Let’s solve the problem step-by-step.
First, identify the given values:
- The mass of a grain of sand is \( 2.6 \times 10^{-3} \) grams.
- The mass of a grain of salt is \( 6.5 \times 10^{-2} \) grams.
Next, we need to determine how many times greater the mass of the grain of salt is compared to the mass of the grain of sand.
To do this, we divide the mass of the grain of salt by the mass of the grain of sand:
[tex]\[
\text{times greater} = \frac{\text{mass of the grain of salt}}{\text{mass of the grain of sand}}
\][/tex]
Substitute the given values into the equation:
[tex]\[
\text{times greater} = \frac{6.5 \times 10^{-2}}{2.6 \times 10^{-3}}
\][/tex]
Now, simplify the fraction:
1. First, divide the coefficients:
[tex]\[
\frac{6.5}{2.6} = 2.5
\][/tex]
2. Next, handle the powers of 10. Subtract the exponent of the denominator from the exponent of the numerator:
[tex]\[
10^{-2} - (-3) = 10^{-2 + 3} = 10^1 = 10
\][/tex]
3. Combine these results:
[tex]\[
2.5 \times 10 = 25
\][/tex]
Thus, the mass of the grain of salt is 25 times greater than the mass of the grain of sand.
So, the grain of salt is [tex]\( 25 \)[/tex] times heavier than the grain of sand.
