Exercises: Writing numbers in scientific notation

Write in scientific notation, $a \times 10^n$ with $1 \leq a < 10$:

1. a) $4,500$

1. b) $72,000$

1. c) $300,000,000$

Write as an ordinary number:

1. a) $3 \times 10^4$

1. b) $6.2 \times 10^3$

1. c) $9.05 \times 10^5$

Which of these is written correctly in scientific notation? Rewrite the others correctly.

1. a) $25 \times 10^3$

1. b) $4.8 \times 10^6$

1. c) $0.7 \times 10^2$

The population of Ireland is about $5,100,000$ and the population of Cork city is about $224,000$.

1. a) Write both in scientific notation.

1. b) Which is bigger, and by what power of ten approximately?

The distance from Dublin to Cork by road is about $2.6 \times 10^5$ m.

1. a) Write this as an ordinary number of metres.

1. b) Convert it to kilometres and write in scientific notation.

Put these in order from smallest to largest:

$3.2 \times 10^5$, $8.9 \times 10^4$, $1.1 \times 10^6$, $450,000$

Light travels at about $3 \times 10^8$ m/s. The Sun is about $1.5 \times 10^{11}$ m from Earth.

1. a) Find the time in seconds for light to reach Earth.

1. b) Write the answer in minutes, correct to one decimal place.

A stadium holds $5.1 \times 10^4$ people. A ticket costs €$4.5 \times 10^1$.

1. a) Find the total income from a full house, in scientific notation.

1. b) Explain why $a \times 10^n$ with $a = 12$ is not in standard form, using this answer if it had been written as $51 \times 45 \times 10^3$.

A tonne of a material has mass $1 \times 10^3$ kg and a grain of sand has mass about $2 \times 10^{-5}$ kg.

1. a) Write $2 \times 10^{-5}$ as a decimal.

1. b) Find how many grains of sand are in one tonne, in scientific notation.

1. c) Explain why your answer is reasonable.