(1) 11×10^-5 .Express it in scientific notation.
(2)The distance between sun☉ and earth🌎 is (1.496×10^11)m and the distance between earth 🌎 and moon 🌙 is (3.84×10^8)m.During solar eclipse moon comes in between earth and sun.At that time what is the distance between moon and sun in scientific notation?
11 x 10^-5 = 1.1 x 10^-4
The distance would be
1.496E11 - 3.84E8
= 1.496E11 - 0.00348E11
= ...
To express a number in scientific notation, we need to write it in the form A × 10^B, where A is a number between 1 and 10, and B is an integer. Let's solve each question step by step:
(1) To express 11 × 10^-5 in scientific notation:
- We start by moving the decimal point to the left until there is only one non-zero digit to the left of the decimal point. In this case, we move it 5 places to the left, which becomes 0.00011.
- After that, we rewrite the number as a decimal between 1 and 10. In this case, 0.00011 can be written as 1.1 × 10^-4.
Therefore, 11 × 10^-5 expressed in scientific notation is 1.1 × 10^-4.
(2) The distance between the sun and earth is given as (1.496 × 10^11) m, and the distance between earth and moon is (3.84 × 10^8) m.
- During a solar eclipse, the moon comes in between the earth and the sun. Therefore, the distance between the moon and the sun can be calculated by subtracting the distance between the earth and the moon from the distance between the sun and the earth.
- Subtracting (3.84 × 10^8) m from (1.496 × 10^11) m gives us:
(1.496 × 10^11) m - (3.84 × 10^8) m = (1.496 × 10^11) m
(3.84 × 10^8) becomes (3.84 × 10^8) × (10^11/10^11) = (3.84 × 10^19) / (10^11) = (3.84 / 10^11) × (10^19) = (3.84/10^11) × (10^19)
- Now we have (1.496 × 10^11) m - (3.84 × 10^11) m = (1.496 - 3.84) × 10^11 m = -2.344 × 10^11 m.
Therefore, the distance between the moon and the sun during a solar eclipse, expressed in scientific notation, is -2.344 × 10^11 m.