Writing Numbers in Scientific Notation

Show your work for each problem.

1.
Which number is written correctly in scientific notation?
1. a)
2. b)
3. c)
4. d)
Answer:
is correct because 3.5 is between 1 and 10. The other options have coefficients that are too large (35, 350) or too small (0.35).
2.
Write in scientific notation. Enter only the exponent (the power of 10).
Answer: 6
. We move the decimal 6 places to the left:
3.
What is the coefficient in ?
1. a)
2. b)
3. c)
4. d)
Answer:
In , the coefficient is . Here, .
4.
Write in scientific notation. Enter only the exponent (the power of 10).
Answer: -3
. We move the decimal 3 places to the right: . Since we moved right, the exponent is negative.
5.
Write in scientific notation.
1. a)
2. b)
3. c)
4. d)
Answer:
. Move decimal 4 places left: . The coefficient 7.25 is between 1 and 10.
6.
Write in scientific notation. Enter the coefficient (the number before ).
Answer: 4.7
. The first non-zero digit is 4, so the coefficient is 4.7.
7.
Convert to scientific notation.
Answer: 3.85 × 10^8
1. What number between 1 and 10 do we get from 385,000,000? 3.85
2. How many places did you move the decimal to the left? 8
3. Is the exponent positive or negative? positive
4. What is the final exponent? 8
8.
Convert to scientific notation.
Answer: 6.2 × 10^(-7)
1. What is the first non-zero digit? 6
2. What number between 1 and 10 do we get? 6.2
3. How many places did you move the decimal to the right? 7
4. What is the exponent? (Include the sign) -7
9.
Correct to proper scientific notation.
1. a)
2. b)
3. c)
4. d)
Answer:
. We divided 45.6 by 10 to get 4.56, so we multiply by 10 to get .
10.
The speed of light is approximately meters per second. Write this in scientific notation. Enter the coefficient.
Answer: 2.998
m/s. The coefficient is 2.998 (approximately 3).
11.
A hydrogen atom has a mass of approximately kg. Write this in scientific notation.
Answer: 1.67 × 10^(-27)
1. What is the coefficient (number between 1 and 10)? 1.67
2. Count the zeros after the decimal point before 167. How many are there? 26
3. The exponent is negative because the number is less than 1. What is the exponent? -27
4. Write the final answer in the form a × 10^n 1.67 × 10^(-27)
12.
Correct to proper scientific notation.
1. a)
2. b)
3. c)
4. d)
Answer:
. So .
13.
The distance to the Andromeda galaxy is about meters. Write this in scientific notation.
Answer: 2.537 × 10^21
1. What is the coefficient (number between 1 and 10)? 2.537
2. How many digits are in the original number? 22
3. What is the exponent? 21
4. Write the complete scientific notation 2.537 × 10^21
14.
What is in standard form?
1. a)
2. b)
3. c)
4. d)
Answer:
, so . Numbers between 1 and 10 already satisfy the coefficient requirement.
15.
The diameter of a virus is approximately meters. Write this in scientific notation and enter the exponent.
Answer: -7
meters. We move the decimal 7 places to the right to get 1.2, so the exponent is .