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Lesson: Operations with Numbers in Scientific Notation

In this lesson, we will learn how to perform arithmetic operations with numbers expressed in scientific notation.

Video

15:45

Sample Question Videos

02:05
03:10
01:28

Worksheet • 25 Questions • 3 Videos

Q1:

Find the value of 4 . 4 × 1 0 ÷ 1 . 1 × 1 0 − 2 − 6 , giving your answer in standard form.

  • A 4 × 1 0 4
  • B 4 × 1 0 1 3
  • C 4 × 1 0 − 8
  • D 0 . 4 × 1 0 5

Q2:

Find the value of 4 . 1 × 1 0 × 9 × 1 0 3 7 , giving your answer in standard form.

  • A 3 . 6 9 × 1 0 1 1
  • B 3 6 . 9 × 1 0 1 0
  • C 3 . 6 9 × 1 0 2 2
  • D 0 . 3 6 9 × 1 0 1 2

Q3:

Express in standard form.

  • A
  • B
  • C
  • D
  • E

Q4:

How many times larger is 6 × 1 0 than 2 × 1 0 ?

  • A300 times
  • B0.03 times
  • C30 times
  • D0.3 times
  • E3 times

Q5:

How many times smaller is 3 × 1 0 − 6 than 9 × 1 0 − 2 ?

  • A 3 0 0 0 0 times
  • B300 times
  • C 3 0 0 0 0 0 times
  • D 3 0 0 0 times
  • E 3 0 0 0 0 0 0 times

Q6:

Light from the sun takes 13 minutes to reach one of the planets. Given that light travels at a speed of 3 × 1 0 8 m/s, determine the distance between the sun and that planet.

  • A 2 . 3 4 × 1 0 1 1 metres
  • B 3 9 × 1 0 1 1 metres
  • C 2 . 3 4 × 1 0 8 metres
  • D 3 9 × 1 0 8 metres

Q7:

If the thickness of a sheet of paper is 0.004 cm, what is the height of a stack of 450 sheets of paper?

  • A 1 . 8 × 1 0 0 cm
  • B 1 . 8 × 1 0 − 2 cm
  • C 18 cm
  • D 1 . 8 × 1 0 − 3 cm

Q8:

Calculate 1 . 2 × 1 0 × 2 . 4 × 1 0 3 2 , giving your answer in scientific notation.

  • A 2 . 8 8 × 1 0 5
  • B 3 . 6 × 1 0 5
  • C 2 . 8 8 × 1 0 6
  • D 2 . 8 8 × 1 0 4
  • E 2 8 . 8 × 1 0 5

Q9:

Calculate ( 8 . 2 × 1 0 ) ÷ ( 4 . 1 × 1 0 ) 4 2 , giving your answer in scientific notation.

  • A 2 × 1 0 2
  • B 2 × 1 0 6
  • C 2 0 × 1 0 2
  • D 2 0 × 1 0 − 2
  • E 2 × 1 0 − 2

Q10:

Evaluate , expressing it in standard form.

  • A
  • B
  • C
  • D
  • E

Q11:

How many times larger is 4 × 1 0 8 than 8 × 1 0 − 4 ? Give your answer in scientific notation.

  • A 5 × 1 0 1 1
  • B 5 × 1 0 1 2
  • C 5 × 1 0 4
  • D 4 × 1 0 4
  • E 4 × 1 0 1 2

Q12:

Given that sunlight travels at a speed of 3 × 1 0 8 m/s, determine how long it takes for sunlight to reach a planet that is 126 million kilometres away from the sun.

Q13:

Find the value of 8 × 1 0 + 7 . 1 × 1 0 1 0 9 , giving your answer in standard form.

  • A 8 . 7 1 × 1 0 1 0
  • B 7 . 9 × 1 0 9
  • C 1 . 5 1 × 1 0 1 0
  • D 1 . 5 1 × 1 0 9

Q14:

Calculate the value of 5 . 9 6 × 1 0 + 6 . 0 4 × 1 0 7 . 9 × 1 0 5 6 − 6 , giving your answer in standard form.

