Question

problems 16-30: write each number using scientific notation.
16 0.000527 = ______
17 0.0000000087 = ______
18 0.00079 = ______
19 0.0000000004 = ______
20 0.00005008 = ______
21 0.000013 = ______
22 0.002 = ______
23 0.0000184 = ______
24 0.0006 = ______
25 0.000039 = ______
26 0.0295 = ______
27 0.000061 = ______
28 0.0000001 = ______
29 0.0000403 = ______
30 0.000007 = ______
© libro studio llc 2022

Explanation:

Step1: Recall scientific notation rules

Scientific notation is \( a \times 10^n \), where \( 1 \leq |a| < 10 \) and \( n \) is an integer. For numbers less than 1, \( n \) is negative, and \( |n| \) is the number of places the decimal moves to the right to get \( a \).

Step2: Solve for 0.000527 (Problem 16)

Move decimal 4 places right: \( a = 5.27 \), \( n=-4 \). So \( 0.000527 = 5.27 \times 10^{-4} \).

Step3: Solve for 0.0000000087 (Problem 17)

Move decimal 9 places right: \( a = 8.7 \), \( n=-9 \). So \( 0.0000000087 = 8.7 \times 10^{-9} \).

Step4: Solve for 0.00079 (Problem 18)

Move decimal 4 places right: \( a = 7.9 \), \( n=-4 \). So \( 0.00079 = 7.9 \times 10^{-4} \).

Step5: Solve for 0.0000000004 (Problem 19)

Move decimal 10 places right: \( a = 4 \), \( n=-10 \). So \( 0.0000000004 = 4 \times 10^{-10} \).

Step6: Solve for 0.00005008 (Problem 20)

Move decimal 5 places right: \( a = 5.008 \), \( n=-5 \). So \( 0.00005008 = 5.008 \times 10^{-5} \).

Step7: Solve for 0.000013 (Problem 21)

Move decimal 5 places right: \( a = 1.3 \), \( n=-5 \). So \( 0.000013 = 1.3 \times 10^{-5} \).

Step8: Solve for 0.002 (Problem 22)

Move decimal 3 places right: \( a = 2 \), \( n=-3 \). So \( 0.002 = 2 \times 10^{-3} \).

Step9: Solve for 0.0000184 (Problem 23)

Move decimal 5 places right: \( a = 1.84 \), \( n=-5 \). So \( 0.0000184 = 1.84 \times 10^{-5} \).

Step10: Solve for 0.0006 (Problem 24)

Move decimal 4 places right: \( a = 6 \), \( n=-4 \). So \( 0.0006 = 6 \times 10^{-4} \).

Step11: Solve for 0.000039 (Problem 25)

Move decimal 5 places right: \( a = 3.9 \), \( n=-5 \). So \( 0.000039 = 3.9 \times 10^{-5} \).

Step12: Solve for 0.0295 (Problem 26)

Move decimal 2 places right: \( a = 2.95 \), \( n=-2 \). So \( 0.0295 = 2.95 \times 10^{-2} \).

Step13: Solve for 0.000061 (Problem 27)

Move decimal 5 places right: \( a = 6.1 \), \( n=-5 \). So \( 0.000061 = 6.1 \times 10^{-5} \).

Step14: Solve for 0.00000001 (Problem 28)

Move decimal 8 places right: \( a = 1 \), \( n=-8 \). So \( 0.00000001 = 1 \times 10^{-8} \).

Step15: Solve for 0.0000403 (Problem 29)

Move decimal 5 places right: \( a = 4.03 \), \( n=-5 \). So \( 0.0000403 = 4.03 \times 10^{-5} \).

Step16: Solve for 0.000007 (Problem 30)

Move decimal 6 places right: \( a = 7 \), \( n=-6 \). So \( 0.000007 = 7 \times 10^{-6} \).

Answer:

1. \( 5.27 \times 10^{-4} \)
2. \( 8.7 \times 10^{-9} \)
3. \( 7.9 \times 10^{-4} \)
4. \( 4 \times 10^{-10} \)
5. \( 5.008 \times 10^{-5} \)
6. \( 1.3 \times 10^{-5} \)
7. \( 2 \times 10^{-3} \)
8. \( 1.84 \times 10^{-5} \)
9. \( 6 \times 10^{-4} \)
10. \( 3.9 \times 10^{-5} \)
11. \( 2.95 \times 10^{-2} \)
12. \( 6.1 \times 10^{-5} \)
13. \( 1 \times 10^{-8} \)
14. \( 4.03 \times 10^{-5} \)
15. \( 7 \times 10^{-6} \)