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The volume of the Earth is approximately 7.67 × 10–7 times the volume of the Sun. Express this figure in usual form.
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At the end of the 20th century, the world population was approximately 6.1 × 109 people. Express this population in usual form. How would you say this number in words?
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While studying her family’s history. Shikha discovers records of ancestors 12 generations back. She wonders how many ancestors she has had in the past 12 generations. She starts to make a diagram to help her figure this out. The diagram soon becomes very complex.
- Make a table and a graph showing the number of ancestors in each of the 12 generations.
- Write an equation for the number of ancestors in a given generation n.
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About 230 billion litres of water flows through a river each day. How many litres of water flows through that river in a week? How many litres of water flows through the river in an year? Write your answer in standard notation.
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A half-life is the amount of time that it takes for a radioactive substance to decay to one half of its original quantity.
Suppose radioactive decay causes 300 grams of a substance to decrease to 300 × 2–3 grams after 3 half-lives. Evaluate 300 × 2–3 to determine how many grams of the substance are left.
Explain why the expression 300 × 2–n can be used to find the amount of the substance that remains after n half-lives.
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Consider a quantity of a radioactive substance. The fraction of this quantity that remains after t half-lives can be found by using the expression 3–t. After how many half-lives will the fraction be `1/243` of the original?
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One Fermi is equal to 10–15 metre. The radius of a proton is 1.3 Fermis. Write the radius of a proton in metres in standard form.
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The paper clip below has the indicated length. What is the length in standard form.
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There are 864,00 seconds in a day. How many days long is a second? Express your answer in scientific notation.
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The given table shows the crop production of a State in the year 2008 and 2009. Observe the table given below and answer the given questions.
| Crop | 2008 Harvest (Hectare) |
Increase/Decrease (Hectare) in 2009 |
| Bajra | 1.4 × 103 | – 100 |
| Jowar | 1.7 × 106 | – 440,000 |
| Rice | 3.7 × 103 | – 100 |
| Wheat | 5.1 × 105 | + 190,000 |
- For which crop(s) did the production decrease?
- Write the production of all the crops in 2009 in their standard form.
- Assuming the same decrease in rice production each year as in 2009, how many acres will be harvested in 2015? Write in standard form.
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Express the following in exponential form:
`(-1296)/14641`
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Express the following in exponential form:
`(-125)/343`
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Express the following in exponential form:
`400/3969`
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Express the following in exponential form:
`(-625)/10000`
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Percentages are ______ to fractions with ______ equal to 100.
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A regular hexagon is inscribed in a circle of radius r. The perimeter of the regular hexagon is ______.
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A four-digit number aabb is divisible by 55. Then possible value(s) of b is/are ______.
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A three-digit number abc is divisible by 5 if c is an even number.
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Find the number of faces in the given shape:
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Find the number of faces in the given shape:
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