A strand of hair has an average mass of 2.17 × 10-5 ounces. A grain of rice has an average mass of 0.002
ounces. How much heavier is a grain of rice than a strand of hair? Express your answer in scientific notation.
(1 point)
? x ? ounces
Light travels at an approximate rate of 1.9 × 10 mi./sec. There are about 3.2 x 107 seconds in a vear. About
how many miles does light travel in a year? Write the answer in scientific notation. Express the answer to the
exact decimal place. (1 point)
? miles
The mass of a strand of hair is 2.17 × 10-5 ounces and the mass of a grain of rice is 0.002 ounces.
To find out how much heavier a grain of rice is than a strand of hair, we subtract the mass of the strand of hair from the mass of a grain of rice:
0.002 ounces - 2.17 × 10-5 ounces
In scientific notation, we can express 0.002 as 2 × 10-3 and 2.17 × 10-5 as is.
Therefore, the difference in mass is:
(2 × 10-3) - (2.17 × 10-5) = 1.998 × 10-3 - 2.17 × 10-5 = 1.998 × 10-3 (since the exponents are the same)
So, a grain of rice is 1.998 × 10-3 ounces heavier than a strand of hair.
We are given that light travels at a rate of 1.9 × 10 miles per second and there are about 3.2 × 10^7 seconds in a year.
To find out how many miles light travels in a year, we need to multiply the rate at which light travels by the number of seconds in a year:
1.9 × 10 miles/second × 3.2 × 10^7 seconds
In scientific notation, we can combine the powers of 10:
1.9 × 3.2 × 10 miles/second × 10^7 seconds
Multiplying the coefficients, we have:
6.08 × 10 miles/second × 10^7 seconds
Since we are multiplying numbers in scientific notation, we can add the exponents:
6.08 × 10 × 10^7 miles
Simplifying, we find that:
6.08 × 10^8 miles
Therefore, light travels approximately 6.08 × 10^8 miles in a year.
To find out how much heavier a grain of rice is than a strand of hair, we need to subtract the mass of a strand of hair from the mass of a grain of rice.
The mass of a grain of rice is 0.002 ounces.
The mass of a strand of hair is 2.17 × 10^(-5) ounces.
To subtract these two values, we need to subtract the numerical values and subtract the exponents of the powers of 10.
0.002 - 2.17 = -2.168 × 10^(-5) ounces
Therefore, a grain of rice is 2.168 × 10^(-5) ounces heavier than a strand of hair.