1. Earth's moon
Scientific notation: 7.35×10²² kg Standard notation:
73,500,000,000,000,000,000,000 kg
2. Mercury
Scientific notation: 3.30×10²³ kgStandard notation:
330,100,000,000,000,000,000,000 kg
3. Venus
Scientific notation: 4.867×10²⁴ kg Standard notation:
4,870,000,000,000,000,000,000,000 kg
4. Jupiter
Scientific notation:Standard notation
1,900,000,000,000,000,000,000,000,000 kg
5. Saturn
Scientific notation (rounded): 5.69×10²⁶ kgStandard notation:
569,000,000,000,000,000,000,000,000 kg
6. Uranus
Scientific notation: 8.68×10²⁵ kgStandard notation:
86,800,000,000,000,000,000,000,000 kg
7. Neptune
Scientific notation: 1.02×10²⁶Standard notation:
102,000,000,000,000,000,000,000,000kg
8. Phobos
Scientific notation: 1.07×10¹⁶ kgStandard notation:
10,700,000,000,000,000kg
9. Ariel
Scientific notation: 1.25×10²¹kgStandard notation:
1,250,000,000,000,000,000,000kg
10. Titam
Scientific notation: 1.35×10²³ kgStandard notation:
135,000,000,000,000,000,000,000kg
Explanation:
The purpose of this exercise is to familiarize yourself with the handling of large numbers using scientific notation.
Standard notation is the numbers written as we know them usually. For instance,
2, 760,0000.5465,321,897.23
Scientific notation displays the numbers in exponential using powers of tens. The number is written with two parts, the mantissa and the power.
The number is in the form A × 10ⁿ, where the mantissa, A, has to be between 1 and less than 10:
1 ≤ A < 10.
Scientific notation is used to work with very large or very small numbers.
For instance:
1.03 × 10⁻⁹8.5 × 10²¹
The masses of the planets and moons are reported in kilograms (kg) using scientific notation because they are very large numbers.
You can find the masses of planets and moons in the internet in scientific notation. Then you can convert to standard notation.
1. Earth's moon
Reported in internet: 7.346×10²² kg
Since the first factor must show until the hundredths place, round the mantissa to 7.35:
Scientific notation: 7.35×10²² kg
To pass to standard notation, you mutiply the mantissa by 10 followed by 22 zeros, which is moving the decimal point to the right 22 places.
Standard notation: 73,500,000,000,000,000,000,000 kg
2. Mercury
Reported in internet: 3.301×10²³ kg
Round to 3.301 to 3.30
Move the decimal point 23 places to the right.
Scientific notation: 3.30×10²³ kg
To pass to standard notation move the decimal point to the right 23 places:
Standard notation: 330,100,000,000,000,000,000,000 kg
3. Venus
Scienfitic notation:
From internet: 4.867×10²⁴ kg Rounded: 4.87×10²⁴ kg
Move the decimal point 24 places to the right.
Standard notation: 4,870,000,000,000,000,000,000,000 kg
4. Jupiter
Scientific notation:
From internet: 1.899×10²⁷ kg Rounded: 1.90×10²⁷ kg
Standard notation (move the decimal point 27 places to the right)
1,900,000,000,000,000,000,000,000,000 kg
5. Saturn
From internet: 5.685×10²⁶ kg
Scientific notation (rounded): 5.69×10²⁶ kg
Move the decimal point 26 places to the right.
Standard notation: 569,000,000,000,000,000,000,000,000 kg
6. Uranus
From internet: 8.682×10²⁵ kg
Scientific notation (rounded): 8.68×10²⁵ kg
Move the decimal point 25 places to the right:
Standard notation: 86,800,000,000,000,000,000,000,000 kg
7. Neptune
From internet: 1.024×10²⁶ kg
Scientific: 1.02×10²⁶
Move the decimal point 26 places to the right:
Standard notation: 102,000,000,000,000,000,000,000,000kg
8. Phobos
From internet: 1.0659×10¹⁶ kg
Round:
Scientific notation: 1.07×10¹⁶ kg
Move the decimal point 16 places to the right:
Standard notation: 10,700,000,000,000,000kg
9. Ariel
From internet: 1.251×10²¹ kg
Round:
Scientific notation: 1.25×10²¹kg
Move the decimal point 21 places to the right:
Standard notation: 1,250,000,000,000,000,000,000kg
10. Titam
From internet: 1.3452×10²³ kg
Round:
Scientific notation: 1.35×10²³ kg
Move the decimal point 23 places to the right:
Standard notation: 135,000,000,000,000,000,000,000kg
