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.
A grain of rice is heavier than a strand of hair by 0.002 - 2.17×10^(-5) = 0.001999783 ounces.
In scientific notation, this is 1.999783 × 10^(-3) ounces.
To find out how much heavier a grain of rice is than a strand of hair, we need to subtract the mass of the hair from the mass of the rice.
The mass difference is calculated as:
Mass of rice - Mass of hair
Given:
Mass of hair = 2.17 × 10^(-5) ounces
Mass of rice = 0.002 ounces
Now we can subtract the two masses:
0.002 ounces - 2.17 × 10^(-5) ounces
To subtract these values, we need to make sure they have the same exponent. We can rewrite the mass of hair as a decimal:
2.17 × 10^(-5) ounces = 0.0000217 ounces
Now we have:
0.002 ounces - 0.0000217 ounces
Performing the subtraction gives us:
0.0019783 ounces
The difference in mass between a grain of rice and a strand of hair is 0.0019783 ounces.
In scientific notation, this is approximately:
1.9783 × 10^(-3) ounces
Therefore, a grain of rice is approximately 1.9783 × 10^(-3) ounces heavier than a strand of hair.
To determine how much heavier a grain of rice is than a strand of hair, we need to subtract the mass of the hair strand from the mass of the rice grain.
The mass of a grain of rice is 0.002 ounces, and the mass of a hair strand is 2.17×10^(-5) ounces.
To subtract these values, we subtract the smaller value (mass of hair strand) from the larger value (mass of rice grain). Let's calculate it:
0.002 ounces - 2.17×10^(-5) ounces
To subtract these two values, we need to convert them to the same unit (either both in the standard form or both in scientific notation). Let's convert the mass of the rice grain to scientific notation:
0.002 ounces = 2.0×10^(-3) ounces
Now we can subtract the two values:
2.0×10^(-3) ounces - 2.17×10^(-5) ounces
To subtract two values in scientific notation, we need to make sure the exponents (powers of 10) are the same. In this case, both exponents are already -3 and -5, so we don't need to do any additional adjustments.
Subtracting the coefficients (the numbers in front of the powers of 10):
2.0 - 2.17 = -0.17
The result is -0.17×10^(-3) ounces.
Since the question asks for the answer in scientific notation, we can simplify it by moving the decimal point one place to the left (since the coefficient is less than 1):
-0.17×10^(-3) ounces = -1.7×10^(-4) ounces
Therefore, a grain of rice is 1.7×10^(-4) ounces heavier than a strand of hair.