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3.04 Standard form

Worksheet
Standard form
1

State whether the following are written in standard form:

a

0.941 \times 10^{3}

b

1.49 \times 10^{14}

c

601.49 \times 10^{14}

d
8.56 \times 10^{14}
e
0.658 \times 10^{3}
f
608.56 \times 10^{14}
g
465.53 \times 10^{21}
2

Write the following numbers in standard form:

a
45
b
128
c
2000
d
884\,000
e
84\,626\,000
f
23\,456
g
6.14
h
9\,700\,000\,000
i
7\,720\,000
j
4.62
k
0.008\,67
l
65\,179\,000\,000\,000
m
74\,400
n
0.000\,755
o
8
p
11.09
q
0.6
r
0.002
s
0.000\,74
t
0.000\,347
u
0.000\,059\,32
3

Write the following numbers in standard form:

a
\dfrac{1}{10\,000}
b
\dfrac{3}{100\,000}
c
\dfrac{92}{1000}
d
\dfrac{126}{10\,000}
4

Express the number: eight hundred and nineteen thousand and three point one in standard form.

5

The world's oceans hold approximately 1\,380\,000\,000\,000\,000\,000\,000 litres of water. Express this volume of water in standard form.

6

The distance between two stars is approximate 9 \times 10^{7} metres. Express this distance as a whole number.

7

Express the following numbers as a basic numeral:

a
2.49 \times 10^{0}
b
8.36 \times 10^{ - 1 }
c
3.66 \times 10^{-6}
d
8.87 \times 10^{-7}
e
3.014 \times 10^{3}
f
7.91 \times 10^{6}
g
2 \times 10^{7}
h
4.13 \times 10^{4}
i
9 \times 10^{ - 3 }
j
8.97 \times 10^{5}
k
5.03 \times 10^{4}
l
3.014 \times 10^{3}
m
8 \times 10^{ 6 }
n
1.3008 \times 10^{7}
o
7.14 \times 10^{ - 3 }
p
9.4 \times 10^{ 4 }
8

Complete the following statements:

a
0.002 = ⬚ \times 10^{ - 3 }
b
⬚ = 7.3 \times 10^{ -4}
c
89\,300\,000 = 8.93 \times 10^{ ⬚}
d
4000 = ⬚ \times 10^{3}
e
⬚ = 7.34 \times 10^{5}
f
0.000\,067 = 6.7 \times 10^{ ⬚}
Standard form on the calculator
9

Enter the following into your calculator and write down the answer as displayed on your calculator:

a
2.7 \times 10^{7}
b
1.67 \times 10^{-3}
c
5.42 \times 10^{12}
d
3.62 \times 10^{-10}
e
2\times 10^6\times 6\times 10^5
f
4\times10^{-3}\times4\times10^{-5}
g
\dfrac{15\times 10^6}{ 5\times 10^3}
h
\dfrac{9\times10^{-3}}{3\times10^{-5}}
10

Use your calculator to find the value of 83\,000^{2} \times 79\,000\,000.

a

Write the answer in standard form

b

Write the answer as a basic numeral

Standard form and significant figures
11

Evaluate the following, writing your answers in standard form correct to three significant figures:

a
728 \times 390
b
192^{4}
c
16^{-4}
d
12\,500 \times 87\,260
12

Evaluate the following, writing your answers in standard form correct to four significant figures:

a
0.0003 \div 1200^{2}
b

\dfrac{7257 \times 3937}{0.0083}

c
\dfrac{8613}{0.0005}
d
182.59 \times 145\,603
13

Use your calculator to find the value of 1319^{3}. Write your answer in standard form, correct to five significant figures.

Applications
14

1\text{ AU} (Astronomical Unit) is the distance from Earth to the Sun, where \\ 1\text{ AU} \approx 149\,597\,900 \text{ km}.

This distance from Earth to Uranus is approximately 18.0\text{ AU}. What is this distance in millimetres? Write your answer in standard form to four significant figures.

15

A light year is defined as the distance that light can travel in one year. It is measured to be 9\,460\,730\,000\,000\,000 metres.

a

Write this distance in standard form.

b

Convert this distance to kilometres. Write your answer in standard form.

c

Convert this distance to centimetres. Write your answer in standard form.

16

A micrometre (\mu\text{m}) is defined as being a millionth of a metre, so 1 \,\mu\text{m} \approx 0.000\,001\text{ m}.

The size of a fog, mist or cloud water droplet is approximately 10 \, \mu\text{m}. How many whole droplets would fit in a 9\text{ cm} sample?

17

The mass of the largest mammal on Earth is approximately 1.5 \times 10^{3} times greater than the mass of an average adult human who weighs 90 \text{ kg}. According to this information, find the approximate mass of the largest mammal on Earth. Write your answer as a basic numeral.

18

Light can travel at a speed of 300\,000\,000\text{ m/s}. Find the following in standard form:

a

The distance light travels in 1 minute.

b

The distance light travels in 1 hour.

c

The distance light travels in 1 day.

19

The distance between Earth and Uranus is 0.000\,316\,9 light years. (1 light year =9.46 \times 10^{15} metres).

a

What is the distance between Earth and Uranus in kilometres? Write your answer as a whole number.

b

The circumference of the earth is approximately 40\,075\text{ km}. How many times must a person travel around the Earth, in order to travel the same distance from Earth to Uranus? Round your answer to the nearest integer.

20

A satellite orbits Earth at a speed of approximately 2.6 \times 10^{4} kilometres per hour. If a particular satellite has been orbiting Earth for 6 \times 10^{3} hours, find the distance the satellite has travelled. Write your answer in standard form.

21

The Earth orbits the Sun at an approximate speed of 8333 metres per second.

a

Calculate how far the Earth travels in one hour.

b

Calculate how far the Earth travels in 8 hours. Write your answer in standard form, rounded to one significant figure.

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Outcomes

MS11-3

solves problems involving quantity measurement, including accuracy and the choice of relevant units

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