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Scientific Notation Word ProblemsScientific Notation Word Problems
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Question 1 of 4
1. Question
The distance between Alpha Centauri and Earth is `39 000 000 000 000 km`. Convert the distance into metres and express in scientific notation.Hint
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Scientific notation is a way to represent very large or very small numbers in a compact form. It is in the format: `a xx 10^n`.Use the conversion factor `1 km = 1000 m` to convert the distance into metres.`39 000 000 000 000 km` `=` `39 000 000 000 000 000 m` Multipying by `1000` is the same as adding `3` zeros Write the obtained value in scientific notation.`39 000 000 000 000 000 m` `=` `3.9xx 10^(16) m` Move the decimal point `16` places to the left `3.9xx10^(16) m` -
Question 2 of 4
2. Question
Find the time it takes light to travel from the Sun all the way to Jupiter, if the distance between them is `778 000 000 000 m`.- (2593) seconds
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Formula for time
$$\color\red{t}=\frac {\color{#a300c1}{d}}{\color{#e85e00}{s}}$$Label Known Values
Distance `= d = 778 000 000 000 m`Speed `= s = 3 xx 10^8 m/s`Convert the distance into scientific notation.`778 000 000 000 m` `=` `7.78 xx 10^(11) m` Move the decimal point `11` places to the left Substitute the values into the formula$$\color\red{t}$$ $$=\frac {\color{#a300c1}{d}}{\color{#e85e00}{s}}$$ $$=\frac {\color{#a300c1}{7.78 \times 10^{11}}}{\color{#e85e00}{3 \times 10^{8}}}$$ Divide the numbers first and then the exponents of `10` separately.$$\frac{\color\green{7.78} \times \color{#004ec4}{10^{11}}}{\color\green{3} \times \color{#004ec4}{10^8}}$$`7.78/3``=``2.593` `(10^11)/(10^8)``=``10^(11-8)``=``10^3` Division property of exponents Combine the obtained values and simplify.`2.593`` xx`` 10^3` `=` `2593` seconds Move the decimal point three places to the right `2593` seconds -
Question 3 of 4
3. Question
The thickness of a thin film of a soap bubble is `11` nanometres. Transform this into numerical notation and express in metres.- (0.000000011)`m`
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Conversion of nanometres to metres
`1` nanometre `=1xx10^(-9)` metreMultiply the given value by the conversion factor.`11` nanometres `=` `11 xx 1 xx10^(-9) m` `=` `11 xx10^(-9) m` `=` `1.1 10^(-8) m` Move one place to the left Write the obtained value in numerical notation.`1.1xx10^(-8) m` `=` `0.000000011 m` Move the decimal point `8` places to the left `0.000000011 m` -
Question 4 of 4
4. Question
The diameter of a strand of hair is `50 000` nanometres. Transform this into numerical notation and express in metres.- (0.00005)`m`
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Conversion of nanometres to metres
`1` nanometre `=1xx10^(-9)` metreMultiply the given value by the conversion factor.`50 000` nanometres `=` `50 000 xx 1 xx10^(-9) m` `=` `5 xx 10^4 xx10^(-9) m` Convert `50 000` into scientific notation `=` `5 xx10^(-9+4) m` Apply Multiplication rule of exponents `=` `5xx10^(-5) m` Simplify Write the obtained value in numerical notation.`5xx10^(-5) m` `=` `0.00005 m` Move the decimal point `5` places to the left `0.00005 m`