  • A 8 . 4 × 1 0 1 1
  • B 8 . 4 × 1 0 1 7
  • C 1 . 5 1 9 × 1 0 1 7
  • D 8 . 4 × 1 0 1 2
  • E 1 . 5 1 9 × 1 0 5

Q15:

Find the value of 8 . 7 × 1 0 − 7 . 7 × 1 0 − 5 − 4 , giving your answer in standard form.

  • A − 6 . 8 3 × 1 0 − 4
  • B 7 . 9 3 × 1 0 − 4
  • C 1 × 1 0 − 4
  • D 1 × 1 0 − 5

Q16:

Write 3 + ( 7 × 1 0 ) + 8 × 1 0 + 6 × 1 0 + 6 × 1 0 + 2 × 1 0 2 3 4 5 in standard form.

  • A 2 . 6 6 8 7 3 × 1 0 5
  • B 2 . 6 6 8 7 3 × 1 0 4
  • C 3 . 7 8 6 6 2 × 1 0 5
  • D 3 . 2 × 1 0 6

Q17:

How many times smaller is 4 × 1 0 8 than 8 × 1 0 1 4 ?

  • A 2 0 0 0 0 0 0 times
  • B 2 0 0 0 0 0 0 0 times
  • C 4 0 0 0 0 0 0 times
  • D 4 0 0 0 0 0 times
  • E 2 0 0 0 0 0 times

Q18:

An electron has a mass of approximately 9 × 1 0 kg. The sun has a mass of approximately 2 × 1 0 kg. How many times heavier is the sun than an electron? Give your answer in the form 𝑎 × 1 0 where 𝑎 is a whole number.

  • A 2 × 1 0
  • B 1 × 1 0
  • C 2 × 1 0
  • D 1 × 1 0
  • E 2 × 1 0

Q19:

The circumference of Earth is about 4 × 1 0 4 km and the circumference of Jupiter is about 4 × 1 0 5 km. How many times larger is the circumference of Jupiter than the circumference of Earth?

  • A10 times
  • B0.01 times
  • C100 times
  • D0.1 times
  • E 1 0 0 0 times

Q20:

How many times larger is 6 × 1 0 − 8 than 3 × 1 0 − 1 3 ?

  • A 2 0 0 0 0 0 times
  • B 2 0 0 0 0 0 0 times
  • C 2 0 0 0 0 0 0 0 times
  • D 2 0 0 0 0 times
  • E 2 0 0 0 times

Q21:

The mass of the sun is about 2 × 1 0 3 0 kg and the mass of Earth is about 6 × 1 0 2 4 kg. To the nearest whole number, how many times larger is the mass of the sun than the mass of Earth?

  • A 3 3 3 3 3 3 times
  • B333 times
  • C 3 3 3 3 3 times
  • D 3 3 3 3 times
  • E 3 3 3 3 3 3 3 times

Q22:

How many times larger is 4 × 1 0 5 than 2 × 1 0 4 ?

  • A20 times
  • B0.02 times
  • C2 times
  • D0.2 times
  • E200 times

Q23:

How many times larger is 4 × 1 0 − 2 than 2 × 1 0 − 5 ?

  • A 2 0 0 0 times
  • B 2 0 0 0 0 0 times
  • C 2 0 0 0 0 0 0 0 times
  • D 2 0 0 0 0 0 0 times
  • E 2 0 0 0 0 times

Q24:

A paper clip has a mass of 5 × 1 0 − 4 kg and a brick has a mass of approximately 3 kg. How many times heavier is the brick than the paper clip?

  • A 6 0 0 0 times
  • B600 times
  • C 6 0 0 0 0 0 0 times
  • D 6 0 0 0 0 0 times
  • E 6 0 0 0 0 times

Q25:

The population of Canada is about 4 × 1 0 7 and the population of the United States is about 3 × 1 0 8 . How many times larger is the popuation of the United States than the population of Canada?

  • A7.5 times
  • B13.33 times
  • C75 times
  • D0.133 times
  • E0.75 times
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