Scientific notation applications

Convert between standard form and scientific notation, perform multiplication and division in scientific notation, and solve real-world problems involving very large and very small numbers.

Worked examples

Converting a small number to scientific notation

Straightforward

Problem

Write

0.000307

in scientific notation.

Multiplying numbers in scientific notation

Moderate

Problem

Calculate

(6.2 \times 10^5) \times (3 \times 10^{-2})

and express the answer in scientific notation.

Solving a real-world problem using scientific notation

Challenging

Problem

A spacecraft travels at

2.4 \times 10^4

km/h. It needs to cover a distance of

1.8 \times 10^9

km to reach a space station. How many hours will the journey take? Express the answer in scientific notation.

Practise

Open Math

Scientific notation applications

Measurement · MA5-MAG-C-01

Name:

Date:

Q1Straightforward

Which of the following is

4\,700\,000

written in scientific notation?

A. $4.7 \times 10^5$
B. $4.7 \times 10^6$
C. $47 \times 10^5$
D. $0.47 \times 10^7$

Q2Straightforward

Which of the following is

0.000052

written in scientific notation?

A. $5.2 \times 10^{-4}$
B. $5.2 \times 10^{-5}$
C. $52 \times 10^{-6}$
D. $5.2 \times 10^{5}$

Q3Straightforward

Write

6.3 \times 10^5

as a basic numeral.

Q4Straightforward

Which number is larger:

7.2 \times 10^5

9.8 \times 10^4

A. $7.2 \times 10^5$ , because it has a higher power of 10
B. $9.8 \times 10^4$ , because 9.8 is greater than 7.2
C.They are equal
D.Cannot be determined without a calculator

Q5Moderate

Evaluate

(3 \times 10^4) \times (2 \times 10^3)

and express the answer in scientific notation.

A. $6 \times 10^7$
B. $6 \times 10^{12}$
C. $5 \times 10^7$
D. $6 \times 10^{43}$

Q6Moderate

Evaluate

\dfrac{8.4 \times 10^9}{2.1 \times 10^3}

and express the answer in scientific notation.

A. $4 \times 10^3$
B. $4 \times 10^6$
C. $4 \times 10^{12}$
D. $6.3 \times 10^6$

Q7Moderate

Calculate

(4.5 \times 10^6) \times (2 \times 10^{-2})

and write the answer as a basic numeral.

Q8Moderate

Calculate

\dfrac{7.2 \times 10^8}{9 \times 10^4}

and write the answer as a basic numeral.

Q9Challenging

A bacterium is

2.5 \times 10^{-6}

m long. A virus is

5 \times 10^{-8}

m long. How many times longer is the bacterium than the virus?

Q10Challenging

The diameter of the Sun is approximately

1.39 \times 10^9

m. The diameter of the Earth is approximately

1.27 \times 10^7

m. What is the difference in their diameters, in metres, written in scientific notation (to 3 significant figures)?

A. $1.38 \times 10^9$ m
B. $1.26 \times 10^9$ m
C. $1.52 \times 10^9$ m
D. $1.38 \times 10^{10}$ m

Q11Challenging

Australia has approximately

2.6 \times 10^7

people. Each person uses approximately

4.0 \times 10^2

litres of water per day. What is the total daily water usage in Australia, in litres, written in scientific notation?

A. $1.04 \times 10^{10}$ litres
B. $1.04 \times 10^9$ litres
C. $10.4 \times 10^9$ litres
D. $6.6 \times 10^9$ litres

Q12Challenging

Light travels at approximately

3 \times 10^8

metres per second. The distance from the Earth to the Sun is approximately

1.5 \times 10^{11}

metres. How many seconds does it take light to travel from the Sun to Earth?

Worked solutions and answers at openmath.au/year-10/measurement-precision/scientific-notation-applications