55,820: Shift decimal left 4 times.
$55,820 = 5.582 \times 10^{4}$

Step4: Move decimal to 1-10, count left moves

For 0.315: Shift decimal right 1 time.
$0.315 = 3.15 \times 10^{-1}$

Step5: Move decimal to 1-10, count left moves

For 0.00973: Shift decimal right 3 times.
$0.00973 = 9.73 \times 10^{-3}$

Step6: Move decimal to 1-10, count right moves

For 10,006: Shift decimal left 4 times.
$10,006 = 1.0006 \times 10^{4}$

Step7: Move decimal to 1-10, count right moves

For 856: Shift decimal left 2 times.
$856 = 8.56 \times 10^{2}$

Step8: Move decimal to 1-10, count left moves

For 0.2058: Shift decimal right 1 time.
$0.2058 = 2.058 \times 10^{-1}$

Step9: Move decimal to 1-10, count left moves

For 0.00072: Shift decimal right 4 times.
$0.00072 = 7.2 \times 10^{-4}$

Step10: Move decimal to 1-10, count right moves

For 5,008: Shift decimal left 3 times.
$5,008 = 5.008 \times 10^{3}$

Step11: Move decimal to 1-10, count left moves

For 0.001216: Shift decimal right 3 times.
$0.001216 = 1.216 \times 10^{-3}$

Step12: Move decimal to 1-10, count left moves

For 0.00145: Shift decimal right 3 times.
$0.00145 = 1.45 \times 10^{-3}$

Answer:

1. $2.59 \times 10^{-2}$
2. $9.02 \times 10^{2}$
3. $5.582 \times 10^{4}$
4. $3.15 \times 10^{-1}$
5. $9.73 \times 10^{-3}$
6. $1.0006 \times 10^{4}$
7. $8.56 \times 10^{2}$
8. $2.058 \times 10^{-1}$
9. $7.2 \times 10^{-4}$
10. $5.008 \times 10^{3}$
11. $1.216 \times 10^{-3}$
12. $1.45 \times 10^{-3}$