Exam style questions
Example 1
If a company produces 35 million packets of crisps and snacks each week, and production is 7 days a week, 24 hours a day. How many packets are produced in one day? Giving your answer in standard form.
35 million = 35,000,000 packets per week
`(35,000,000)/7=5,000,000`
`5,000,000=5times10^6`
Answer:
`5,000,000=5times10^6` packets are produced in one day.
Example 2
A builder has 7200kg of sand
a.) Write 7200kg in grams. Giving your answer in standard form
b.) If one grain of sand weighs 0.0006g write the weight of one grain of sand in standard form.
c.) How many grains of sand are there in 7200kg of sand?
Giving your answer in standard form.
Answers:
a.) `7200kg=7200times1000g=7,200,000g`
`7,200,000g=7.2times10^6g`
`7.2times10^6g`
Answer:
`7.2times10^6g`
b.) `0.0006g=6times10^-4g` in standard form is
`6times10^-4g`
Answer:
`6times10^-4g`
c.) 7200kg sand is 7,200,000 grams
1 grain sand = 0.0006g
(see our work on percentages to help)
| `7,200,000` grams | `=` | `x` Number of grains | |
| `0.006` grams | `=` | `1` grain |
Therefore `(7,200,000)/0.0006= x`
`x=12,000,000,000`
In standard form this would be
`1.2times10^10`
Answer:
7200kg of sand has `1.2times10^10` grains of sand in it.
Example 3
Astronomers measure distances in the solar system in astronomical units (AU). One AU is 150 000 000 kilometres. The distance from the Sun to Pluto is 39.5 AU. How many kilometres is the Sun from Pluto? Give your answer in standard form to a sensible degree of accuracy.
`39.5times150,000,000=5,925,000,000`kilometres
`5,925,000,000=5.925times10^9`kilometres
Answer:
`5.925times10^9`kilometres
